Calculate the force of Earth's gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth's surface if its mass is 1250 kg .

Answer 1

Gravitational force F_g = GMm/r² where M is mass of Earth in this case (5.98 x 10²⁴ kg), m is mass of the satellite, and r is distance from Earth's center to the satellite. So r = R_E + 2R_E = 3 (6.40 x 10³ km) = 19.2 x 10⁶ m, and F_g = (6.673 x 10^-11) (5.98 x 10²⁴) (1.25 x 10³) / (1.92 x 10⁷)² = 1,350 N.

For comparison, the weight of the satellite back on Earth was mg = 12,300 N, 9 times greater because it was 3 times closer to Earth's center.