I asked a question on reddit.com and I am pasting it here. Question of gravity

Assume a simpler universe – a planet orbiting in a perfectly circular orbit around its stationary star. We know that if they were travelling in straight parallel lines with constant velocities, they don’t need to spend any energy for that ever. But circular motion involves acceleration, force, angular acceleration, moment of inertia, force, torque, energy, etc. If one looks at the system from outside the system, apparently no energy is going outside the system even in the circular motion case. But when I enter the system and start looking how much mechanical work is happening, where the energy is needed, which object among two is supplying how much energy, energy is getting transferred from where to where, how the energy is conserved, I get nonplussed. Will these objects remain rotating like this eternally if no disturbance is there? What about the entropy stuff, it keeps on rising as more and more work is done, right? So when will it play role in deciding how the system is looking if at all? Once this is done, there is a jumbo confusion in my mind. Suppose I use gravity to do a mechanical work, say, to fell a stone from space on a planet. After the fall, everything is same (mass, etc) as the old system. Then, what was spent to do that work? Like limited fuel means limited energy. But can a fixed mass of planet (and a fixed gravitational energy associated with it) be used to infinite work? Fell infinite number of stone? Is anything spent at all? Isn’t this going against the principle of conservation of energy?

The question was not conveyed well to the people who wanted to answer. Hence I explained it further.

That being said, I’m not sure what your question is.

Friend, yes that is true. But it is not your problem. I agree there is an issue with my language, the way I have presented the question and the flow of what is written.

No work is required to keep the two bodies orbiting each other in space.

Yes. I know this. But I know this as a fact. I don’t know how this is so or why this is so. That is the question. We are not talking of how satellites reach tidal locking, etc. That is digression. We are talking of a theoritical experiment in an ideal and perfect world. So let’s not bring in worldly imperfections.

That is why I started with linear motion. Had this star and the planet gone in straight lines, parallel/etc to each other and had they no mass/gravity, no question of force/energy arises as Newton’s first law makes that amply clear.

But in case of perfectly circular motion, it is little dificult for a confused person like me to understand how forces are working and how energy is conserved. So we are not talking about the observation and beyond, but before it.

Also what I am asking is not anything new or complex or serious or sort. It must be very rudimentary, simple and fundamental. The question is to put it in a right way so that it is logically understood.

Here goes the problem statement:

Now let me tell how I think and where I get nonplussed. Take an initial position where there is a stationary star and a STATIONARY planet at some distance from it. None is rotating around itself or around any other. There is no mass/gravity in them to even to have any linear motion. Following things happen instantaneously; 1. There is mass in them 2. (assume that) gravity propagates instantaneously 3. A tangential (to orbit) force corresponding to that perfect circular orbit ( I don’t think any force would do.) on the planet acts (I think from somewhere outside) and it sets in circular motion.

Here are observations:

What all happens then? 1. So far as I understand, the star is still stationary and doesn’t rotate around its axis, etc after this. 2. The gravitational force is cancelled by the centrifugal force of the circular motion of the planet hence there is no linear motion (I am confused about why the centrifugal force stuff arises out of nothing. Even in a simple example where I rotate a key with its chain in my fingers, upon stabilization and when I stop providing my energy, the kinetic energy of keys provides tangential force and there is nothing to provide centrifugal force, rather the rigid finger provides inward pull, but still the keys don’t suddenly fall down. They go on for a couple of rounds more. I know that moment of inertia is conserved, etc. But note that it is just different terminology for a specific type of motion and there are no separate laws used. So this is an attempt to understand angular acceleration, moment of inertia as they are based on laws of linear motion and their derivation can’t be very easily visualized. If irrelevant, this whole centrifugal stuff might be called digression and can be parked aside. Let it be your call.) 3. Some net external unbalanced force keeps on changing the direction of motion of the planet. So some net force is acting on it. So mechanical work is being done.

The confusion:

1. The star is still as it is without ANY change in it. It needn’t rotate, etc. So who/what is doing this mechanical work? BASICALLY HOW CAN THE STAR DO SUCH WONDER WITHOUT GETTING AFFECTED AT ALL? 2. I initially kicked the planet into circular motion by giving it energy from outside, but that is in the form of 1/2Iw^{2} or the kinetic energy of the planet. 2. Even if it is said that THIS energy was used to do the work said above, it won’t suffice for any longer period. 3. If work is being done continuously on the planet, thermodyamics comes into play. If work is being done, isn’t there continuous shifting of energy from one point to another? Newton spoke of linear motion. But if this is continuous circular motion, forces are acting, energy is flowing!!! From where to where?? What is the end result? Why the temperature of on the object on which forces are acting won’t rise? Why won’t the entropy rise? Isn’t the nature of gravity misterious in the sense that it keeps on doing work eternally?

The question asked in the planet and stone case is entirely different. It might have very less to do with this question. I thought, they can be answered in a single shot.

Now here is the second part. Assume a stationary planet and a stone at some distance in space in a simple, idealistic and perfect case. The stone would fall on the surface on the planet. Consider the WORK DONE FROM THE MOMENT THE STONE IS THERE AND TILL IT FALLS ON THE PLANET. Suppose, I one after another I keep on putting a stone there, all of them will fall. This work will be done by the gravity of the planet (and the stone). Now you can’t say that the work done or the energy supplied is only of the stone. The force is F= gMm^2/r^2 and energy is E=F*distance. I can’t say either only the planet is giving the energy or only the stone is giving the energy. There must be sharing of this contribution (may be in propotional of mass, but keep it aside for now). Now if keep on supplying a new stone at that point one after another near infinitely (using my own near infinite outside resource), always a fraction of planet’s energy is used. But shouldn’t the planet’s gravitational energy be limited??? How can it pull as many stones? Let’s not get confused with effect of mass of newly accumulated stones. Let’s make a case where the stones are radioactive and vanish into anything other than mass after they fall.

The existence of gravitation force depends upon two independent masses, and existence of two masses is a necessary condition for it to exist. Even if it starts to exists, it acts on the two masses involved. Thus how do we break up the contributions?

Let’s later see the confusions regarding electric, magnetic, weak and strong nuclear.