Suppose the moon has a radius of *R* miles and a payload weighs *P* pounds at the surface of the moon (at a distance of *R* miles from the center of the moon). When the payload is *x* miles from the center of the moon (*x* ≥ *R*), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation:

required force = *f*(*x*) = *R*^{2}*P*

*x*^{2}

*pounds*

For example, the amount of work done raising the payload from the surface of the moon (i.e., *x* = *R*) to an altitude of *R* miles above the surface of the moon (i.e., *x* = 2*R*) is

work = *b*

*f*(*x*) *dxa*

= 2*R*

*R*^{2}*P*

*x*^{2}

*dxR*

= *RP*

2

mile-pounds

How much work would be needed to raise the payload from the surface of the moon (i.e., *x* = *R*) to the "end of the universe"?

work = mile-pounds

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- Thank you very much!
- zby1998221
- May 15, 2018 at 11:42pm