Question

A SpaceX Crew Dragon with a mass of 5,000 kg is approaching the International Space Station (ISS). The mass of the ISS is 420,000 kg. The table below shows the magnitude of the gravitational forces each object exerts on each other at various ranges:

Range Force on Crew Dragon Force on ISS
1 km 1.4 E−7 N 5.4 E−8 N
500 m 5.6 E−7 N 1.3 E−6 N
200 m 3.5 E−6 N 3.5 E−6 N
100 m 1.4 E−5 N 1.4 E−7 N

Which of the following table entries is correct for their interaction?
A. 1 km
B. 500 m
C. 200 m
D. 100 m

Answer 1

C. 200 m

The gravitational force between two objects is determined by the mass of each object and the distance between them. The gravitational force is inversely proportional to the square of the distance between the objects and directly proportional to the product of the masses. The gravitational force exerted by the ISS on the Crew Dragon is equal in magnitude but opposite in direction to the force exerted by the Crew Dragon on the ISS.

In the table provided, at a range of 200 m, the force on the Crew Dragon is 3.5 E-6 N and the force on the ISS is 3.5 E-6 N, showing that the forces are equal and opposite in direction. At other ranges, the force on the Crew Dragon and the force on the ISS are not equal, this means that the gravitational force at 200m is correct for their interaction.