Question

The gravitational force between two asteroids is 6.2 × 10^8 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 × 10^15 kg
1.1 × 10^16 kg
1.4 × 10^31 kg
4.1 × 10^31 kg

Answer 1

You can solve this by using The Universal Gravitation Equation:
F = Gm1m2/r^2
where G is gravitational constant 6.67x10^-11, m1 and m2 are the masses and r is the distance between the two masses.

It is also given that Y=3Z.
Also, don't forget to convert 2100 km into meters = 2.1 x10^6 meters

Substituting the values we have:
6.2x10^8 = (6.67x10^-11)(3Z)(Z)/(2.1x10^6)²
Z = 3.697x10^15 kg
Y = 3Z = 1.11 x10^16 kg

The answer is B.