Why does the gravity of Earth appear in this formula estimating speed?

I'm currently reading the wonderful book The Dinosaurs Rediscovered by Michael J. Benton. It contains the formula

$$v = 0.25 * g^{0.5} * SL^{1.67} * h^{-1.17}$$

where $v$ denotes velocity, $SL$ is stride length in $m$, $h$ is hip height in $m$ and $g$ is the gravity of earth. Not being a biologist (in fact not being really familiar with any natural science), I don't quite understand why gravity appears in this formula. I can't imagine this would hold in any meaningful way in circumstances where gravity where different from earth's, so why not simply express the term $0.25 * g^{0.5}$ as $0.78 m^{0.5}/s$, which I assume stems from some fitting of terms to observed speeds given stride length and hip height.


G is going to be different depending on what units you use, the original formula was derived using FEET not meters. As it stands the formula works both with metric and imperial units. With your change this would not be true. Paleontology is often uses both units so a formula that is not unit dependent is preferable.

This is because a leg can be modeled as an inverted pendulum (like a metronome). A pendulum is a function of gravity. This creates a simple relationship between hip height, stride length and speed. There is more to it but you would need to ask the physics community for details.

You can in facts build a mechanical robot that walks downward slopes by itself with nothing else than 2 inverted pendulums.

McGeer, T. (1990). Passive dynamic walking. I. J. Robotic Res., 9(2), 62-82.

Do I weigh less on the equator than at the North Pole?

Yes, you weigh less on the equator than at the North or South Pole, but the difference is small. Note that your body itself does not change. Rather it is the force of gravity and other forces that change as you approach the poles. These forces change right back when you return to your original latitude. In short, a trip to the equator is not a viable long-term weight-loss program.

Your weight is the combination of all the large-scale, long-term forces on your body. While the earth's gravity is by far the strongest large-scale force, it is not the only one. What you experience as "something pulling you down" is actually the total of all the forces and not just gravity. The four dominant large-scale, long-term forces are:

  1. The earth's gravity
  2. The sun's gravity
  3. The moon's gravity
  4. The earth's centrifugal force

Note that although earth's Coriolis force plays a major role in shaping hurricanes and ocean currents, since it is not a static force, it does not contribute to your overall weight. Also, additional forces appear when you ride a roller-coaster, an elevator, a swing, or another vehicle, but these forces are transient, so they do not contribute to your overall, long-term weight. Finally, electromagnetic and nuclear forces are either too small-scale, or too short-term to contribute to your overall weight.

For our purposes, we want to consider the forces that differ significantly at the equator versus the poles. While the sun's gravity is strong enough to keep us and the earth in orbit, the sun's position relative to a spot on the equator versus the poles is constantly changing. As a result, averaged over a few days, the gravitational force of the sun on a spot on the equator is the same as the gravitational force of the sun on a spot on the poles. The same situation applies to the moon. This leaves only earth's gravity and earth's centrifugal force as the two forces that contribute to your weight differing at the equator versus the poles.

As we learned in high school, earth's gravity is approximately constant all over the surface of the earth. But this is only an approximation. If the earth were perfectly spherical and if its density were perfectly uniform, then the strength of earth's gravity would be exactly constant at all points on its surface. But it's not. There are three major complications to earth's gravitational field. First the earth is not a sphere. The earth is spinning, causing it to slightly flatten like a pizza crust thrown and spun in the air. As a result, the earth is an oblate spheroid and not a perfect sphere. If you stand at sea level on the equator, you are 6378 km from the center of the earth. In contrast, at each pole, you are only 6357 km from the center of the earth. Since the strength of gravity weakens as you get farther away from a gravitational body, the points on the equator are farther and have weaker gravity than the poles. The other two complications to earth's gravitational field non-uniform internal density and local surface mass variations such as mountains are small enough factors that we will neglect them here. Therefore, assuming the entire mass of the earth is located at its center, we can calculate the force of earth's gravity at the equator and at the poles. Using Newton's law of gravity, we find that the force of earth's gravity on your body at the equator is 9.798 m/s 2 times the mass of your body, whereas at the poles it is 9.863 m/s 2 times the mass of your body.

The earth's centrifugal force also varies with latitude. The centrifugal force is the outward force felt whenever you are in a rotating reference frame. While the centrifugal force is a non-fundamental force caused ultimately by the inertia of bodies, it is very real for the body in a rotating reference frame, such as your body on the surface of the rotating earth. The centrifugal force is proportional to the tangential speed of the rotating reference frame. The equator is moving quickly as the earth's spins, so it has a lot of centrifugal force. In contrast, the poles are not spinning at all, so they have zero centrifugal force. Since centrifugal force points outwards from the center of rotation, it tends to cancel out a little bit of earth's gravity. If the earth were not spinning, you would be heavier as you would feel the full force of gravity. Since there is more centrifugal force at the equator to cancel gravity, your overall weight at the equator versus at the poles is even less. The centrifugal force on your body at the equator is 0.034 m/s 2 times the mass of your body. The centrifugal force at the poles is zero.

Your total weight at sea level at the equator (gravity minus centrifugal force) is therefore 9.764 m/s 2 times your mass, whereas your weight is 9.863 m/s 2 times your mass at the poles. If we use a more accurate model (such as taking into account the shape of the continents) these numbers will be slightly different, but the overall point will be the same: you weigh about 1% less at the equator than at the poles. If you weigh 200 pounds (90.7 kg) at the North Pole, you will weigh 198 pounds (89.8 kg) at the equator. Note that we have focused on the equator and the poles as the extremes, but the same effect applies to all latitudes. You weigh slightly less in Mexico City than in New York City, as Mexico City is closer to the equator.

Disclaimer: The following material is being kept online for archival purposes.

The Moon orbits around the Earth. Since its size does not appear to change, its distance stays about the same, and hence its orbit must be close to a circle. To keep the Moon moving in that circle--rather than wandering off--the Earth must exert a pull on the Moon, and Newton named that pulling force gravity.

Was that the same force which pulled all falling objects downward?

    In the year 1666 he retired again from Cambridge . to his mother in Lincolnshire & while he was musing in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon thought he to himself & that if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a-calculating what would be the effect of that superposition.

If it was the same force, then a connection would exist between the way objects fell and the motion of the Moon around Earth, that is, its distance and orbital period. The orbital period we know--it is the lunar month, corrected for the motion of the Earth around the Sun, which also affects the length of time between one "new moon" and the next. The distance was first estimated in ancient Greece--see here and here.

To calculate the force of gravity on the Moon, one must also know how much weaker it was at the Moon's distance. Newton showed that if gravity at a distance R was proportional to 1 / R 2 (varied like the " inverse square of the distance "), then indeed the acceleration g measured at the Earth's surface would correctly predict the orbital period T of the Moon.

Newton went further and proposed that gravity was a "universal" force, and that the Sun's gravity was what held planets in their orbits. He was then able to show that Kepler's laws were a natural consequence of the "inverse squares law" and today all calculations of the orbits of planets and satellites follow in his footsteps.

Nowadays students who derive Kepler's laws from the "inverse-square law" use differential calculus, a mathematical tool in whose creation Newton had a large share. Interestingly, however, the proof which Newton published did not use calculus, but relied on intricate properties of ellipses and other conic sections. Richard Feynman, Nobel-prize winning maverick physicist, rederived such a proof (as have some distinguished predecessors) see reference at the end of the section.

Here we will retrace the calculation, which linked the gravity observed on Earth with the Moon's motion across the sky, two seemingly unrelated observations. If you want to check the calculation, a hand-held calculator is helpful.

Calculating the Moon's Motion

We assume that the Moon's orbit is a circle, and that the Earth's pull is always directed toward's the Earth's center. Let RE be the average radius of the Earth (first estimated by Erathosthenes)

The distance R to the Moon is then about 60 RE (see here). If a mass m on Earth is pulled by a force mg, and if Newton's "inverse square law" holds, then the pull on the same mass at the Moon's distance would be 60 2 = 3600 times weaker and would equal

If m is the mass of the Moon, that is the force which keeps the Moon in its orbit. If the Moon's orbit is a circle, since R = 60 RE its length is

Suppose the time required for one orbit is T seconds. The velocity v of the motion is then

v = distance/time = 120 π RE/T

(Please note: gravity is not what gives the Moon its velocity. Whatever velocity the Moon has was probably acquired when it was created. But gravity prevents the Moon from running away, and confines it to some orbit.)

The centripetal force holding the Moon in its orbit must therefore equal

mv 2 /R = mv 2 /(60 RE)

and if the Earth's gravity provides that force, then

mg/3600 = mv 2 /(60 RE)

dividing both sides by m and then multiplying by 60 simplifies things to

g/60 = v 2 /RE = (120 π RE) 2 /(T 2 RE)

Canceling one factor of RE , multiplying both sides by 60 T 2 and dividing them by g leaves

T 2 = (864 000 π 2 RE)/g = 864 000 RE (π 2 /g)

Providentially, in the units we use g

9.87, so that the term in parentheses is close to 1 and may be dropped. That leaves (the two parentheses are multiplied)

With a hand held calculator, it is easy to find the square roots of the two terms. We get (to 4-figure accuracy)

864 000 = (929.5) 2 6 371 000 = (2524) 2

T ≅ (929.5) (2524) = 2 346 058 seconds

To get T in days we divide by 86400, the number of seconds in a day, to get

pretty close to the accepted value

    The above looks like a simple and straightforward calculation. However, it assumes something we nowadays accept without second thought: that the pull of the Earth would be the same if all the mass of the Earth were concentrated in its center.

It wasn't obvious to Newton, That falling apple. sure, there was mass pulling it down, but there was also mass pulling it sideways in all directions, pulls which largely canceled. Even if the sum-total of all pulls pointed towards the center of the Earth, who was to say it obeyed the same inverse-square law as a mass concentrated at a point? Newton did not trust the above calculation until he proved to his satisfaction that the Earth's attraction could always be replaced by the one of a mass concentrated at its center.

The Formula for the Force of Gravity

Newton rightly saw this as a confirmation of the "inverse square law". He proposed that a "universal" force of gravitation F existed between any two masses m and M , directed from each to the other, proportional to each of them and inversely proportional to the square of their separation distance r . In a formula (ignoring for now the vector character of the force):

Suppose M is the mass of the Earth, R its radius and m is the mass of some falling object near the Earth's surface. Then one may write

The capital G is known as the constant of universal gravitation. That is the number we need to know in order to calculate the gravitational attraction between, say, two spheres of 1 kilogram each. Unlike the attraction of the Earth, which has a huge mass M, such a force is quite small, and the number G is likewise very, very small. Measuring that small force in the lab is a delicate and difficult feat.

It took more than a century before it was first achieved. Only in 1796 did Newton's countryman Henry Cavendish actually measure such weak gravitational attraction, by noting the slight twist of a dumbbell suspended by a long thread, when on of its weights was attracted by the gravity of heavy objects. His instrument ("torsion balance") is actually very similar to the one devised in France by by Charles Augustin Coulomb to measure the distance dependence of magnetic and electric forces. The gravitational force is much weaker, however, making its direct observation much more challenging. A century later (as already noted) the Hungarian physicist Roland Eötvös greatly improved the accuracy of such measurements.

Gravity in our Galaxy (Optional)

What about still larger distances? The solar system belongs to the Milky Way galaxy , a huge wheel-like swirl of stars with a radius around 100,000 light years. Being located in the wheel itself, we view it edge-on, so that the glow of its distant stars appears to us as a glowing ring circling the heavens, known since ancient times as the Milky Way. Many more distant galaxies are seen by telescopes, as far as one can see in any direction. Their light shows (by the "Doppler effect") that they are slowly rotating.

Gravity apparently holds galaxies together. At least our galaxy seems to have a huge black hole in its middle, a mass several million times that of our Sun, with gravity so intense that even light cannot escape it. Stars are much denser near the center of our galaxy, and their rotation near their center suggests Kepler's third law holds there, slower motion with increasing distance.

The rotation of galaxies away from their centers does not follow Kepler's 3rd law--indeed, outer fringes of galaxies seem to rotate almost uniformly. This observed fact has been attributed to invisible " dark matter " whose main attribute is mass and therefore, gravitational attraction (see link above). It does not seem to react to electromagnetic or nuclear forces, and scientists are still seeking more information about it.

Figure it out

    "NASA did not land on the moon on 19 JUL 1969 but, as we see on the T.V scenario movie made in Hollywood, if NASA landed on the Moon, it must have approached and landed like the shuttle [docking] with the space station"

Exploring Further

A detailed article: Keesing, R.G., The History of Newton's apple tree , Contemporary Physics, 39, 377-91, 1998

Richard Feynman's calculations can be found in the book " Feynman's Lost Lecture: The Motion of Planets Around the Sun " by D. L Goodstein and J. R. Goodstein (Norton, 1996 reviewed by Paul Murdin in Nature, vol. 380, p. 680, 25 April 1996). The calculation is also described and expanded in " On Feynman's analysis of the geometry of Keplerian orbits " by M. Kowen and H. Mathur, Amer. J. of Physics, 71 , 397-401, April 2003.

The Institute for Creation Research

Gravity holds us firmly on the ground and also keeps the earth circling the sun. It draws rain from the sky and causes the tides. This mysterious gravity force continues to puzzle scientists even as it gives stability to the universe. How is gravity able to act across empty space, and why does it exist in the first place? Science has never been very successful in explaining such "natural" laws. After all, these universal rules cannot slowly arise by mutation or natural selection they have been here since the very beginning. Gravity, as well as every other intricate physical law and constant, is actually an absolute testimony to creation.

Galileo (1564-1642) first explored the motion of falling objects. Isaac Newton (1642-1727) later described the law of gravity: All objects in the universe attract each other. This attractive force is proportional to the objects' masses and decreases as the square of the distance separating them. Figure 1 illustrates the gravity force Table 1 gives some representative values. Henry Cavendish (1731-1810) finally measured the gravitation constant which allowed the gravity force to be precisely calculated. Comments from these science pioneers show their respect for gravity's origin:

Galileo: From the Divine Word, the Sacred Scripture and Nature did both alike proceed.[1]

Newton: This most beautiful [gravitational] system of the sun, planets, and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.[2]

Newton: When I wrote my treatise [principia] about our [solar system], I had an eye on such principles as might work with considering men for the belief in a Deity and nothing can rejoice me more than to find it useful for that purpose.[3]

The origin views of Cavendish are not known because he left very little written material. One will search in vain for these creation quotes, or anything similar, in most science books. Texts typically give only half the story they accept gravity without any discussion of its origin and implications.

The properties of gravity illustrate just how unique this essential force is. Consider six points, chosen from many others.

  1. Gravity does not change with time. Many researchers have looked for a possible variation in the strength of gravity, without success. Some feel that stronger gravity in the distant past might possibly have helped trigger star formation or the Big Bang itself. Even with a long time scale, however, gravity appears to be perfectly constant.[4] Gravity therefore does not solve the problems of Big Bang cosmology.
  2. Aside from air resistance, large and small objects fall downward in exactly the same time. Drop two compact objects and you should see and hear them hit the floor simultaneously.
  3. Gravity is always attractive, while other forces such as magnetism can either repel or attract. This beneficial property makes gravity the universal "Elmer's Glue" which binds the universe together. Even the distant galaxies, which appear to have been created with an outward expanding motion, are gradually slowing due to the inward gravity pull from all other galaxies in the universe.
  4. Gravity cannot be fumed off or shielded in any way. Intervening objects have no effect on the original gravity force between two separated masses. This means that there is no antigravity chamber available in which the occupants can continually float freely. The weightless, gravity-free feeling you may have experienced on an amusement park ride results from a temporary falling motion. Orbiting astronauts appear weightless only because their fall toward the earth is balanced by the outward directed centrifugal force.
  5. Gravity attraction does not depend on the composition of objects, only on their mass or weight. Several blocks composed of glass, lead, ice, or Styrofoam, if they all have equal mass, will attract each other identically.
  6. The gravity force decreases with distance but is actually infinite in its extent. Gravity acts instantly between the earth and moon, as well as across the millions of light years of space between galaxies, according to classical theory.

Two Bible verses especially help us understand the nature of gravity. First, Colossians 1:17 explains that Christ is before all things, and by Him all things consist. The Greek verb for "consist" (sunistano) means to cohere, preserve, or hold together. Extra-biblical Greek use of this word pictures a vessel holding water within itself. The word is used in Colossians in the perfect tense, which describes a present continuing state arising from past action. This perfect tense also implies permanence of the act of holding the universe together. One mechanism used is obviously gravity, established by the Creator and still maintained without flaw today. Consider the alternative: If the Lord turned His back on the universe for one moment, instant chaos would result. Without gravity, the earth, moon, and stars would immediately disintegrate.

A second reference, Hebrews 1:3, declares that Christ upholds all things by the word of His power. Uphold (Greek, fero) again describes the sustaining or maintaining of all things, including gravity. The word uphold means much more than simply supporting a weight. It includes control of all the ongoing motions and changes within the universe.[5] This infinite task is managed by Christ's almighty Word, whereby the universe itself was first called into being (Hebrews 11:3).

We know of just four fundamental forces in nature. First, there is the electromagnetic force which operates electric motors, radio, television, and particle accelerators. Second and third, the strong and weak nuclear forces arise within the nuclei of atoms. Finally, there is gravity, actually 1040 times weaker than electromagnetism, and the only force known in Newton's day. Gravity dominates other forces on the larger scale of space objects (Figure 2).

TABLE 1 Some example values of the attractive
gravity force between objects.
Objects Gravity Force (Pounds)
You and this Impact article 10 -10
You and the moon .001
Two locomotives .005
You and the earth Your Weight
Moon and earth 7 x 10 19
Earth and Sun 8 x 10 21

Physicists have long attempted to unify these four basic forces into just one entity or theory. Initial success was shown by Faraday and Maxwell 150 years ago when electricity and magnetism were combined. So far, however, gravity has proven a special challenge to the experts. Gravity should reveal both wave and particle (quantum) properties, to fit the pattern of the other forces. Traveling gravity waves, suggested by some researchers, should slightly compress or curve space-time, according to Einstein. The hypothesized particles called gravitons, with no mass or charge, are thought to stream back and forth continually between the earth and moon, resulting in the observed gravity force. Neither gravity waves nor graviton particles have been observed yet. One wonders if scientists will ever discover the actual method by which the Lord maintains the gravity system. Perhaps, similar to the creation process itself, such details lie forever beyond our probing.

It is a fair question to ask natural science why basic laws such as gravity exist. Why is the universe filled with intriguing technical relationships, symmetry, and unity? Some experts are quick to reply that the task of science is only to find out the how of nature, not the why. But this excuse simply reveals the incompleteness of natural science alone. Ultimate truth about the universe must also deal with God's initial provision and his continuing care for us. The Creator is clearly an intimate part of every physical detail, including gravity.

Get a Straight Answer

What is a "Sun Synchronous" orbit?
(b) Why are satellites launched from near the equator?

(1) Why don't its particles separate by weight?
(2) What accelerates the solar wind?

If you have a relevant question of your own, you can send it to
stargaze ["at" symbol]
Before you do, though, please read the instructions

170. Spacecraft Attitude


Concerning the "self-position" of a satellite, you probably mean its orientation in space or " attitude ." It is a big subject and much depends on how accurate do you want it to be determined. If you are happy with half a degree, a "sun sensor" and an optical "horizon sensor" may give you enough information--for other uses, star cameras exist and have been used.

A related question is, how do you rotate a satellite from one orientation to another? The usual way is to have gyroscopes , flywheels in constant rotation. Forcing the rotation axis into a new position causes the entire satellite to rotate in a way that preserves its angular momentum, then when you think it has rotated far enough, you return the axis of the gyroscope to its original direction and the satellite stops rotating. You can mount the gyroscope on gimbals and point it in different directions, or have independent gyroscopes for the (x,y,z) axes and spin them up and down. The Hubble telescope, whose attitude (orientation) must be constantly adjusted, has several gyroscopes, and one of the reason for visiting it from time to time is to replace gyroscopes, because their bearings etc. do wear out.

Still another question is how to you express the direction of the satellite in space. You need two angles in spherical coordinates, which express the right ascension and declination of some axis on it, and you also need an angle to characterize rotation around that axis. With those you express (x,y,z) coordinates of points on the satellite. Rotating the satellite in space to a new (x',y',z') requires a calculation with matrices. A simple example is in problem 8 of,
which continues at

171 What makes the Earth rotate?


We believe that the entire solar system started as a cloud of gas and dust which gradually pulled itself together by its own gravity. In such a process, a measure of rotation, known as angular momentum , is preserved. Angular momentum of a collection of matter is proportional to its mass, the square of the average distance R of the mass from the rotation axis and to the frequency F of rotations per second (or per year, or century. whatever units you choose).

Any time a rotating cloud of matter gets reduced in size--as it did when Earth originated--R gets smaller. Therefore, to keep the angular momentum the same, F has to increase. It follows that even if the original nebula rotated very slowly, by the time it formed the Earth, it must have speeded up quite a bit.

An analogy can be taken from the tornado , forming during times of severe thunderstorm activity. Usually thunderstorms are associated with vertical hot air rising and giving up energy (see section S-1A in "Stargazers") but there also exist horizontal flows of warm humid air into the storm (low down) and cold dry air out of it (high up).

Usually everything is pretty symmetric, but sometimes a row of thunderstorms is formed ("squall line") and the flow of air in neighboring storms can set one of them slowly rotating. That is all it takes! As humid warm air is sucked into the rotating thunderstorm, its rotation gets faster and faster, and a tornado can result. Unlike hurricanes,though, tornadoes are too small for their direction of rotation to be related to the Earth's rotation.

172. Energy from the Earth's Rotation?


Using the energy of the Earth's rotation is an interesting idea, and it is feasible , but the way it's done is probably not what you had in mind . The problem is, to affect the rotation you need some other object which brakes it. It must be outside the earth--nothing on Earth will do it.

Such an object exists: our Moon. The interaction between the Earth's rotation and the motion of the Moon raises tides in the oceans, and schemes to extract energy from tides therefore takes energy from the rotation of the earth and from the orbital energy of the Moon. Such schemes exist, but they are hard to implement (tides are low, salt water is corrosive) and give a low yield.

See also next question, below.

173. How were planets created?

In your reply to Q 78 you write - ". It was established not when the planets cooled but before that, a relic of the swirling of the cloud of gas and dust from which the solar system (and the sun) formed. "

My question is: From where did the "swirling cloud of gas and dust come? What is the SCIENTIFIC explanation.


From the evidence we have, all matter in the universe appeared--very hot, very dense--in the " big bang ", about 13.8 billion years ago. I hope you do not expect me to recount all that evidence--expanding universe, microwave radiation etc.

Applying to this event what we know about atomic nuclei tells us that when that matter cooled enough to form atoms, these were mainly hydrogen , some helium and a little lithium . The materials from which planets are made (also, you and me)--elements such as carbon, nitrogen, oxygen and the rest-- --are more complicated, and must have appeared later. Without those elements, no dust would exiss--and no Earth, either, since our planet is largely made up of them.

It is generally held--and again, evidence exists, as well as theory, in which the late Hans Bethe, who just passed away at 98, had a big part--that heavier elements are "cooked," in part in the processes which even now power the Sun, but in addition (and especially the heaviest ones) in the sudden collapse of a supernova , which preceded the solar system. That includes such elements as uranium, which decay radioactively. From the radioactive content of moon rocks, they were dated about 4.7 billion years ago, and it is believed the Earth formed around that time, too.

The material from which the solar system formed must have been the cloud of dust and gas left from the supernova (or maybe from more than one), gradually pulled together by gravity. And it must have been swirling even then, because the amount of swirl--angular momentum--is preserved in mechanical systems. Furthermore, astronomers have observed (using the Hubble telescope, among others), disks of swirling dust which presumably mark the birth of other planetary systems, or perhaps systems of binary stars.

That, in a nutshell, is the "scientific explanation." We weren't there when it happened (the way the Almighty was, perhaps--see Job 38, v. 4), but we have plenty of evidence. You may also look up

174. Does Precession of the Equinoxes shift our Seasons?


Your friend had in mind a real phenomenon of nature, but it actually happens differently, and the results are not the ones your friend credited to it.

The Earth orbits the Sun in a large flat plane, known as the ecliptic . The reasons we have winter, summer etc., is that the axis around which the Earth turns is not perpendicular to the ecliptic, but makes an angle of about 23.5 degrees to that perpendicular.

Thus in the summer , the northern hemisphere is tilted towards the Sun , the north pole gets 24-hour sunshine and countries north of the equator also get longer days and more concentrated sunlight. Six months later, the axis still faces the same way in space, but now the Sun is on the other side, the north pole is in the shade all the time, the northern hemisphere gets longer nights and sunlight falls there at a more shallow angle, reducing its power to heat the land.

All this is described in "Seasons of the year" at which also shows how seasons south of the equator are in opposite parts of the year.

Now what your friend is aware of is that the direction of the Earth axis changes . It always makes an angle of about 23.5 degrees with the line perpendicular to the ecliptic plane--but while keeping this angle, it wanders around a cone , whose axis is perpendicular to the ecliptic. It takes about 26,000 years to go completely around that cone. The technical name for this phenomenon is " Precession of the Equinoxes " and it is described in

Precession, however, does not make the seasons different from what they are now. The picture given in "Seasons of the Year," of the Earth tilted by 23.5 degrees while orbiting the Sun, still describes the situation, except that over the thousands of years, it is slowly rotated in space, relative to the rest of the universe. (If you made a flat paper model of it and put it on a table top, what happens is that the model gets slowly rotated on top of the table). The orbital plane remains the same, only the Earth rotation axis goes around a cone.

Since the picture is the same, the seasons are the same. Our calendars are all adjusted to include this phenomenon, to keep (for instance) the date of the shortest day of the year around December 21.

What does change are the background stars . Since the pattern rotates relative to them, the seasonal presentation of the stars slowly rotates, too. Nowadays we see the constellation Orion in the sky after sunset in winter, and the constellation of Scorpio in mid summer, with its bright portion of the Milky Way. In 13,000 years, the rotation will make Orion shine in the evening in midsummer, and Scorpio in mid-winter. The pole star, too, will shift, and the evening constellations may also shift closer or further from the horizon. (Stars have motions of their own, too, and in 13,000 years, constellations may somewhat change.).

All that, however, deals with the stars at night. Seasons are tied strictly to the relative positions of Earth and Sun, and that will not change.

I have not heard about winters arriving later , but it may seem that way, because winters are also getting warmer, part of the "global warming" trend. There is little doubt that global warming is happening. Some people still wonder whether it is part of a slow fluctuation which will ultimately reverse itself. More and more however accept that it is caused by the increase of molecular gases (carbon dioxide, methane) due to human activities, which makes it harder for the atmosphere to radiate (shine) its heat back to space.

175. "Zenial Days" on Hawaii

I live in Kaunakakai, Hawaii, on the island of Molokai. The busiest intersection on the island is more or less at 21.0893 N, 157.0227 W. We'll use that for Kaunakakai.

As I understand it, the longest day of the year in our tropical town is not the summer solstice . We should have two longest days of the year, one shortly before the summer solstice, one shortly afterward. The sun should be directly overhead once as it travels north to the Tropic of Cancer, and once as it heads back south for its rendezvous with the equator and the equinox.

How can I find out exactly when those dates are? The sunrise and sunset times on our local tide calendar are too imprecise for me to figure it out that way. Is there a celestial almanac that will list the latitude of the sun for each date? Is there a formula a 7th grade English teacher can figure out?


You indeed seem to have a clear understanding of the motions of the Sun.

Every day the Sun rises somewhere near east and sets somewhere near west, and at noon (in the continental US) it passes to the south and reaches its largest elevation angle above the horizon (largest for the day). In those states, that angle is always less then 90°, so the Sun never passes overhead--"at zenith." Also (because of the tilt of the Earth's axis), that angle depends on the date. In summer it grows larger as the date approaches midsummer day on 21 June, then it decreases again (see "From Stargazers to Starships").

Hawaii is close to the equator, so the Sun's noontime elevation there in midsummer actually exceeds 90°, making it pass north of the zenith. The noon elevations before and after that day get smaller, and you are asking, when are they 90° , so that the noontime Sun passes exactly overhead.

I would guess those dates are May 26 and July 18 . (These are " zenial days " and were apparently noted by Maya astronomers).

But you seem to want more than numbers-- you also want understanding . I therefore ask you to draw a picture on a sheet of paper, a simplified north-south cross-section of the celestial sphere at Kaunakakai. Then go through the reasoning below, very slowly, making sure you understand every step. You might want to draw additional sketches, and also to consult suitable parts of "From Stargazers to Starships."

First draw a horizontal line (x-axis), which represents the north-south axis on the ground (north at right). Add to it (above it) a perpendicular line (y-axis) which points up to zenith, straight overhead. The origin is where you stand.

On the right, add a straight line northwards from the origin, making an angle 21.09° with the x-axis (you need no accuracy, this is just a sketch). It represents the direction to the celestial pole (or the pole star, very nearly) from Kaunakakai. And finally, a line from the origin, making a 90° angle with the preceding one--i.e. tilted southwards from the zenith, by an angle 21.09 degrees. It represents the direction to the celestial equator.

Over the year the Sun (in its apparent motion relative to the stars) traverses the ecliptic , a circle on the celestial sphere making an angle 23.5° with the celestial equator. At equinox it is on the intersection of equator and ecliptic, during the summer it is north of the equator, during winter south of it.

On any day of the year, it will have on that sphere a certain "distance" (actually, an angle) north or south of the equator. Suppose it is summer. Imagine a line on the celestial sphere, from the celestial pole to where the Sun is, and you continue it until it hits the equator. The size (in degrees) of that last section is the Sun's "declination angle" at that time, its elevation angle above the equator. On midsummer day it is 23.5°, at equinox, zero, and you can extend the definition to find its value on midwinter day as (󈞃.5°).

Now go back to your drawing, of the north-south sky at Kaunakakai. On midsummer day at noon , the direction to the Sun makes an angle of 23.5° with the direction to the celestial equator. You can add that direction to your sketch as a broken line, if you want, and because 23.5° is larger than the latitude of Kaunakakai, it is tilted past zenith, northward of the y-axis. Not the highest possible elevation! You want the Sun to be at zenith, which means the declination--the elevation (above the equator) of the point of the ecliptic where the Sun is located--has to be 21.09°, or about 21 degrees, 5.5 minutes.

The web has many sites which calculate or tabulate the position of the Sun, and the US Naval Observatory publishes a yearly astronomical almanac , but (as of 2016) the site answering your questions, , is no longer posted on the web . It had a tabulation of many variables, some specific to a location at latitude 45 north--but all you need is the declination of the Sun, which was tabulated day by day. Look on what days it comes closest to 21 degrees, 5.5 minutes, and you have your answer.

Please let me know how clear the above explanation has been. I could probably do a better job in a short session with you in front of a blackboard or a sheet of paper, but I'm retired and no one will pay me to fly to Hawaii to do so. (Curses!).

176. Sun's Temperature and Energy Density of Sunlight

I cannot seem to find the temperature of the Sun at the surface. Memory tells me is of the order of 10 to the 28th degrees centigrade. Please tell me where I am wrong.

Secondly, is it possible to determine the Joules per cubic centimeter (cc) at the surface or is there another way of discussing solar energy? I'm not talking about solar panels. I'm trying to get to the real meaning or power of a cubic centimeter of solar energy. It's going to be in Joules per cc--equal to what?

Can you help me with this? I was watching a movie in which a man invented a laser which had a zillion times more power per cc than the Sun. Or, is that an incorrect way of thinking about the Sun's energy?


The radiation from the visible surface of the Sun approximates what is given out by a hot object at temperature 5800° absolute , give or take a few degrees (in Sun1lite.htm I wrote 5780 deg.)..

The number is not important. Students and teachers should not memorize too much--at most, remember where the answer can be found. The important question is, "how to be know"? There exists a general law by which colors are distributed in the emissions of hot dense objects ("black bodies" which favor no color--the way emissions from gases then to favor colors characteristic of their atoms). The hotter the object, the shorter the wavelength, that is the further the peak emission migrates from infra red to dull red to bright red to orange to bright white (all colors). And maybe beyond. Colors of stars tell how hot they are.

That law is also important because it gave us the first inklings of quantum theory. See more in That file has not yet released, pending more work, but you may like it.

Asking for the volume density of sunlight is the wrong question. The mantra for electromagnetic radiation (e.g. light) is " spreads like a wave, deposits article like a particle, like a photon ." A wave in theory fills all space, though not equally (brighter in the light than in shade). Considering 1 cc of this volume does not tell much. A photon is a little point, an atom absorbing radiation--also not useful in terms of volume.

What is important it the flux --the rate of energy flow through a unit area (think of rain falling: how many gallons per minute per acre [or liters per second per hectare]?). Surround the Sun with a sphere at the Earth's orbit: through every meter squared flow 1380 watts of power, 1380 joule each second . That is the "Solar Constant"--see first paragraph of section S-7.

We are about 200 solar radii from the Sun, and light weakens as the inverse of the distance squared, so 200 squared is 40,000, and the energy flow at the "surface" of the Sun is about 40,000 times larger. The energy density there is about (3/2)nkT, where T=5800 deg., n is the density of the gas (which you will have to look up) and k is "Boltzmann's constant" which you will also have to look up. A laser is a non-thermal source of radiation--as far from a "black body" as you can get--so one really cannot assign to it a temperature. The energy flux of a laser beam, or course, can be high--laser beams can melt holes in thin metal, and sunlight cannot, so it is much more than 1380 joule/meter squared. How much higher, depends on the laser.

177. Teaching about energy in 8th grade

( from a message by an 8th grade teacher )

My 8th grade students are having problems with physical science -- they are a Title 1 school that is not meeting "proficiency levels" in math and in language arts. I spent a large amount of time, starting with measurements and the metric system. But nothing seems to be connecting in their long term memory banks. They conduct experiments and write down notes, but they do not understand the concepts and they don't appear curious. I am not reaching them. ..

From my reply: . I would recommend that in the remaining month you stress energy and work--it's a concept one encounters more and more.

From the response: "In what way will their exposure to work and energy be a more significant learning experience for them?"


You asked "In what way will their exposure to work and energy be a more significant learning experience for them?" (for your students). In several ways.

You wrote that you were teaching 8th grade. Your students are probably getting their first exposure to physics in a systematic ways, and therefore it is important to convince them that understanding it (not always easy!) is useful and provides knowledge which they can apply.

Energy is fundamental in this respect. They surely have heard about the cost of energy, about conserving it and about its various forms: moving cars and trains, heating homes and lighting them, running computers and TVs--all these involve energy. Food gives them something called "calories"--that is a unit of energy too. Therefore, as they learn about energy, they encounter examples in which physics enters their lives (and that of the community around them) in many ways.

Energy is also a good framework for unifying physics. Physics has many branches--mechanics (study of motions), heat, electricity, optics, atomic and nuclear, for starters (also, the physics which forms the foundation of chemistry and biology!)--all these come together in energy, as the table in the energy unit of "stargazers" shows. And there exists a good analogy, described there: energy is like money, paying for various processes. You can even hint about the second law of thermodynamics--tell them that heat is a 'soft currency", what you invest in heat can never be fully recovered but spreads around, more and more diffuse.

Work is the basic example of energy: overcoming a force over distance--such as lifting a brick against gravity, or climbing stairs--also overcoming friction, which creates heat (e.g. in the braking of a car, or armor piercing shells, which melt their way through a tank's armor, as their kinetic energy becomes heat) Work has many familiar examples makes the concept real.

The simplest example of kinetic and potential energy is of course a pendulum--or a kid on a bike, coasting down into a valley and losing speed as one gets up the next hill. Or a roller coaster. Burt Rutan's "Spaceship One" last year fired its rocket to accelerate to 3.5 times the speed of sound, then coasted up to 62 miles, then down again, braking its fall in the atmosphere by swiveling parts of its wings to create an obstacle.

Then, if you want something extra--you can tell (section 18d) about work against electric attraction, creating high voltage--in a Van de Graaf generator (The Boston Museum of Science has some giant ones, demonstrated to visitors), in lightning and in prying apart sheets coming out of a xerox copier, stuck together electrically. That however is extra.

Not much math is needed. You mix 5 liters of water at 60 degrees C with 2 liters at 10 degrees--what is the final temperature? (Energy is conserved). How many joules needed for a 60-kg kid to climb to the next floor, 3 meters up? How much is that in calories? If the kid ate a 6-gram chunk of chocolate (about 1/4 of a bar), providing 9 calories per gram (that's for fat--the sugar lowers it a bit), and converts the calories with 10% efficiency--how high can that kid climb, on this energy? And so on. Only arithmetic is used, no algebra (except maybe in the formula for kinetic energy, which can be explained separately)..

178. About the jetstream

One question was bothering me since long, thanks again in advance for the answer

I saw some time back on science TV channel a documentary which says that within the oceans are rivers which flow in certain directions and the flow within is relatively faster. The documentary further says that sometimes submarines get themselves into these rivers to travel faster or to just to save some fuel.

My question is does the earth atmosphere also has such channels? & if so, can they be utilized by commercial aircrafts the same way as a sub does?

Regards & keep up the good work.


You asked if "the earth atmosphere also has such channels?" Good question, and the answer is, yes it does.

The predominant flow at middle latitudes consists of the "Westerlies", a flow around the Earth from west to east, subject to large excursion north and south, the "Rossby Waves". This is discussed in

The flow is fastest at higher altitudes, where it is known as the "jet stream" and yes, airliners do take advantage of it. You may look up airline schedules for some direct flights between, say, New York and San Francisco. I would not be surprised if the estimated time of flight TO San Francisco is longer than the one FROM San Francisco (do not neglect the 3-hour difference in local time!). At one time airlines actually selected routes according to where the jet stream was strongest, but I do not think they do it any more.

179. What would a breach in a space station do?

I'm 37-year-old librarian and a bit of a science fiction fan, and I found your site while trying to determine how accurate certain scenes in some movies and television shows are. While watching a Dr. Who episode, I became annoyed at something I had previously noticed during several Star Trek episodes (ALL series). The scene is always this: a hole in a spaceship or space station opens up , and one character gets sucked out into space, while the rest hold on for dear life until the breach is sealed or they are rescued.

I realize the scene is already inaccurate because the characters in the ship or station are still breathing, while in reality, the air would almost instantaneously leave the room. I wonder, however, how likely it is that any of them would not be immediately sucked out into space if this really happened. At first, I assumed they would be dragged out with the air. I then wondered if the ship's or space station's gravity would keep them inside if they were not directly in front of the opening. What would really happen if this occurred?


I like science fiction, too, especially the older stuff which has some science in it. Modern writing gravitates towards fantasy, drifting from the highly improbable to the downright impossible.

Also, your are probably right, a large hole of a spaceship would result in very rapid loss of all air, in the process sucking out all sorts of other loose objects. Even passengers, though I would suspect light objects would go first, and passengers may be too big to go through the hole. The ship's gravity is no match.

If I were designing a space station the design might include in it a number of hollow balls , like the rubber balls kids play with, but made of real tough plastic, maybe Kevlar, with an outer layer of soft rubber. If the breach is not too, big, sooner or later one of the balls will be sucked into it and seal it. Ah, here is a nice story for you to write!

A question like yours was asked before. See question #152 (listed in error as #150) " Sudden decompression, 5 miles up ".

180. Gravity at the Earth's center


The answer is zero . No gravity at the center!

Newton proved this for a sphere--see 3rd paragraph in the reply to stargaze/StarFAQ3.htm#q45
Look at this another way: if gravity existed there, in what direction would it pull? There is no preferred direction in the middle of a spherical distribution of mass.

181. Freak waves on the ocean

I have attached a text document copied from the BBC which talks about waves tracked by the ESA satellites on the worlds oceans in the recent past. The article mentions their association with calm seas and mild weather.

I actually researched into this some years ago out of personal interest and found that on many occasions mariners have told stories of the sea rising up from a calm surface to a great height often even baring the sea floor. After closely assessing the data from the ESA I concluded that many of these waves are not physically possible based only on the wind and ocean currents and that there was no seismic activity in the region that would warrant such a wave.

The waves are typically very steep, travel very quickly and are generally short lived. they remind me very much of the flares often seen on the surface of the sun. (much smaller of course).

Do you think there is any foundation to the idea that these waves and flares could be caused by natural 'eruptions' of electro-magnetic fields from the cores of the sun and Earth


Freak waves have been known for a long time. The "Queen Mary" was almost sunk by one during WW II--see
An Italian liner (the Michelangelo?) had part of its bridge swept away in the North Atlantic, and only recently a serious wave hit a cruise liner:

The cause is not completely known, but it is certainly not electromagnetic energy --there is not enough such energy in electromagnetic disturbances arriving from space (nothing arrives from below) and its much too spread out.

Different waves can combine randomly, and sometimes reinforce each other. That may happen, but solitary high waves may be different. There exist mathematical models of "solitons", solitary waves which do not diminish with distance from the source, as ordinary waves do. They may play a role maybe steady winds, too. The trouble with freak waves, like some other phenomena, is that they happen unexpectedly at unpredictable locations, and do not last long, making it hard to collect reliable measurements about them.

182. Citation on "Bad Greenhouse" web page

I have serious questions about your terminology. In your web page
you make atmospheric analogies with greenhouses and blankets. You also, later, refer to water being 'forced out' of the air.

which wrote: " But don't ever teach nonsense by claiming that the radiation is trapped, or that the atmosphere reradiates, or that the atmosphere behaves as a greenhouse (or parked car), or that greenhouse gases behave as a blanket." Also

according to which: "The idea that it is the air which determines the amount of water vapor which can be present through some sort of holding capacity is an eighteenth century idea which was shown to be false both empirically and theoretically about two hundred years ago! The fact that it is still taught in our schools and defended by teachers and (gulp) professors, is a testimony to the mindless persistence of myth."


I looked up Dr. Fraser's web page and don't care either for his style or for his claims. His style is opinionated, and the passages you cite are a fair example of that. It reminds one of the joke of the cleaning woman who tidied up the church after services, and found the pastor's notes for his sermon, with a notation in one place "argument is weak here--raise voice."

I try to be careful not to inject opinions, but instead cite the reasons--observations, interpretations--why a claim is made. Dr. Fraser's arguments have a different style.

The atmosphere absorbs heat, yet its temperature does not rise without limit: it must re-radiate. It does so in the infra-red, because it consists of molecules, and these absorb and emit infra-red--their energy levels are in the IR range, whereas in the visible (bigger photons) they are transparent. This is the "long wave" radiation in

Of course, whatever the atmosphere emits is often reabsorbed by other layers in the atmosphere, or even by the ground. But that is the essence of the greenhouse effect--it does not prevent the flow of heat to the high atmosphere (where it is radiated to space), it just impedes it. Fraser is right on one thing--without greenhouse gases, Earth would be mighty cold.

Water vapor has a complex role. It too, is a greenhouse gas, an important one. In addition, it contains energy. It takes 100 calories to bring a gram of liquid water from freezing to boiling, but 540 calories to evaporate it, and in that sense, humid air is a store of energy of two types--in its temperature and in its content of water vapor. It can release energy either by cooling down (e.g. radiating to space) or by getting rid of the water (as in a thunderstorm). Air which got rid of its water is then warmer and rises, and can give up its heat in the high levels.

In short: I stand by what I wrote

183. How can radio waves carry sound?

Firstly could I thank you for producing such an educational and informative website. I am now beginning to understand the wonders of magnetism and electromagnetic waves, and also be fascinated by the fact this "energy " is completely natural. Maybe God does exist!!

Anyway I digress. The question that I have relates to radio communications. I have read that radio comms use a carrier wave to "transport" sound waves. Could you tell me how that is actually achieved. How is the sound wave of somebody`s voice, ie a radio DJ physically attached to the carrier wave. I would appreciate it very much if you could answer this question and I will continue to use your website to learn more about other related topics.


To give a full answer to your question is not easy. You are of course aware that sound waves and radio waves are quite different t--radio involves electric and magnetic phenomena, while sound does not, it depends on the exchange of pressure and motion.

The energy of a piece of music transmitted to you over the radio has undergone several changes:

(1) The sound vibrations are converted to electric vibrations , using an instrument known as a microphone .

(2) Another electric vibration is created, of much higher frequency, and the electric vibrations corresponding to the music are encoded as variations in it .

(3) The high-frequency electric vibration (with its encoded signal) is channeled to an antenna , an electric conductor open to space, which radiates it away as radio waves.

(4) Another antenna, in your radio receiver, captures some of the radio wave. Of course, only a tiny part of the energy reaches this antenna--the rest if broadcast in all other possible directions. As a result, the signal received is very weak, and needs to be amplified : the energy for this is largely derived from the battery or electric power supply of your radio.

(5) The original electric vibration , corresponding to the sound of the music and encoded in the radio signal, is extracted from the high-frequency "carrier wave."

(6) The electric signal is re-converted to sound, using an instrument known as loudspeaker .

In principle, you could feed the electric vibration from (1) into an antenna, recover it at your radio (step 4), amplify it and turn it back to sound using a loudspeaker. In practice, it won't work, because radio waves propagate much more efficiently when the frequency is high. It therefore pays to create a high frequency "carrier wave" and let it carry the signal, encoded as a variation of the strength of the carrier wave ("amplitude variation" or AM), or (a later development, more challenging but with certain advantages) as a variation of the frequency of the carrier wave ("frequency modulation" or FM).

There exist various designs of microphones. A simple one has a little box filled with carbon grains, and one side of the box can move in and out, moved by a round membrane. The sound of music hits the membrane, makes it oscillate, and this compresses the carbon grains and changes the electric resistance. An electric current led through the box therefore varies with the sound. Other, newer methods also exist.

The loudspeaker also has a membrane. Attached to its middle is a coil, and inside that is a magnet. The electric current with the signal flows through the coil, and as the current gets stronger or weaker, the coil senses a magnetic force which is stronger or weaker, and it pushes and pulls the membrane, creating sound which imitates the electric signal.

The high-frequency signal and amplification are generated by special electronic amplifiers--transistors nowadays, electronic vacuum tubes before transistors were invented. There is more, much more. But I hope you get the idea.

184. Do Cosmic Rays produce lightning?

We are a French tv production company that specializes in documentaries and are currently working on a program about weather reports on the solar system.

We recently came across the electrical discharge theory that claims the origins of lighting on earth is actually from a constant shower of cosmic gamma rays from the sun. We would like to use the theory as a subject for our program so we've contacted you to ask the almighty question, "is the theory really true"?


Lightning is clearly generated by thunderstorms (and sometimes volcanic eruptions--a different process). Cosmic rays are found all over Earth, but lightning occurs only in thunderstorms, and clearly gets its energy from their violent air motion--a combination of hot warm air rising and raindrops (or hail) falling down. See

Processes driven by that combination create high voltages. The problem is that air is an insulator, and for lightning to discharge the voltage, the insulation must somehow break down. It probably does so somewhat like a wedge splits wood--the "sharp tip" of concentrated voltage gradually extends the strong electric field, until it reaches the ground.

Cosmic rays are not gamma rays and do not come from the Sun. They are fast protons and other nuclei (mainly protons), filling our galaxy and probably originating in supernova explosions: see

As they collide with atmospheric atoms, they tear off electrons ("ionize the atoms") and by this allow the air to conduct electricity (for a very short moment, until those electrons find their way back). Cosmic rays also undergo nuclear collisions which create other fragments, and these too add to the ionization. The idea (I believe) is that cosmic ray ionization helps the high voltage break down the insulation of the air. In addition, the lightning process concentrates the high voltage, and it can then accelerate electrons (torn off by cosmic rays, say) to high energies, to create more ionization which also helps get the lightning started.

That is the little I know or guess. Better get some expert to help you with the program, before you start serious work.

185. Star positions shifted by the atmosphere

My name is Siddhartha and I live in India. I am 12 years old and am in the 8th grade.

Recently while studying about 'The Universe', our Physics teacher told us that from the earth, the stars do not appear at their original position due to refraction of light coming from the stars as it passes through the 4 layers of the atmosphere of the earth. That means, even stars like Alpha Centauri, the star nearest to the earth after sun, when viewed from earth, do not appear at their original position. That even means that the Sun also, when viewed from earth, does not appear to be in its original position.

My question is that how can the distance between the original position and the refracted position of the stars, that are in space, be measured? That means that how can the original position of the star be determined?


Twelve years old and studying physics in the 8th grade! Wow, I admire your ability and hope you will realize its full extent as you get older.

Yes, the positions of the stars and Sun are shifted by refraction in the atmosphere, but the shift is small and occurs mainly near the horizon, where sunlight and starlight slices diagonally and has a relatively long path through the atmosphere.

This was discovered by Tycho Brahe even before the telescope was introduced, but the effect is easiest to measure using a modern telescope. Telescopes (all but the simplest) have a clockwork or motor which slowly turns them to compensate for the rotation of the Earth--see picture of a telescope mounting in

Without this, the rotations of the Earth (which is greatly magnified by the telescope) causes any star to quickly drift to the edge of the field of view and be lost. If your telescope has crosshairs in the middle of the field of view and you place a star there, those crosshairs track where the star SHOULD be, taking into account only the rotation of the Earth.

Place in the crosshair a star near the horizon--for instance, the evening star Venus just before it sets. You will see that it drifts more and more away from where it is supposed to be, because as it gets closer to the horizon, refraction by the atmosphere shifts its image. You may even measure the refraction using this trick.

Astronomers of course know all this and take it into account. Before the "Hubble" telescope was sent into orbit, a huge computerized catalog of star positions was assembled for it, and since the telescope is outside the atmosphere, these all are true positions and no correction is necessary.

The Sun's position is also shifted--when you watch the Sun setting, it is really already below the horizon, and only the bending of light makes it visible. We therefore get (at any location) a little extra sunlight, our day is made a few minutes longer. Some time ago I got asked about this and you might like to read the correspondence here .

Give my greetings to your teacher!

186. The equation of time

I have enjoyed your article "A Millennium of Geomagnetism" and your website on sundials. I have a question regarding ephemeris . My research project involves magnetostratigraphy and we use a solar compass to orient our rock cores. We use the following equation to calculate solar time:

Solar time = standard time + 4 (T-L-E) minutes[1]

Standard time = local time minus one hour in summer.
T = longitude of time zone (in degrees).[2]
L = longitude of site (in degrees).[3]
E = ephemeris (in degrees). See table.[4]

Dec. 30 --Jan. 7: + 1 deg
8 --Jan. 19: + 2 deg
Jan. 20 --Mar. 15: + 3 deg
Mar. 16 --Mar. 25: + 2 deg
Mar. 26 --Apr. 5: + 1 deg
Apr. 6 --Apr. 26: 0
Apr. 27 --June 1: - 1 deg
June 2 --June 26: 0 (summer solstice)
June 27 --Aug. 21: +1 deg
Aug. 22 --Sept. 8: 0
Sept. 9 --Sept. 20: - 1 deg
Sept. 21 --Oct. 1: - 2 deg
Oct. 2 --Oct. 16: - 3 deg
Oct. 17 --Nov. 18: - 4 deg
Nov. 19 --Dec. 3: + 3 deg
Dec. 4 --Dec. 12: - 2 deg
Dec. 13 --Dec. 20: - 1 deg
Dec. 21 --Dec. 29: 0 (winter solstice)

I would like to know more about the role of ephemeris in the solar time equation and solar compasses. I would greatly appreciate any suggestions you could offer.


The dictionary defines "Ephemeris" as a tabulation of astronomical positions. While the quantity you denote E is something like that, it is usually called " The Equation of Time ." It is a historical name--it's not what we call an equation, but probably "something that makes (time) equal."

A SOLAR day is the time from noon to noon, and noon is when the Sun passes exactly to the south, which is also the noon indicated by a sundial.

You would think that since the Earth rotates at a fixed rate, all solar days are equally long, but they are not. The vary because (1) the Earth moves around the Sun in a slightly eccentric path, and its velocity varies (Kepler's 2nd law), and (2) the angle between the Earth's orbital plane ("ecliptic") and the Earth's equatorial plane (i.e. the tilt angle of the Earth) also creates a small variation.

Our clocks are based on the " mean solar day " averaged over the year, and the times of "noon by the clock" are always spaced apart the same 24 hours. The south passage of the Sun can vary from this time by up to 15 minutes or so, and the difference is your E, the equation of time. Look up

The equation of time is mentioned briefly on the web page about the sundial, at the end of the section on "Accuracy." Want more? See an earlier question by a user, What is the Analemma? linked at the end there, which also cited yet another link.

187. Launch window of the Space Shuttle

    [Written about the planned first shuttle launch on 13 July 2005, after years of delay caused by the Columbia disaster. That launch was later delayed]

I was wondering if there was a reason that the space shuttle. or other space launches have to take off at a certain time? For instance, today's launch should have been at 3:51, why not 3:50 or 4:00. is there a reason physically or is it just NASA following a timeline?


I can only guess, like you. Shuttles have been launched at all times, even at night, but this time NASA declared it wants to launch in daylight, so that cameras can track the flight in detail and check for debris, etc.

In addition, the shuttle is meant to reach the space station, which has its own orbit. To match speeds with the station, the shuttle orbit should be in the same plane as the orbit of the space station . The direction of launch is also prescribed: it must be eastwards (to take advantage of the Earth's rotation--a small extra margin, but every bit helps) and at an angle to match the inclination of the orbit of the space station, I think it's 57 degrees.

So imagine the orbital plane of the space station : it passes through the center of the Earth and cuts the equatorial plane of the Earth at 57 degrees. As the Earth rotates, that plane stays fixed in space, but the point where it intersects the line of latitude of Cape Canaveral (28.5 deg north) marches around that line, going all around it each rotation of the Earth. Only twice in each 24 hours is Cape Canaveral located at that intersection, and a shuttle launched at such a time will match the orbital plane of the space station. However, only one of those times is suitable--the other one would require launch in the opposite direction.

Gravitation – Notes

Ans: The first man who came up with the idea of gravity was Isaac Newton. It was an evening of 1665 when he was trying to solve the mystery why planets revolve around the Sun. Suddenly an apple fell from the tree under which he was sitting. The idea of gravity flashed in his mind. He discovered not only the cause of falling apple but also the cause that makes the planets to revolve around the Sun and the moon around the Earth. This unit deals with the concepts related to gravitation.

Q2. What is meant by the force of gravitation?

Ans: The force of gravitation:

There exists a force due to which everybody of the universe attracts every other body. This force is called the force of gravitation.

Q3. Explain Newton’s law of gravitation?

Ans: See Q # 5.9 from Exercise.

Q4. Explain that the gravitational forces are consistent with Newton’s third law of motion?

Ans: Law of gravitation and Newton’s third law of motion:

It is to be noted that mass m1 attracts m2 towards it with a force F while mass m2 attracts m1 towards it with a force of the same magnitude F but in the opposite direction. If the force acting on m1 is considered as action then the force acting on m2 will be the reaction. The action and reaction due to the force of gravitation are equal in magnitude but opposite in direction. This is in consistence with Newton’s third law of motion which states, to every action there is always an equal but opposite reaction.

Q5. Explain gravitational field as an example of a field of force?

The field in a region space in which a particle would experience a gravitational force is called gravitational field.

It is assumed that a gravitational field exists all around the Earth due to the gravitational force of attraction of the

The weight of a body is due to the gravitational force with which the Earth attracts a body. Gravitational force is a non-contact force.

For example, the velocity of a body, thrown up, goes on decreasing while on return its velocity goes on increasing. This is due to the gravitational pull of the Earth acting on the body whether the body is in contact with the Earth or not. Such a force is called the field force. It is assumed that a gravitational field exists all around the Earth. This field I directed towards the center of the Earth.

Q6. Explain, what is meant by gravitational field strength?

Ans: Gravitational field strength:

In the gravitational field of the Earth, the gravitational force per unit mass is called gravitational field strength of the Earth. It is 10 N kg -1 near the surface of the Earth.

The gravitational field becomes weaker and weaker as we got farther and farther away from the Earth. At any place, its value is equal to the value of g at that point.

Q7. How the mass of the Earth can be determined?

Ans: See Q # 5.10 from Exercise.

Q8. Why does the value of g vary from place to place? Explain how the value of g varies with altitude.

Ans: See Q # 5.13 from Exercise.

Q9. Explain the variation of ‘g’ with altitude.


What is the effect of the following on the gravitational acceleration?

Mass of a freely falling body.

Distance of freely falling body from the center of the Earth.

Is there any difference between the values of g at the equator and the poles? Explain.

Ans: (a) Since g = G Me / R 2 …….. (i)

Equation (i) shows that the value of g does not depend upon the mass of the body. This means that light and heavy bodies should fall toward the center of the Earth with the same acceleration.

(b) The value of g varies inversely as the square of the distance i.e. g  1 / R 2 if the distance from the center of the earth is increased then the value of g will decrease. That is why the value of g at hills (Murree) is less than its value of the seashore (Karachi).

(c) Earth is not a perfect sphere. It is flattened at the poles, for this reason, the value of g at the pole is more than at the equator. Because polar radius is less than equatorial radius. (g  1 / R 2 )


Does an apple attract the Earth towards it?

Ans: Yes, according to the law of gravitation an apple attracts Earth towards it but its attraction is very small and cannot be felt.

With what force an apple weighing 1N attracts the Earth?

Ans: The force of attraction is equal to the weight of the object. So, an apple weighing 1N attracts the Earth with 1N force.

Does the weight of an apple increase, decrease or remain when taken to the top of a mountain?

Ans: The value of g varies inversely as the square of the distance i.e. g  1/ R 2

Therefore, the weight of an apple decreases when taken to the top of a mountain due to less gravity of Earth.


Value of g on the surface of a celestial object depends on its mass and its radius. The radius of g on some of the objects is given below:

Object g(ms -2 )
Sun 274.2
Mercury 3.7
Venus 8.87
Moon 1.62
Mars 3.73
Jupiter 25.94

Q10. What are artificial satellites?

Ans: See Q # 5.14 from Exercise.

Q11. What are geostationary satellites also write their uses.

Ans: Geostationary satellites whose velocity relative to Earth is zero. These satellites remain stationary concerning the Earth at a height of about 42300 km from the surface of Earth. These are used for global TV transmissions and other telecommunication purposes.

As Earth also completes its one rotation about its axis in 24 hours, hence, these communication satellites appear to be stationary concerning Earth. It is due to this reason that the orbit of such a satellite is called geostationary orbit.

Dish antennas sending and receiving the signals from them have fixed direction depending upon their location on the Earth.

Uses of geostationary satellites:

Such satellites are useful for the following purposes.

(iii) Navigation (iv) Other military uses

Note: Three geostationary satellites can cover the whole earth.


Geostationary satellite:

The height of a geostationary satellite is about 42,300 km from the surface of the Earth. Its velocity concerning Earth is zero.


Global Positioning System (GPS):

Global Positioning System (GPS) is a satellite navigation system. It helps us to find the exact position of an object anywhere on the land, on the sea or in the air. GPS consists of 24 Earth satellites. These satellites revolve around the Earth twice a day with a speed of 3.87 kms -1 .

Q12. How Newton’s law of gravitation helps in understanding the motion of satellites? On what factors the orbital speed of a satellite depends?


Derive the formula for the orbital speed of an artificial satellite?

Ans: See Q # 5.15 from Exercise.


Moon is nearly 3, 80, 000 km away from the Earth. It completes its one revolution around the Earth in 27.3 days.

The Moon moves at about a thousand metres per second, but it's a long way away so it only appears to move slowly. Most of the apparent movement of the Moon is actually due to the rotation of the Earth. We see it appearing to go round the Earth once a day, but it actually takes about 28 days to complete an orbit.

The Wikipedia article on the Moon's orbit has these and many other stats about the Moon.

The moon is in orbit of the earth, an ellipse. A circle is a good approximation for the orbit, due to the low eccentricity. It's potential energy in radial direction is at a minimum. The speed is $v_< ext>=1022,frac< ext>< ext>$. Thats triple speed of sound. An airplane travelling at this speed would take not much time to appear oit of sight. The moon however appears slower. Due to its distance to the viewer it appears to travel slowly at the sky: low angular velocity $omega=frac<>>><>>>=frac<1>$.

Estimating the speed of the moon

Earth also rotates and the period of a moon cycle is longer. One cycle takes $T=27.32$ days to complete. Assuming a circular orbit with mean distance $r_< ext>=385,000$ km allows calculation of the speed of the moon. This calculation yields the velocity of about one kilometer per second.

The motion of the moon has a fun fact: Due to tidal locking one side of the moon always faces towards the earth.

When we stand on the side of a street and watch a car zooming at 100 Km/H we feel that the car is moving fast. But when you look at the same car from a distance of 10 Km, it appears slower because of the car and the observer. This is because when you are standing 10 Km away, the span of perpendicular view of your eyes has increased while the speed of the car remained at 100 Km/H. So the car has to spend more time to travel across your span of view so it appears slower. When you are standing on the same street as the car, you span of perpendicular view is very small and so the car car appears to zoom past it. Same with the moon.

The Moon orbits the Earth at a mean distance of 384,400 Km with a mean orbital velocity of 1.023 Km/S which is thrice the speed of sound. But it is at a distance of 384,400 Km so your the span of view is the entire sky due to which it appears to move slowly to us.

14.2 Groundwater Flow

If you go out into your garden or into a forest or a park and start digging, you will find that the soil is moist (unless you’re in a desert), but it’s not saturated with water. This means that some of the pore space in the soil is occupied by water, and some of the pore space is occupied by air (unless you’re in a swamp). This is known as the unsaturated zone. If you could dig down far enough, you would get to the point where all of the pore spaces are 100% filled with water (saturated) and the bottom of your hole would fill up with water. The level of water in the hole represents the water table, which is the surface of the saturated zone. In most parts of British Columbia, the water table is several metres below the surface.

Water falling on the ground surface as precipitation (rain, snow, hail, fog, etc.) may flow off a hill slope directly to a stream in the form of runoff, or it may infiltrate the ground, where it is stored in the unsaturated zone. The water in the unsaturated zone may be used by plants (transpiration), evaporate from the soil (evaporation), or continue past the root zone and flow downward to the water table, where it recharges the groundwater.

A cross-section of a typical hillside with an unconfined aquifer is illustrated in Figure 14.5. In areas with topographic relief, the water table generally follows the land surface, but tends to come closer to surface in valleys, and intersects the surface where there are streams or lakes. The water table can be determined from the depth of water in a well that isn’t being pumped, although, as described below, that only applies if the well is within an unconfined aquifer. In this case, most of the hillside forms the recharge area, where water from precipitation flows downward through the unsaturated zone to reach the water table. The area at the stream or lake to which the groundwater is flowing is a discharge area.

What makes water flow from the recharge areas to the discharge areas? Recall that water is flowing in pores where there is friction, which means it takes work to move the water. There is also some friction between water molecules themselves, which is determined by the viscosity. Water has a low viscosity, but friction is still a factor. All flowing fluids are always losing energy to friction with their surroundings. Water will flow from areas with high energy to those with low energy. Recharge areas are at higher elevations, where the water has high gravitational energy. It was energy from the sun that evaporated the water into the atmosphere and lifted it up to the recharge area. The water loses this gravitational energy as it flows from the recharge area to the discharge area.

In Figure 14.5, the water table is sloping that slope represents the change in gravitational potential energy of the water at the water table. The water table is higher under the recharge area (90 m) and lower at the discharge area (82 m). Imagine how much work it would be to lift water 8 m high in the air. That is the energy that was lost to friction as the groundwater flowed from the top of the hill to the stream.

Figure 14.5 A depiction of the water table in cross-section, with the saturated zone below and the unsaturated zone above. The water table is denoted with a small upside-down triangle. [SE]

The situation gets a lot more complicated in the case of confined aquifers, but they are important sources of water so we need to understand how they work. As shown in Figure 14.6, there is always a water table, and that applies even if the geological materials at the surface have very low permeability. Where there is a confined aquifer — meaning one that is separated from the surface by a confining layer — this aquifer will have its own “water table,” which is actually called a potentiometric surface, as it is a measure of the total potential energy of the water. The red dashed line in Figure 14.6 is the potentiometric surface for the confined aquifer, and it describes the total energy that water is under within the confined aquifer. If we drill a well into the unconfined aquifer, the water will rise to the level of the water table (well A in Figure 14.6). But if we drill a well through both the unconfined aquifer and the confining layer and into the confined aquifer, the water will rise above the top of the confined aquifer to the level of its potentiometric surface (well B in Figure 14.6). This is known as an artesian well, because the water rises above the top of the aquifer. In some situations, the potentiometric surface may be above the ground level. The water in a well drilled into the confined aquifer in this situation would rise above ground level, and flow out, if it’s not capped (well C in Figure 14.6). This is known as a flowing artesian well.

Figure 14.6 A depiction of the water table and the potentiometric surface of a confined aquifer. [SE]

In situations where there is an aquitard of limited extent, it is possible for a perched aquifer to exist as shown in Figure 14.7. Although perched aquifers may be good water sources at some times of the year, they tend to be relatively thin and small, and so can easily be depleted with over-pumping.

Figure 14.7 A perched aquifer above a regular unconfined aquifer. [SE]

In 1856, French engineer Henri Darcy carried out some experiments from which he derived a method for estimating the rate of groundwater flow based on the hydraulic gradient and the permeability of an aquifer, expressed using K, the hydraulic conductivity. Darcy’s equation, which has been used widely by hydrogeologists ever since, looks like this:

(where V is the velocity of the groundwater flow, K is the hydraulic conductivity, and i is the hydraulic gradient).

We can apply this equation to the scenario in Figure 14.5. If we assume that the permeability is 0.00001 m/s we get: V = 0.00001 * 0.08 = 0.0000008 m/s. That is equivalent to 0.000048 m/min, 0.0029 m/hour or 0.069 m/day. That means it would take 1,450 days (nearly four years) for water to travel the 100 m from the vicinity of the well to the stream. Groundwater moves slowly, and that is a reasonable amount of time for water to move that distance. In fact it would likely take longer than that, because it doesn’t travel in a straight line.

Exercise 14.1 How Long Will It Take?

Sue, the owner of Joe’s 24-Hour Gas, has discovered that her underground storage tank (UST) is leaking fuel. She calls in a hydrogeologist to find out how long it might take for the fuel contamination to reach the nearest stream. They discover that the well at Joe’s has a water level that is 37 m above sea level and the elevation of the stream is 21 m above sea level. The sandy sediment in this area has a permeability of 0.0002 m/s.

Using V = K * i, estimate the velocity of groundwater flow from Joe’s to the stream, and determine how long it might take for contaminated groundwater to flow the 80 m to the stream. [SE drawing]

It’s critical to understand that groundwater does not flow in underground streams, nor does it form underground lakes. With the exception of karst areas, with caves in limestone, groundwater flows very slowly through granular sediments, or through solid rock that has fractures in it. Flow velocities of several centimetres per day are possible in significantly permeable sediments with significant hydraulic gradients. But in many cases, permeabilities are lower than the ones we’ve used as examples here, and in many areas, gradients are much lower. It is not uncommon for groundwater to flow at velocities of a few millimetres to a few centimetres per year.

As already noted, groundwater does not flow in straight lines. It flows from areas of higher hydraulic head to areas of lower hydraulic head, and this means that it can flow “uphill” in many situations. This is illustrated in Figure 14.8. The dashed orange lines are equipotential, meaning lines of equal pressure. The blue lines are the predicted groundwater flow paths. The dashed lines red lines are no-flow boundaries, meaning that water cannot flow across these lines. That’s not because there is something there to stop it, but because there’s no pressure gradient that will cause water to flow in that direction.

Groundwater flows at right angles to the equipotential lines in the same way that water flowing down a slope would flow at right angles to the contour lines. The stream in this scenario is the location with the lowest hydraulic potential, so the groundwater that flows to the lower parts of the aquifer has to flow upward to reach this location. It is forced upward by the pressure differences, for example, the difference between the 112 and 110 equipotential lines.

Figure 14.8 Predicted equipotential lines (orange) and groundwater flow paths (blue) in an unconfined aquifer. The orange numbers are the elevations of the water table at the locations shown, and therefore they represent the pressure along the equipotential lines. [SE]

Groundwater that flows through caves, including those in karst areas — where caves have been formed in limestone because of dissolution — behaves differently from groundwater in other situations. Caves above the water table are air-filled conduits, and the water that flows within these conduits is not under pressure it responds only to gravity. In other words, it flows downhill along the gradient of the cave floor (Figure 14.9). Many limestone caves also extend below the water table and into the saturated zone. Here water behaves in a similar way to any other groundwater, and it flows according to the hydraulic gradient and Darcy’s law.

Figure 14.9 Groundwater in a limestone karst region. The water in the caves above the water table does not behave like true groundwater because its flow is not controlled by water pressure, only by gravity. The water below the water table does behave like true groundwater. [SE]

Is It True that Newton’s Gravity is Not as Good as Einstein’s Gravity ?

Unfortunately, Einstein’s imagination lead him to the biggest blunder in modern physics for more than 100 years.

“Einstein started with the assumption that Newton’s gravity must be incorrect.” (Prof.Brian Koberlein)

Ask Ethan #106: We know that Einstein’s general relativity is superior to Newton’s gravity, but where did Newton go wrong?

Einstein’s Theory of General Relativity ru l es over Newton’s Laws. We get that.
What I would like to know is this Using Newton, there is a discrepancy in the precession of Mercury’s orbit. What are we observing? Is there more gravity than we calculate by Newton, or less? Or is the problem something else?

But this question goes a little further. As you can see, above, every planet that orbits in our Solar System goes around the Sun. In particular, it goes around not in a perfect circle, but rather in an ellipse, as Kepler noticed nearly a full century before Newton. The orbits of Venus and Earth are very close to circular, but both Mercury and Mars are noticeably more elliptical, with their closest approach to the Sun differing significantly from their greatest distance.
Mercury, in particular, reaches a distance that’s 46% greater at aphelion (its farthest point from the Sun) than at perihelion (its closest approach), as compared to just a difference of 3.4% from Earth. This part of the story has nothing to do with anyone’s theory of gravity this is merely the conditions which these planets formed under that led to these orbital properties.

And that’s the story of not only Newton’s gravity being superseded, but in what way(s) Newton’s theory came up short. There have been many other victories for general relativity since (and, honestly, no failures as of yet), but in all the cases where Newton’s and Einstein’s theories differ, it’s Einstein — with stronger gravitational effects close to massive bodies — who emerges victorious. Science marches forward, but sometimes each new step takes a very long time!

Where did Newton go wrong? Not only Newton’s gravity being superseded, but in what way Newton’s theory came up short. (How, exactly, did Newton fail?)

“Not only Newton’s gravity being superseded, but in what way Newton’s theory came up short.” This statement is not correct. Until now, we still use Newton’s gravity, so far.

For example, if knowing mass of Sun, mass of Earth, mass of Moon, distance Earth to Sun, and distance Earth to Moon can someone calculate gravitational force (F) Sun to Earth and Moon to Earth using units and measurement of Einstein’s gravity ? And can someone predicts tides in Oregon, USA, at the day of 2017 solar eclipse, August 21 using units and measurement of general relativity?

If anyone can, I will agree that Einstein’s theory of gravity superior than Newton’s theory of gravity. If nobody can do it, “Einstein’s theory of gravity superior than Newton’s theory of gravity” is nonsense. Because Newton’s theory of gravity predicts tides very accurate, for example in Oregon or in all places/harbor in the world.

Thanks to Sir Isaac Newton

Some Applications of Newton’s Laws of Gravitation

1.Solving Fnet = ma problems with multiple bodies

2.Forces and circular motion

9.Determining Tides: Hydrographic Office

Today we receive about 400 hydrographic surveys a year, in various forms, including those by the Royal Navy Surveying Squadron, contract survey companies and other contractors and developers. Though the quality of these surveys varies, all are registered and copied before being evaluated by the relevant chart branch, then placed in the archive with their accompanying field data.

The Hydrographic Office has been collecting surveys since 1795 and we hold an estimated 60,000 examples, mainly executed by the Royal Navy. Many have been published in their entirety, or included in part, in printed Admiralty charts. We predominantly hold survey information from 1830 to the present.(

For example, Singapore Tide Table Year 2017

This 275-page book contains Tidal Height and Tidal Stream Predictions covering stations in Singapore Port waters and selected stations along the Malacca and Singapore Straits. Mariners, shipping communities, port users and other interested parties will find this book useful.

The predictions consist of 5 main segments to facilitate easy reference:

1.High and Low Water Predictions

2.Hourly Tidal Height Predictions

3.Hourly Tidal Stream Predictions

4.Maximum and Slack Tidal Stream Predictions

5.Malacca Strait — High and Low Water Predictions.

GPS doesn’t need Einstein‘s relativity

There is an application of Einstein’s relativity that is often proud, if Einstein’s relativity is not used then the GPS would be inaccurate.

“People often ask me ‘What good is Relativity?’. It is a commonplace to think of Relativity as an abstract and highly arcane mathematical theory that has no consequences for everyday life. This is in fact far from the truth.
The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system. For example, to counteract the General Relativistic effect once on orbit, the onboard clocks were designed to “tick” at a slower frequency than ground reference clocks, so that once they were in their proper orbit stations their clocks would appear to tick at about the correct rate as compared to the reference atomic clocks at the GPS ground stations. Further, each GPS receiver has built into it a microcomputer that, in addition to performing the calculation of position using 3D trilateration, will also compute any additional special relativistic timing calculations required, using data provided by the satellites.

Relativity is not just some abstract mathematical theory: understanding it is absolutely essential for our global navigation system to work properly!”

“The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system.” This statement is also incorrect

Van Flandern goes on to discuss GPS clocks, which are often cited as being proof positive of Einstein’s relativity. It may surprise you, but the GPS system doesn’t actually use Einstein’s field equations. In fact, this paper by the U.S. Naval Observatory tells us that, while incorporating Einstein’s equations into the system may slightly improve accuracy, the system itself doesn’t rely on them at all. To quote the opening line of the paper, “The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require.” (Why Einstein was wrong and Newton was right)

Truth about Mercury’s Orbit: Knowing the answer.

Its about Mercury’s orbits. that is not in harmony with the Newton’s gravity. But, actually, that is better than Einstein’s gravity where has no units of measurement. Einstein had no idea of the units and disciplines of measurement as the goal of using mathematics in physics. Einstein’s gravity is nothing about force, how did Einstein come true on Mercury’s orbits?

Here the answer:
Einstein’s Mercury orbit was challenged by several scientists including Dr. Thomas Van Flandern astronomer who worked at the U.S. Naval Observatory in Washington.

Excerpt of Tom Van Flandern Articles:

“Fact: The equation that accounted for Mercury’s orbit had been published 17 years earlier, before relativity was invented. The author, Paul Gerber, used the assumption that gravity is not instantaneous, but propagates with the speed of light. After Einstein published his general-relativity derivation, arriving at the same equation, Gerber’s article was reprinted in *Annalen der Physik* (the journal that had published Einstein’s relativity papers). The editors felt that Einstein should have acknowledged Gerber’s priority. Although Einstein said he had been in the dark, it was pointed out that Gerber’s formula had been published in Mach’s Science of Mechanics, a book that Einstein was known to have studied. So how did they both arrive at the same formula?

Tom Van Flandern was convinced that Gerber’s assumption (gravity propagates with the speed of light) was wrong. So he studied the question. He points out that the formula in question is well known in celestial mechanics. Consequently, it could be used as a “target” for calculations that were intended to arrive at it. He saw that Gerber’s method “made no sense, in terms of the principles of celestial mechanics.” Einstein had also said (in a 1920 newspaper article) that Gerber’s derivation was “wrong through and through.”

So how did Einstein get the same formula? Van Flandern went through his calculations, and found to his amazement that they had “three separate contributions to the perihelion two of which add, and one of which cancels part of the other two and you wind up with just the right multiplier.” So he asked a colleague at the University of Maryland, who as a young man had overlapped with Einstein at Princeton’s Institute for Advanced Study, how in his opinion Einstein had arrived at the correct multiplier. This man said it was his impression that, “knowing the answer,” Einstein had “jiggered the arguments until they came out with the right value.”

According to paper ‘The Perihelion Precession of Mercury’: ”It took me a while to get around to a full analysis of Mercury’s orbit, but now that I have done so I have managed to surprise even myself by the sheer number of errors I have uncovered — and I am not easily surprised by errors anymore. But the quality as well as the quantity of these errors is enough to impress anyone, as I hope you will agree by the end. I say quality, because the magnitude of these errors may be even more surprising than their number. As I will show, the most basic rules of math and logic have been flagrantly ignored in full view of history, and not one person has deigned to notice in almost a century”.

According to the book ‘Logical Fallacies of Special and General Theory of Relativity ‘:There are at least 5 logical fallacies of Einstein’s special and general theory of relativity. This book explains the invalidity of Einstein’s hypothesis,and tries to convey prediction using astronomical test of general relativity at 2017 total solar eclipse, Monday, August 21, in USA.. This book explains the fatal mistakes of Einstein’s theory and explains all sorts of things that no one has ever explained before.

The problems of general relativity arise when you look at the Universe at very small or at very large scales.

Acccording to Alpha Institute for Advanced Studies (AIAS): Fundamental Errors in the EFE

It is shown that there are several irretrievable errors in the Einstein theory of cosmology used in the standard model, and in all derivative theories thereof. The root cause of these errors is that Einstein’s theory used a connection in Riemann geometry that is symmetric in its lower two indices. The connection must however be antisymmetric in its lower two indices as shown in previous papers of this series ( The incorrect use of a symmetric connection means that the general relativity of the last ninety years or so is incorrect and should be developed with Einstein Cartan Evans (ECE) theory. All the major assumptions of Einsteinian cosmology are based on an assumed symmetric connection, notably the second Bianchi identity used in the field equation, and the geodesic method used by Einstein in deriving the Newtonian limit. Derivative theories such as the Hawking-Penrose singularity theorems also assume a symmetric connection, and are therefore mathematically incorrect and physically meaningless. All metrics of the Einstein field equation are incorrect. An error free cosmology based on ECE theory has been developed in earlier papers of this series. (Fundamental Errors in the Einstein Field Equation)

A famous critic of Theory of relativity is Nikola Tesla, who called it a “…magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king … its exponents are brilliant men but they are metaphysicists, not scientists.

“Mathematics is nothing but a way of modeling patterns we see in the real world. If the model doesn’t match up with reality to some degree, it’s useless. The foundation of mathematics is based on assumptions. Changing the basic assumptions of mathematics would just make mathematics useless, in which case, no one would use it, and people would have an incentive to invent models that actually do match up to reality. This is in fact what happens repeatedly any time a new area of mathematics is formalized. Someone takes a guess at the assumptions that will result in a usable model, and then they discover some shortcoming of the model, so they revise it until it fits.”(Quora).

And Dr Louis Essen, inventor of atomic clock rejects Einstein’s Relativity Theory, wrote in 1988: “Einstein’s use of a thought experiment, together with his ignorance of experimental techniques, gave a result which fooled himself and generations of scientists.”

“Their measurement had been sheer luck, or a case of knowing the result they wanted to get.” (Stephen Hawking)

The biggest thing Einstein was wrong about, because Einstein had no idea on the basic of astronomy: Published on 1916, Einstein predicts light from a distance star passing by the limb of the Sun would be deflected by 1.75 arc seconds.This prediction without any explanation the altitude of star/the Sun during eclipse. Therefore, this prediction has no scientific meaning, because calculation for deviation of star all depend on the altitude of star.

Something weird and magical when experimental tests of general relativity via eclipse using optical telescopes (1919, 1922, 1927, 1936, 1952, 1973) and test using radio telescope after 2004, the result is declared general relativity is correct.That is very embarrasing to the world of science. They are not aware of making themselves look so foolish: had no idea on the basic of astronomy.

And why didn’t they know the two fatal mistakes of Einstein? Einstein wants to measure deflection of light by the Sun but he proposed test measuring deflection of light by Earth’s atmosphere he had not realized about that. Ironically, this test is not scientifically correct and deeply wrong, (Now you know Einstein was wrong, Newton was right).

No consequences of general relativity for everyday life. Claims of general relativity on redshift, lensing, time dilation, GPS, binary pulsars, speed of gravity, waves driven by gravity and gravity itself all can be explained without Einstein’s theory.

How could things that wrong rule over things that right? How could a bird without wings can fly over a bird with strong wings?

How could Newton can not be defeated happen? Here the answer: Standing upon the shoulders of giants

Here you’ll find my thoughts on writing and links to my published works: Medium, Twitter, Amazon, Quora. Read story about Science, Military, and Religion: My Blog and care on Health and Safety in this blog: Princess Mandalika. Thank you!

Development of gravitational theory

Newton argued that the movements of celestial bodies and the free fall of objects on Earth are determined by the same force. The classical Greek philosophers, on the other hand, did not consider the celestial bodies to be affected by gravity, because the bodies were observed to follow perpetually repeating nondescending trajectories in the sky. Thus, Aristotle considered that each heavenly body followed a particular “natural” motion, unaffected by external causes or agents. Aristotle also believed that massive earthly objects possess a natural tendency to move toward Earth’s centre. Those Aristotelian concepts prevailed for centuries along with two others: that a body moving at constant speed requires a continuous force acting on it and that force must be applied by contact rather than interaction at a distance. These ideas were generally held until the 16th and early 17th centuries, thereby impeding an understanding of the true principles of motion and precluding the development of ideas about universal gravitation. This impasse began to change with several scientific contributions to the problem of earthly and celestial motion, which in turn set the stage for Newton’s later gravitational theory.

The 17th-century German astronomer Johannes Kepler accepted the argument of Nicolaus Copernicus (which goes back to Aristarchus of Samos) that the planets orbit the Sun, not Earth. Using the improved measurements of planetary movements made by the Danish astronomer Tycho Brahe during the 16th century, Kepler described the planetary orbits with simple geometric and arithmetic relations. Kepler’s three quantitative laws of planetary motion are:

During this same period the Italian astronomer and natural philosopher Galileo Galilei made progress in understanding “natural” motion and simple accelerated motion for earthly objects. He realized that bodies that are uninfluenced by forces continue indefinitely to move and that force is necessary to change motion, not to maintain constant motion. In studying how objects fall toward Earth, Galileo discovered that the motion is one of constant acceleration. He demonstrated that the distance a falling body travels from rest in this way varies as the square of the time. As noted above, the acceleration due to gravity at the surface of Earth is about 9.8 metres per second per second. Galileo was also the first to show by experiment that bodies fall with the same acceleration whatever their composition (the weak principle of equivalence).

Watch the video: So wirkt die Schwerkraft. Terra X plus (January 2022).