The energies of a satellite

A $750\ \text{kg}$ satellite can be put in a circular orbit at any height. You will make the program draw its kinetic, potential and total energies against the height, find the energy it takes to raise it from $300\ \text{km}$ to $3000\ \text{km}$, and find its speed in every orbit.

The idea. In a circular orbit of radius $r$: $K = \dfrac{GMm}{2r}$, $U = -\dfrac{GMm}{r} = -2K$, and $E = K + U = -K$. Raising it costs the rise in $E$, and its speed comes from $K = \tfrac12 mv^2$.

Your tasks.

1. Work out K, U and E for every height in h.
2. Find the energy needed to raise the satellite from $300\ \text{km}$ to $3000\ \text{km}$.
3. Work out the speed v in every orbit, from K.