Gravity and energy.

[alpha2cen]

Gravity is a force.

Let's think about this case.

When an object move from low gravity planet to very high gravity planet.

It's mass is same on two planets.

But their energy is very different. The object's energy of the high gravity planet is very high.

How can we explain this phenomena with the energy conservation law?

Edited December 29, 2010 by alpha2cen

[D H]

Gravity is a force.

Let's think about this case.

When an object go form low gravity planet to very high gravity planet.

For example, from the surface of the Moon to the surface of the Earth? I'm trying to clarify what you mean here. If your native language is not English, I understand the difficulty in expressing yourself in a foreign language. On the other hand, if your native is English, you very much need to practice and improve your writing skills.

 

 

But their energy is very different. The object's energy of the high gravity planet is very high.

How can we explain this phenomena with the energy conservation law?

Are you talking about gravitational potential energy? You need to be specific, as there are several forms of energy. What exactly do you see as the problem here?

 

 

[alpha2cen]

I mean initial energy << final energy state

There is no energy input to be that state.

And system energy is increased.

[D H]

You appear to be thinking that gravitational potential energy increases with proximity to a planet. It doesn't. First off, potential energy, in any form, involves an arbitrary constant. Two typical choices for this constant regarding gravitational potential energy are:

 

1. Arbitrarily set the potential at the surface of the planet to zero. With simplifications, this leads to the PE=mgh relation used in elementary physics.
2. Arbitrarily set the potential at infinity to zero. With simplifying assumptions, this leads to the PE=-GMm/r relation used in slightly more advanced physics.

Let's look at the former convention, PE=mgh. This is an approximation that is only valid when the height h is much, much smaller than the planet's radius. Note that potential energy decreases as the height above the planet decreases. Suppose you release an object with zero initial velocity at some height h₀ above the ground. If it weren't for air friction, the object would gain speed as it falls per conservation of energy, ½mv²+mgh=mgh₀. This means the velocity of this object is given by v²=2g(h₀-h). This is exactly the same result that obtains from assuming a constant gravitational force of mg directed downward.

 

Now let's use the latter convention, PE=-GMm/r. This assumes the planet has a spherical mass distribution (i.e., density is a function of distance from the center). Note that once again potential energy decreases as the distance to the planet decreases. Suppose you release an object with zero initial velocity at distance r₀ from the center of the planet. If it weren't for air friction, the object would gain speed as it falls per conservation of energy, ½mv²-GMm/r=-GMm/r₀. This means the velocity of this object is given by v²=2GM(1/r-1/r₀). This is exactly the same result that obtains from assuming a gravitational force of GMm/r² directed toward the center of the planet.

[alpha2cen]

Think about this example.

There is a stone on the surface of the asteroid.

We move it to near Black hole.

Which one is the high energy state between the stone on the asteroid and near the Black hole?

The stone near the Black hole is able to make a fusion reaction without adding more energy.

[D H]

You are uttering nonsense.