Answer
$W=1.39\times10^{11}J$
Work Step by Step
1) Find the speed of the satellite at 2 orbits:
Recall the equation to calculate the speed of a satellite orbiting the earth in an orbit with radius $r$: $$v=\sqrt{\frac{GM_E}{r}}$$
$G=6.67\times10^{-11}Nm^2/kg^2$, mass of earth $M_E=5.97\times10^{24}kg$. Orbit 1 has radius $r_1=3.3\times10^7m$ and orbit 2 has $r_2=7\times10^6m$
- Speed of the satellite in orbit 1: $$v_1=\sqrt{\frac{GM_E}{r_1}}=3478.5m/s$$
- Speed of the satellite in orbit 2: $$v_2=\sqrt{\frac{GM_E}{r_2}}=7543.2m/s$$
2) According to the work-energy theorem, $$W=\frac{1}{2}m(v_2^2-v_1^2)$$
The mass of the satellite is $m=6200kg$. The work the external force must do is $$W=1.39\times10^{11}J$$
