Can Gravity Create a Perpetual Motion System in Planetary Orbits?

[neurotic]

A friend and myself were having a conversation today just about the nature of planets in motion and orbits

(Originally we were talking about getting a rocket to Mars but I digress)

The Earth and sun, assuming no other bodies were in the solar system and the system was as it is now - Earth orbiting around the sun.

Assuming space was a perfect vacuum and the Earth never came into contact with any other particles in space (including the solar wind etc), the Earth would continue to orbit the sun...indefinately??

The sun obviously exerts a force on the Earth via gravity, which changes the Earth's velocity (though not its speed component).

If this force is constant and never ending, doesn't this represent a perpetual motion system? Or is this simply a system at equilibrium?

This led us to the question of gravity. How does gravity work in terms of force and conservation of energy? It seems that gravity is able to constantly change the velocity of a body in motion. We can't reconcile how this works...

Can someone please clarify this??

 

[FunkyDwarf]

Well that's a slightly oversimplified senario, as the Earth would cause the sun to wobble a bit and both would rotate about the centre of mass, but given the size of the Earth its more or less irrelevant (though with Jupiter its not).

Gravity is a conservative force like EM. If you do work to move a particle a certain distance away from a gravity well the same amount of work will be done moving it back to that position.

Energy is conserved because all the energy in that system is all the energy out. The energy in the gravity field is due to the mass of the sun. The Earth will not 'fall in' because angular momentum in conserved. In order for any particle to fall into a point mass generating a gravity well it must lose all angular velocity and thus momentum, otherwise it will just orbit. That is if you fired a rocket intent on hitting the sun (assuming the sun a point mass for the time being) you would have to fire it in such a way as to remove all of the Earth's influence on its velocity relative to the sun, ie fire it backwards.

When you come to questions like this its hard to think of the Earth on a string being swung around by the sun because when you get to the nitty gritty gravity doesn't behave like that. Mass tells space how to curve and space tells matter how to move, which is this force of gravity we experience.

Now i realize this is possibly the worst and most unrelated answer in the history of crap and unrelated answers, in a nut shell; yes its in equilibrium, just as if the Earth were on a string being swung by the sun. The centripetal force in this case is going into changing the direction of motion, not the magnitude. The energy for that force is the string, or the tension or bonds holding it together or whatever you like.

Hope this helps (and is right)

 

[neurotic]

Whats a conservative force?

Also the other question we came up with was since there IS matter in space (gas, dust, solar wind etc) is the magnitude of the Earth's velocity being affected over time such that we will eventually slow down and the suns gravity will draw the Earth into it?

 

[LURCH]

This might also help a little. The current model of gravity (General Relativity) pictures it as a curvature of space. This can be imagined by taking a piece of lined paper and bending it. On the 2-dimensional surface, the lines are all still straight, they travel parallel to one another and don't get closer together or farther apart. If you were a flat, 2-dimensional character living on that surface, and you wlkaed along one of the lines, you would be going straight; according to all the senses you have. If the paper is curved, you can't see that curvature, because you are just as curved. But, to an outside observer (not living on the surface of the paper), the lines appear curved.

That's a 2-dimensional surface curved in a third direction. G.R. views gravity as a 3-dimensional surface (space) being curved in a fourth direction. Now don't fret if you can't see that in your head, 'cause nobody can. But it does describe quite nicely how objects appear to change course in a gravitational field without losing momentum. So, neglecting all other minor factors (like the rotation of the wto bodies on their axes), a planet orbitting a star is traveling a straight line (in terms of our 3-dimensional reality) through a curved space. An object traveling a straight line at a constant speed is the same hing as an object sitting still, and that's why it doesn't lose momentum and coast to a stop. It is already "stopped"!

Now the bit about gas and dust and stuff, I'll have to scrounge around to verify this answer, but reason would seem to indicate that we would not experience frictional drag from these btis of matter. These particles would have to be in our vecinity in order to hit us. That puts them at the same distance from the sun as we are, which means the same rules of motion that apply to the Earth apply to them as well. So, they are in orbit too. everything in this area of space is sort-of moving along with us. If a dust particle's orbit perfectly matches ours, it would never hit us. If their orbit does not perfectly match ours, then something moved them (since our orbit is the closest thing to "sitting still" that you can get in our local space). The direction and speed of their impact with us would be dependent on what set of conditions caused their orbit to differ from ours. Like, are they coming out from closer into the sun, or falling in from farther out? Or were they in an orbit identical to ours when the passage of some outside object disturbed that orbit.

Since these conditions could result in motion in any direction, local space is filled with particles moving in all directions and at all sorts of different speeds. The chances of something hitting us from the "front" or from "behind" are about equall, so we get collisions that slow us down in our orbit, and others that push us faster. The net result should be zero.

 

[chronon]

Assuming space was a perfect vacuum and the Earth never came into contact with any other particles in space (including the solar wind etc), the Earth would continue to orbit the sun...indefinately??

General relativity says that the system will emit gravitational waves and so the Earth will gradually spiral into the sun, but I wouldn't expect it to happen any time soon. Its much quicker for Binary Pulsars

 

[tony873004]

General relativity says that the system will emit gravitational waves and so the Earth will gradually spiral into the sun, but I wouldn't expect it to happen any time soon. Its much quicker for Binary Pulsars

Wouldn't there need to be distant objects being perturbed by these gravity waves for Earth to spiral in? If Earth and Sun were the only objects, would Earth still spiral?

 

[russ_watters]

If this force is constant and never ending, doesn't this represent a perpetual motion system? Or is this simply a system at equilibrium?

First of all, it is important to understand what "perpetual motion" means. If you just take it to literally mean "unending motion", it most certainly exists in the universe as a direct consequence of Newton's first law. The motion of planets is an example of that. http://csep10.phys.utk.edu/astr161/lect/history/Newton3laws.html

However, when people talk about perpetual motion breaking the laws of physics, what they are talking about is actually just anything that violates the laws of thermodynamics. As such, there are two types of perpetual motion machines:

-Type 1 perpetual motion machines violate conservation of energy. Ie, energy is created.

-Type 2 perpetual motion machines violate the law of entropy, converting thermal energy to other types of energy without loss.

http://en.wikipedia.org/wiki/Perpetual_motion
http://www.emc.maricopa.edu/faculty/farabee/biobk/BioBookEner1.html

This led us to the question of gravity. How does gravity work in terms of force and conservation of energy? It seems that gravity is able to constantly change the velocity of a body in motion. We can't reconcile how this works...

Well, it is important to understand that force and energy are not the same thing. Look at the units. So there is nothing that says that a force has to require consumption of energy.