Hello StarkMate

Welcome to Math Help Forum! Originally Posted by

**StarkMate** Granddad, could you please elaborate on dot points 3 and 4? I get the integral of F to be (-2km)/x^3 but what am I to do with the mass??? please help

I think you've differentiated.$\displaystyle \int -\frac{km}{x^2}\; dx = -\frac{kmx^{-1}}{(-1)}$

$\displaystyle =\frac{km}{x}$

Now you need to evaluate this integral between the limits $\displaystyle x_0$ and $\displaystyle x_1$ (where $\displaystyle x_0 = (6370+6220)\times 10^3$ and $\displaystyle x_1 = 383000\times 10^3$).

This, when you've worked out the value of $\displaystyle k$, gives an expression in terms of $\displaystyle m$, which is equal to the loss of KE of the spacecraft. This will be equal to $\displaystyle \tfrac12mv^2$, where $\displaystyle v$ is the velocity required. The $\displaystyle m$'s then cancel, leaving an expression for $\displaystyle v$.

Grandad