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

Let m =  mass of asteroid y.
Because asteroid y has three times the mass of asteroid z, the mass of asteroid z is m/3.

Given:
F = 6.2x10⁸ N
d = 2100 km = 2.1x10⁶ m
Note that
G = 6.67408x10⁻¹¹ m³/(kg-s²)

The gravitational force between the asteroids is
F = (G*m*(m/3))/d² = (Gm²)/(3d²)
or
m² = (3Fd²)/G
     = [(3*(6.2x10⁸ N)*(2.1x10⁶ m)²]/(6.67408x10⁻¹¹ m³/(kg-s²))
    = 1.229x10³² kg²
m = 1.1086x10¹⁶ kg = 1.1x10¹⁶ kg (approx)

1.1x10¹⁶ kg