Thank you.
If you are pushing the mass through a gravitational field at a constant speed, you
will be adding kinetic energy to it. After all, if you pushed it once, and then let it move, it would slow down.
BD: Actually, as I said if you are pushing it at a constant speed, there is no change in KE.
The equation you have just quoted describes the gravitational
force. This will tell you how the masses will accelerate. What you're looking for is gravitational
potential, which isn't the same thing. To get potential from force, calculus can be used. (Specifically, integrating GMmr^-2dr.) The result is that the gravitational potential is actually
-GMm/r. As you can see, that equation includes a negative sign, hence negative gravitational potential.
BD: Of course -you're right. The PE (grav.) = mgh - directly proportional to the distance of separation. So the PE = 0 when touching and increases as you get further apart. Correspondlingly, the work needed to separate them = Fd.
But remember that they
gain energy when they fall together. Two pieces of matter closer together will collide sooner then if they were further apart, and so can "fall" for less time, and so gain less energy. That is why potential energy increases with distance.
BD: Actually, the energy changes form. Energy cannot be created/destroyed. Agreed about PE increasing w/ distance.
The third law of thermodynamics tells us that the energy content of a closed system is constant, and that the temperature is not zero. This is not quite the same as "Energy is not 0," since there are some mechanics that generate negative energy.
BD: It says that we cannot reach absolute zero (0 K). Name a mechanic that generates "negative energy." I'm not disputing you, but the issue is that the total E does not change. And the third law of thermodynamics states that "the entropy of a system at absolute zero is a well-defined constant." [and not "0"] Entropy is energy related to disorder of disorder.
There are many solutions in Relativity that allow for zero total energy, even with non-flat spacetime and non-empty universes.
BD: Can you give an example? Thx.
In quantum mechanics, uncaused causes are commonplace.
BD: ?? Example?
Actually, the Big Bang does not require an uncaused cause at all. It does this by saying that there is a
first moment of time, at which point the universe
already existed. Talking about what came before the first moment in time is nonsensical.