system
Given the following post, respond as if you're commenting on Reddit:
human
How does the concept of potential energy apply once you've escaped Earth's gravity?

The idea of potential energy seems pretty simple in a "high school physics" sense: if you lift a rock 1000 meters, then drop it, it will accelerate with the same amount of energy you put into lifting it against gravity in the first place (minus energy lost to friction, air resistance, etc., of course.) I assume this works the same way when you put something into orbit around Earth, that it has the same potential to fall back to Earth, minus the same factors. That's all well and good.

Now say that we send a probe to Jupiter. Eventually, the probe reaches a point very close to Jupiter, where Jupiter's gravity is influencing it far more than the Earth's gravity is. The probe accelerates towards Jupiter, converting potential energy into kinetic energy, and due to the greater mass/gravitational force, speeds up far more energy. Obviously, this has nothing to do with the "potential energy built up with respect to Earth," that is, the energy used to overcome the Earth's gravity. Our theoretical probe could also be attracted to a billion different stars depending on it's position, each of them accelerating it according to both of their masses and the gravitational force between them, but completely independent of whatever energy it used to escape Earth's gravity, or Jupiter's gravity, or whatever.

So, taking this to the extreme, does it mean that every bit of matter has potential energy due to its potential to be attracted to, and therefore accelerate towards, every other piece of matter in the universe? Sitting at my computer on Earth, do I have a massive amount of potential energy because, if I were launched out into space, I could accelerate towards whichever of the billions of stars exerted the greatest gravitational force on me, depending on my location at that moment? And to extrapolate even further, would most of this potential energy have been imparted to mass at the moment of the Big Bang, when everything moved away from each other and therefore developed the potential to accelerate due to gravity back towards itself?

So, what part of the concept am I missing?
gpt
Potential energy is written a bit differently when you're talking about outer space rather than small displacements within Earth's gravity well (which is what your question is based on). The first thing is that **the sign of gravitational potential energy is negative**. Right now you have negative gravitational potential energy because it would require a lot of energy to get you off of Earth and into space.

The GPE equation is:

**E*_grav_* = - G M m / r**

G is the gravitational constant, M is the mass you're being attracted to, m is your mass, and r is your distance from the center of that mass. 

An object in very deep space, outside galaxies and such, has a gravitational potential energy which is small in magnitude. Of course, the whole universe is subject to gravitational fields, so nothing has *zero* gravitational potential energy. But the GPE of a particle on the surface of a neutron star is far more negative (larger in magnitude) than that of a particle on Earth's surface, which in turn is more negative than that of a particle in transit between Earth and Jupiter.