Gravity Made Really Simple

I would like to describe how gravity operates in my own terms. This is not a new discovery or anything like that but, I have yet to see gravity described in the way that it's operation appears to me.

We know that the moon is 1/81 the mass of the earth and that it's surface gravity is 1/6 that of the earth. But you may be wondering, if the mass of the moon is only 1/81 that of the earth, then why isn't it's surface gravity also 1/81 that of the earth?

The answer is that the surface gravity of a spherical body, such as a planet, is proportional to the total mass divided by the surface area. The diameter of the moon is 1/4 that of the earth, meaning that it's surface area is 1/16 that of the earth. If the moon's mass is 1/81 that of the earth and it's surface area is 1/16 that of the earth, it's surface gravity should be about 1/ ( 81/16), or about 1/5 that of earth, which is fairly close to the measured figure of 1/6.

This simple formula does not take into account that the planet or moon may not be of uniform density. If a body is more dense toward it's core, it's mass will be more concentrated and it's surface gravity will be stronger than if it was of uniform density.

The reason that the surface gravity of the moon is somewhat weaker than the formula indicates it should be, 1/6 that of the earth instead of 1/5, can only be because the mass of the earth is more concentrated than that of the moon. The moon is made of the same type of rock as the earth's mantle but the earth has a heavy iron core that the moon lacks.

This concept of surface gravity being proportional to mass/surface area means that we can easily calculate what the gravity would be at any altitude above the earth's surface. The radius of the earth is about 4000 miles or 6450 km. Suppose we wanted an estimate of the gravity at an altitude of 10 miles or 16 kilometers, we would only need to add that figure to the earth's radius and then calculate what the earth's surface area would be if that were, in fact, the radius. Then, divide the actual radius of the earth by that number to get the gravity at that altitude in comparison with the earth's surface gravity.

So, if the earth's radius were 4,010 miles, instead of the actual 4,000 miles, it's surface area would be the smaller number divided by the larger number and then the result squared, in comparison with it's actual surface area. This gives us .9975 squared = .995.

This means that the gravity at an altitude of 10 miles or about 16 km above the earth's surface should be about .995 of the earth's surface gravity. In dealing with the earth, we should not try to be too accurate by using more significant figures simply because the surface gravity and the land altitude of the earth is not exactly uniform.

Next, I would like to describe my version of why an object falls from a height to the surface of the earth or other body. An object falls not because of gravity, but because of a difference in gravity. This difference in gravity due to distance ratio from a body is usually referred to as tidal force.

If an object at some distance above the earth's surface will experience a stronger pull of gravity from the earth by edging closer to the earth, then that object will do just that and will fall to the earth's surface. If there is only a very minimal difference in the strength of the earth's gravitational pull on the object if it edged closer to the earth and if the object has lateral momentum that can negate this minor tidal force, the object will not fall to the earth.

The earth's gravity is, however, strong enough to hold onto the object even if it does not fall to the surface. The result is that vector of the direction of earth's gravitational pull on the object combines with the vector of the lateral momentum on the object to give the object an orbit around the earth.

The center of our galaxy exerts a very strong gravitational pull on the earth, as well as on the entire Solar System. We do not move any closer to the center because there is only a minimal tidal force on us from the galactic center. It's gravitational pull is immense, but the difference in it's gravitational pull, if we should move a little bit closer to the center, is not. The reason is simply the great distance between the earth and the galaxy's center, as well as the diffuse arrangement of matter at the center.

An ideal example of tidal force is, as you may expect, the tides in the earth's oceans. Tides are caused not just by gravity, but by a difference in gravity. As the moon passes overhead, the surface of the ocean is closer to the moon than is the bottom of the ocean. This causes more of a pull at the surface by the moon's gravity than at the bottom of the ocean. The result is the well-known bulge in the surface of the ocean, known as a tide.

The sun produces tides on the earth's oceans also. But solar tides are less than half as high as lunar tides. How can this be when the sun is so massive compared to the moon? The answer is in the relative distance. The sun is about 400 times as far from earth as the moon is. There is a difference in the pull of the sun's gravity on the ocean's surface compared with the pull on the ocean floor. But because the sun is so far away, the proportional difference in this pull is much less than that of the much closer moon.

As you may notice, falling operates by exactly the same principle as tides. Not just by gravity, but by a difference in gravity. Falling does not make sense unless the place that the falling object is going to has a stronger gravitational force than the place that it is coming from.

People who live near the Great Lakes of North America may wonder why, if there are tides in the oceans, there are no real tides in the Great Lakes. The answer is that the lakes are so shallow. The proportion of the distance from the moon to the surface of the lakes in comparision with the distance from the moon to the bottom of the lakes is too slight to produce tides. If the moon were closer to the earth, this proportion would be greater and there could be tides in the Great Lakes.

Remember that the gravity exerted by a body or arrangement of bodies, such as the galactic center, is inversely proportional to either the surface area of the body or the diffuseness of the arrangement of bodies. Thus, the gravitational force exerted on the earth by the galactic center is somewhat spread out, rather than highly concentrated. If the galactic center were to coalesce into one vast body, it's gravity would be concentrated and we could possibly be pulled in as well.

I looked up at night a while ago, and saw the Pleiades. This is the cluster of stars in the northern winter sky that is otherwise known as The Seven Sisters. It got me thinking some more about the nature of gravity and today I would like to describe, in my own terms, how we should look at gravity as a conservative force.

Our sun is a single star, but this is the exception rather than the rule. Most stars exist in pairs, with a certain number in multiple star systems. Many more, such as those making up the Pleiades, are members of closely packed clusters of stars. Such groupings are the result of the conservative nature of gravity.

I find that a fundamental principle of gravity is that it can never work against itself in a given gravitational system. Gravity is, of course, the seeking of the lowest possible energy state in the arrangement of matter in space. We saw in "The Weight Hypothesis", on the physics and astronomy blog, how the manifestation of weight is a result of this movement by gravity to the lowest energy state being blocked by the electron repulsion of matter in contact with other matter.

Put simply, a gravitational mass can never be divided by it's own internal gravitational workings. The mass can redistribute itself while seeking the lowest possible energy state, but the center of mass must remain constant. A given amount of mass has a consistent amount of gravitational pull in the sorrounding space, and the result is the clusters and systems of stars that we see in the sky.

The best illustration of this conservation of gravity is the formation of stars from clouds of dust, gas and, debris in space. If the cloud is relatively uniform in shape and density it will tend to form one large star, rather than multiple stars. But the more unevenness, the more likely multiple stars will form from the cloud. When enough mass is pulled together by gravity so that it's internal gravity, at it's center, can crush smaller atoms together into larger atoms, a star is born.

But the conservation of gravity comes into play when multiple stars form from a cloud of dust and debris that had been bound together by it's internal gravity. The stars which form from such a cloud must remain bound together by gravity. They must exist as a pair, a multiple star system, or a cluster like the Pleiades. The stars which form from a gravitational system, such as the cloud, cannot go their separate ways, barring outside gravitational influence.

Neither can the stars fall together into one mass, if it would shift the original center of mass of the cloud from which the stars formed. Unless outside mass is introduced into the system, or the system is unstable and has a a reason to shed a star to regain stability, the original gravitational configuration must be conserved.

In summary, a star cluster such as the Pleiades must remain gravitationally bound together if the stars formed from a gravitationally bound cloud of dust and debris. The original gravity, and center of mass, must be conserved. This explains not only why stars form pairs, multiples and, clusters, but also why stars are arranged in galaxies and groups of galaxies.

Rotation must also be conserved. If the cloud of dust was undergoing rotation before the stars formed from it, then those stars must also undergo mutual rotation. It is true that contraction of the cloud into a star may bring about faster rotation, and this may throw off some outer mass. But if the mass that is thrown outward was part of the original gravitational mass of the cloud, it cannot be thrown clear of the star's gravitational domain and must continue in rotation around the star.

There are a number of answers online for the basic question of why the orbits of planets around the sun are elliptical, rather than circular. However, I cannot see that anyone has come up with the same explanation that I have and I would like to provide this explanation today. We have seen the cosmology behind elliptical orbits in the posting "Basic Physics And Cosmology, but our explanation today will be the conventional science three-dimensional one and it will not be necessary to delve into the cosmology of outer dimensions here.

The basic question is as follows. It was established long ago, by the German astronomer and mathematician Johannes (pronounced Yo-han) Kepler, that planets orbit the sun in ellipses, rather than circles, with the sun being at one of the two foci of the ellipse. An ellipse is a flattened circle, with two foci rather than one. This is why the earth is closest to the sun in January, and furthest away in June.

The proportional difference between the perihelion, the closest distance from the central body in the orbit, and aphelion, the furthest distance from the central body in the orbit, is referred to as the eccentricity of the orbit. The less eccentric the orbit, the closer is the ellipse to being a circle.

So, here is the question: If the orbits of planets around the sun take the form of an ellipse, then why is this not true of the orbits of the asteroids, in the asteroid belt between Mars and Jupiter, around the sun? Why is it not true of the rings around the planet Saturn or the gradual orbits of stars around the center of the galaxy?

The rings of Saturn are not solid, as they may appear from earth, but are composed of dust and particles of ice. Apparently, the particles composing the rings are close enough to the planet that it's gravity prevents the particles from coalescing into a moon. There is a boundary around Saturn, within which the planet's gravity will prevent such formations of moons so that the ice and dust forms rings around the planet. Jupiter, Uranus and, Neptune also have ring systems, although much fainter than that of Saturn.

Galaxies take a number of common forms but the largest ones, including our own, are spiral in form. There are many photos taken of spiral galaxies, which appear much like ours would if we could see it from outside. In spiral galaxies vast numbers of stars, at various distances from the center, gradually orbit the central hub of the galaxy.

We saw the fundamental rule that a system, bound by gravity, which undergoes gravitational coalescing cannot work against itself as it seeks the lowest energy state. The center of mass must remain constant and the original gravitational configuration must be conserved, barring outside influence.

In the article, "Why Is The Earth Tilted On It's Axis?" which is now a supporting document in the posting "The Story Of Planet Earth" on the geology blog www.markmeekearth.blogspot.com, we saw another example of this conservation of gravity. When the earth's continents moved tectonically northward, it changed the center of mass of the planet. But, according to the rule that the original gravitational configuration must be conserved, the line between the center of the earth and the center of the sun could not be changed by any internal re-configuring of the system.

So, what happened is the earth tilted on it's axis 23 1/2 degrees to accommodate the change in it's center of mass without changing the established line of gravitational axis between the center of the earth and the center of the sun. I cannot see another satisfactory explanation for the tilt of the earth's axis, which gives us the seasons of the year.

If we look at a diagram of the asteroid belt, we get a glimpse into the early Solar System. There was a vast amount of debris that had been thrown out across space by an exploding star, a supernova. Most of this debris coalesced by gravity into another star, a second-generation star, which is the sun. The rest was in orbit around the sun, and gradually coalesced in concentric rings by gravity into the planets. The asteroids remain as they were because the tremendous gravity of Jupiter prevented them from coalescing into a planet in the same way that the gravity of Saturn prevented the particles composing the rings from coalescing into a moon.

When various rocky and metallic debris, similar to the asteroids today, coalesces into a planet by gravity, it does so over a concentric ring zone centered on the sun. The planets, at periodic distances from the sun, are the result of this coalescing. But when this happens, some of the debris is closer to the sun and some is further from the sun. The debris that is further would have a longer orbital period around the sun than that which was closer. This is in accordance with Kepler's Law that a line from the central body to the orbiting body will sweep over equal areas of space in equal periods of time.

But, according to the rule that gravitational relationships must be conserved as long as there is no outside force, new orbits cannot just be created when the coalescing takes place. The debris from further away from the sun cannot just merge their orbits with the debris from closer to the sun, because that would be changing the fundamental gravitational relationship.

Just as the gravitational axis line from the center of the earth to the center of the sun cannot be changed because of an internal re-configuring of the earth's mass with the shifting of the continents, the orbits of debris around the sun cannot be changed by an internal re-configuring with adjacent debris if there is a difference in the nature of their orbits.

The nearer and further debris, which coalesces by gravity to form a planet, cannot merge their orbits together to create a new orbit because that cannot be done by matter whose orbits are dominated by the central body. Both the further orbits and the nearer orbits must be maintained after the debris coalesces into a planet. The only way to accomplish this is, like the earth tilting on it's axis, an elliptical orbit with both aphelion to represent the orbit of the furthest debris and perihelion to represent the orbit of the nearest debris that coalesced to form the planet. Galileo, who said that orbits should be circles, was at least partially correct.