Originally Posted By: Bill S.
Consider a rock lying on the ground. If you pick up that rock, then let go of it, it will fall back to the ground. Your action in picking it up has involved a transfer of energy: some energy from your muscles has been converted into gravitational potential energy as you raise the rock. If, when you have lifted the rock, you place it on a shelf, and let go of it, it will not fall, but it will still have the energy you transferred to it, still in the form of potential energy. Obviously, if it is pushed off the shelf it will fall back to the ground. The argument here is that the energy you put into the rock as you lift it equals the energy that would be necessary for gravity to bring it back to the Earth’s surface, so there is no net expenditure of energy. Could this explain how gravity seems to work without any apparent energy source? A little thought about this situation must raise some doubts. For example, if the attraction of gravity is directly related to the amount of energy put into the rock you are lifting, why does gravitational attraction not increase with distance, as would be the case if you were stretching a spring? If, having picked up the rock you altered your position so that you were holding your rock over an open well. When you released the rock it would fall to the bottom of the well, in spite of the fact that you transferred to it only enough energy to take it as far as the ground surface. Finally, we would have to wonder why a spacecraft that travelled from Earth to the moon would be attracted by the moon’s gravity. Not only would it not have been lifted from the surface of the moon, but it should have enough potential energy to whisk it straight back to Earth as soon as it stops moving away.


So, let's talk about potential energy. The first thing to remember about potential energy is that it is relative. The potential energy that anything contains is relative to the lowest energy level it can move to. So if you pick up the rock from the ground its potential energy is relative to ground level. But if you move it over a well its potential energy is relative to the bottom of the well. The difference is strictly due to the fact that over the well it can fall longer and achieve a greater speed before it hits bottom. The potential energy an object contains is the amount of kinetic energy that it can gain by falling to the ground or other surface below it. The kinetic energy it can gain by falling a few feet to the ground is much less than the kinetic energy it can gain by falling many feet to the bottom of a well.

Now let's talk about how the attraction of gravity falls off with distance.

F = G*M1*m2/r^2

That one should be familiar to you. Newton's law of gravitation. Notice that the force between 2 bodies is inversely proportional to the distance between them. This is known as the inverse square law. That distance is actually the distance between their centers. Let's look at why that is.

I'm not going to find a diagram and insert it here, I will let you make your own. First draw a circle. Now draw a bunch of straight lines through the center of the circle at 15 degree increments. There is nothing magic about the increment size, I just chose 15 degrees because it means the circle will be evenly divided by the lines. Let the ends of the lines all stick out a long way beyond the circle. Now let's pretend that the lines represent the gravitational field from a body. This is a standard representation of field lines around any kind of source. Now draw another circle around the first one, but twice as far out. Notice that the field lines are much more widely separated where they pass through the second circle. If you imagine the circles to be spheres and the field lines drawn at 15 degrees intervals in all 3 dimensions you will see that the area between field lines varies with the square of the radius. Well, gravity works just the same way. Close to the center of a body the gravitational attraction of a body is much greater than it is farther away from the body. That is why gravitational attraction doesn't act like a spring. It works the same way as electromagnetic radiation (light). If you look at a light source up close it is very bright, but as you move away it begins to be dimmer and dimmer. It is also obeying the inverse square law.

Now you may say, but I don't see any difference in gravity between different heights. I better mention that. Let's assume that there is a enormously large planet, say a million km in radius. Never mind that such a planet couldn't exist, this is just a thought experiment. Now if you start drawing your lines through the center of the planet you will find that 15 degree separation means that you can't even see one line when you are standing by another one. So you keep on drawing more lines until you finally get a whole bunch of them in your field of view. Well, the angle between those lines is going to be extremely small. In fact it would take some very fine measurements to find out that there was an angle between them. And the force produced by those almost parallel lines would chage very slowly with altitude. Guess what! The Earth is large enough that the angle between force line is almost undetectable. However, it can be measured, particularly from a space craft. So at great altitudes the force of gravity from the Earth is smaller.

Of course the Moons gravity works the same way, so its gravitational attraction is greater than the Earths gravitational attraction when a spacecraft get closer to it than it is to the Earth. There is a point between the Earth and the Moon (on a line between their centers) where the gravitational attraction is equal from both of them. So before that point a spacecraft would tend to fall to Earth and beyound it would tend to fall to Moon. Of course it doesn't actually "fall". The thing is that spacecraft don't travel in straight lines. They always travel in orbits. The orbits may not be closed orbits, but they are orbits, so that they have enough sideways speed to keep from falling directly to the ground.

Bill Gill

C is not the speed of light in a vacuum.
C is the universal speed limit.