gravitational potentialenergy2

Gravitational potential energy after integration
= -GMm/ r + C

C =constant

We can write this because potential energy is relative, it is only the change in potential energy that matters.

If we take the certain point say r1 to be zero potential,
C = GMm/r1

Then potential energy becomes:
= -GMm/ r + GMm/r1

which look clumsy

If we take r1----> infinity, C--->0

Then potential energy U becomes:
= -GMm/ r with zero potential energy at infinity which looks much more beautiful.

Moreover, we can never take r1 =0, becuase C will ---> infinity.

Then potential energy U becomes:
= -GMm/ r + infinity which looks even more ridiculous


Also, in writing energy equations:

U(x1) + KE(x1) = U(x2 ) + KE(x1)

-GMm/ x1 + C + 1/2 m(v1)^2 = -GMm/ x2 + C + 1/2 m(v2)^2

-GMm/ x1 + 1/2 m(v1)^2 = -GMm/ x2 + 1/2 m(v2)^2

Isn't it more convenient to use -GMm/ r rather than -GMm/ r + C?

Remenber, it is only the CHANGE in potential energy that matters.

To define infinity as place where the (gravitational) potential energy is zero is not only a mathematical interest, but is of physical significance.

Remember that gravity of a mass extends to infinity. That is to say, any point in space is under the influence of gravity produced by that mass. The strength of gravity decreases as distance from the mass increases (the inverse square law). Hence, infinity is the only place where gravity becomes zero, and hence there exists no potential energy. It is because of this physical phenomenon that infinity is taken as place where the potential energy is zero.

Taking the centre of mass of an object as zero potential energy only gives you a relative value for the potential energy for distances away from the centre, but not the absolute potential energy. The potential energy so obtained is the one relative to the potential energy of the object. To obtain the absolute potential energy for these distances, you still need to know precisely the absolute potential energy of the object. This is why a place where the zero absolute potential energy needs to be defined.