Why Is Achieving Orbit Considered Halfway to Anywhere?

[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.

 

[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.