Question

The gravitational force between two asteroids is 6.2 × 108 N. Asteroid Y has three times the mass of asteroid Z.

If the distance between the asteroids is 2100 kilometers, what is the mass of asteroid Y?

3.7 × 1015 kg
1.1 × 1016 kg
1.4 × 1031 kg
4.1 × 1031 kg

Answer 1

Use Newton's law: F = G mY mZ / r^2. With mY = 3mZ, F = G(3mZ^2)/r^2 so

mZ = sqrt(Fr^2 / (3G)), mY = 3mZ.

Plug in F = 6.2×10^8 N, r = 2100 km = 2.1×10^6 m, G = 6.67×10^-11 N·m^2/kg^2:

mZ ≈ sqrt[(6.2×10^8)(2.1×10^6)^2 / (3·6.67×10^-11)] ≈ 3.70×10^15 kg

mY = 3mZ ≈ 1.11×10^16 kg.

Answer: 1.1 × 10^16 kg.