Question

2. Gravitation A 1,000 kg satellite orbits Earth at a constant altitude of 100 km. How much energy must be added to the system in order to move the satellite into a circular orbit with a radius of 10,000 km? G 6.67 x 10-11 Nm2kg2, radius of Earth: 6.37 x 10 m, Mass of Earth: 5.98 x 104kg.

Answer 1

(a) E_t0 + as = -G M m/2r delta E = G M m/2(1/r + h_i - 1/r + h_f) implies delta E = 6.67 times 10^-11 times 5.98 times 10^24 times 1000/2(1/(6.37 times 10^6 + 100 times 10^3 - 1/(8.37 times 10^3 + 106 7) implies delta E = 6.67 times 106-11 times 5.98 times 10^24 times 1000 times 9.397 times 10^-8 implies delta E = 1.864 times 10^10 J implies delta E = 186 times 10^8 j implies delta E = 186.414 M J