Why was infinity chosen as the place of zero GPE and why does this make the GPE value always negative?

Answer 1

Look at the definition of GPE

U = -GMm/r²

G, M, and m never change, they are all constants.

r, which measures the distance between the two masses, can change. So, where will zero occur??? Intuitively, the further away you move from an object, the less you feel it's gravitational force acting on you. We don't feel the effects of Mars too often, do we??

The same works with potential energy. The further you go from the object, the less work you have to do to move even further away. So, what's the furthest away you can from an object? Theoretically, it's infinity.

Your second question is a little off. Infinity is chosen as the place of zero GPE, so it makes the GPE zero at that location. You probably meant why is GPE always less than zero at some point other than infinity?

Again, it's from the definition of potential energy. There's a little negative sign sticking out in front. Think of it this way... if we wanted to get away from earth, we'd have to put work into the system. However, gravity is always trying to suck us back in, so the more work we put into the system, the more work gravity takes out. Since it's counteracting our work, it's negative.

Hope this helps.

Answer 2

Here's a counterexample to that thought. Suppose we take the entire confident integers (a million,two,three,four,five,6...), of which there are a vast quantity. Now, allow's take out the entire even numbers, there is a vast quantity of the ones too. We have thus taken a vast quantity of matters clear of a vast quantity of matters, and what are we left with? All the abnormal numbers, and bet what number of of the ones there are? So, infinity minus infinity is same to infinity. But you do not simply get infinity. Instead of eliminating the entire abnormal numbers, you would do away with the entire integers higher than 10, and once more, there is a vast quantity of the ones. Then, you would be left with 10 precise numbers after eliminating a vast quantity, so infinity minus infinity may be same to ten (or some other arbitrary quantity). Finally, what if we took away the entire confident integers higher than zero (i.e. they all) Then we are left with zero numbers, so infinity minus infinity may be same to zero. That's what it approach once we say infinity is a idea, now not a certain quantity. Operations with infinity, like subtraction, are easily now not outlined in average math. It's like dividing by way of zero; you easily can not do it in any significant manner.

Answer 3

Because it is the only place that can have a definite value. Elsewhere, it would depend on the distribution of masses in the area. The energy is negative because energy is released when a test mass falls toward a gravitational attractor; this must be balanced by a negative change in PE to conserve energy.

Answer 4

infinity was chosen as place of zero potential energy
because at infinity no force acts on the body

it is just a convention,because we can not measure absolute potential energy,we can just measure change in potential energy