Planets

Yes, so for the record, I agree with Timber and he is saying the same thing that I did.

I agree with Timber also.

The part of his statement which I have been addressing is this:



I believe there are several elements to the answer of the original question. One of the elements is "why are spheres the most energy efficient gravimetric shape instead of cubes or pyramids or anything else", and the core answer is a conservation law related to mechanical energy. Thus my answer.

Please, Ross, please stop playing the fool.

If a planet were in a cube shape, there would be more particles at the corners of the cube which would create more inward force at the corners which would squish the corners out until there were no corners. Take away all the corners and you are left with a sphere.

This is because of the gravitational force and the way that forces add together and move particles only; that is, newton's laws 1-3 + newtons law of gravity, like I keep telling you.

Is it not that all these answers are correct? It is just that people look at it from different angles?
For instance, the motion of a projected body can be look at through Newtons laws, the equations of motion or using energy equations; they are different but nevertheless all equally correct?

Yeah, I suppose you can think of it in terms of energy...although it is not so straightforward this way.

In terms of energy, you could say that any corners on the surface would have a greater distance from the center and therefore have greater gravitational potential energy. This will be converted into kinetic energy in order to reach a lower energy level. In terms of energy we do not have individual directions that the particles will move, but we can observe that if the shape were spherical then there would be homogeneous potential energy across the entire surface area, so that would be the global energy minimum. It is more difficult to prove that there are no local minimums that would be reached first, but I think it is logically obvious.

In order for our energy explanation to work, we must assume conservation of energy. This does not mean that conservation of energy has anything to do with the problem. It just means that we cannot use this method in a situation where we lack conservation of energy.

However, as we have already proven by considering the problem in terms of forces, we can find ways to break conservation of energy that still yield the same spherical solution. Conservation of energy is not the reason that they become spherical, although if we consider a universe without conservation of energy, it is possible to think of ways to break the solution...but that is like saying "the reason the Earth is round is because pink elephants in space are not sitting on it."

Yeah, it's true that if there were giant pink elephants in space squishing the Earth it would not be round, but that has nothing to do with the reason why it would be round in the first place.