Question

Calculate the force of gravity on a spacecraft 12800 km (2 earth radii) above the earth's surface if its mass is 1600 kg. n (toward the earth)

Answer 1

Since the spacecraft is two earth radii the surface of the earth, it is three earth radii above the center.

Given: Radius of the earth re = 6.38 x 10⁶ m  r = 1.91 x 10⁷ m

           Mass of the spacecraft Ms = 1600 Kg

           Mass of the earth Me = 5.98 x 10²⁴ Kg

           G = 6.67 X 10⁻¹¹ N.m²/Kg²

Formula: F = GMeMs/r²

           F = (6.67 X 10⁻¹¹ N.m²/Kg²)(5.98 x 10²⁴ Kg)(1,600 Kg)/(1.91 x 10⁷ m)²

           F = 6.38 X 10¹⁷ N/3.65 X 10¹⁴ m²

           F = 1,748.5 N