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
