Newton's Law of Gravitation states that two bodies with masses $M$ and $N$ attract each other with a force $$F=G\frac{MN}{r^2},$$ where $r$ is the distance between the bodies and $G$ is the gravitational constant.

Use Newton's Law of Gravitation to compute the work (in J) required to launch a 1000-kg satellite vertically to an orbit 1000 km high. You may assume that Earth's mass is $5.98 \times 10^{24}\, kg$ and is concentrated at its center. Take the radius of the Earth to be $6.37 \times 10^6\, m$ and $G = 6.67 \times 10^{-11}\, N\cdot m^2/kg^2.$

Work done = J