# Energy required to move an object to an altitude twice the radius of Earth

• aero_zeppelin
In summary, the question is asking for the amount of energy needed to move a 1 000-kg object from the surface of Earth to an altitude twice the radius of Earth. The formula for potential energy is used to calculate this, taking into account the difference in potential energy between the two distances. The correct answer is found by considering the altitude to be three times the radius, not two times.

## Homework Statement

How much energy is required to move a 1 000-kg object
from the Earth’s surface to an altitude twice the Earth’s

U = - G Me m / r

## The Attempt at a Solution

I'm just using the above equation with 2r (twice the radius) and get 3.1 x 10e10 J, but the book says different...

Any help?? Thanks!

Plugging in a certain radius just tells you the potential energy an object has at that distance from the center. The question is asking you how much energy it takes to move from 1 radius (the surface) to another radius. So you need to find a difference in potential energy.

In this case, you need to find the potential energy difference between the mass at the surface and at that 2r altitude. This must be the energy required to bring it from the surface to the high up distance.

actually, I think I figured it out. The problem is somewhat bad worded and I believe it can confuse people. It says an ALTITUDE twice the radius of Earth, which means two times that distance ONCE the object has left the Earth, so actually it would be 3r... right?

I guess it's right, I got the correct answer ;) thanks for the help!