Expert: Paul Klarreich - 2/20/2006

Question
A 5-ton rocket is fired from the surface of the earth into outer-space.
a)How much work is required to overcome the earth's graviatational force?
b)How far has the rocket traveled when half the total work has ocurred?

I'm thinking the force equation for this one is

F(x)=C/x^2, which would produce
5=C/(4000)^2, C=80000000, so the value for work (if I'm right, of course) would be given by the integral of 80000000/x^2, but I do not know from where to where.  When does an object overcome the earth's graviational force?

Answer
Hi, Jose,

It has been too long (try 48 years) since I took physics, but it seems to me that you would integrate:

{r=infinity
|             F(r) dr
}r=4000 miles

The object overcomes earth's gravity when the gravity becomes zero, which occurs when r = infinity.  

(Those satellites stay up because they are in orbit, not stationary.  If they were stationary, then they would eventually fall.)

This integral converges, so all you have to do is get the units and forces correct.