# Help with gravitational fields

1. Dec 7, 2008

### dswatson

The science fiction writer Robert Heinlein once said, "If you can get into orbit, then you're halfway to anywhere". Justify this statement by comparing the minimum energy needed to place a satellite into low Earth orbit (h=400km) to that needed to set it completely free from the bonds of Earth's gravity. Neglect any effects due to air resistance.

E = KE + U
E = 1/2mv^2 + U
U = -(int)[F*dr]
U = -G(Mm/r^2)
E = m( (1/2)v^2 - G(M/r^2)

m = mass satellite
M = mass earth

Im stuck because I am not given a mass for the satellite and I know that excape velocity does not depend on mass. It is approxmately 7mi/s but I am unsure of how to show that energy is not mass dependent and then solving for the equation with no mass.

2. Dec 7, 2008

### Irid

Well, first of all, the total energy is

$$E = m\left( \frac{v^2}{2} - \frac{GM}{r}\right)$$

(you got the power wrong). It depends on m, but if you set it equal to zero E=0, then m cancels and you can solve for v without knowing m.