Question

A satellite with mass 6000 kg is orbiting the planet at 2500 km above the planet's

Answer 1

By the law of universal gravitation, the gravitational force F between the satellite (mass m) and planet (mass M) is

F = G M m / R ²

where

• G = 6.67 × 10⁻¹¹ m³/(kg•s²) is the universal gravitation constant

• R = 2500 km + 5000 km = 7500 km is the distance between the satellite and the center of the planet

Solve for M :

M = F R ² / (G m)

M = ((3 × 10⁴ N) (75 × 10⁵ m)²) / (G (6 × 10³ kg))

M ≈ 2.8 × 10¹⁴ kg