A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket…

Q: A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the gravitational influence of earth? Mass of the satellite is 200 Kg, Mass of earth = 6.0 × 10^24 kg,radius of earth = 6.4 × 106 m, G = 6.67 × 10-11 Nm2 kg-2.

Sol: Total energy of orbiting satellite at a height h is

$\large = – \frac{G M m}{2(R + h)}$

Energy expended to rocket the satellite out of the earth’s gravitational field. = – (Total energy of the satellite)

$\large = \frac{G M m}{2(R + h)}$

$\large = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24}\times 200}{2(6.4 \times 10^6 + 4 \times 10^5)}$

= 58.85 × 108 J