- #1

etotheipi

- Homework Statement
- Explain how to calculate the kinetic energy of a body brought from rest at infinity to some distance x from another massive body by its gravitational field.

- Relevant Equations
- PE = -GMm/r

Usually when setting up an energy equation I use the general form, (Initial KE) + (Initial PE) + (Any other work done to the body) = (Final KE) + (Final PE) ...

For this I said the initial GPE and KE are 0, and the work done by the field is GMm/x (derived by integrating a force of -GMm/r^2 from infinity to x)

, so I end up with the equation:

0 + (Work done) = (Final PE) + (Final KE)

GMm/x = - GMm/x + KE

However this gives me a result of KE = 2GMm/x, whilst other sources I have found state that we can simply equate the work done to the kinetic energy. I was wondering what the correct solution would be? Thank you in advance

For this I said the initial GPE and KE are 0, and the work done by the field is GMm/x (derived by integrating a force of -GMm/r^2 from infinity to x)

, so I end up with the equation:

0 + (Work done) = (Final PE) + (Final KE)

GMm/x = - GMm/x + KE

However this gives me a result of KE = 2GMm/x, whilst other sources I have found state that we can simply equate the work done to the kinetic energy. I was wondering what the correct solution would be? Thank you in advance