Question

A particular satellite with a mass of m is put into orbit around Ganymede (the largest moon of Jupiter) at a distance 300 km from the surface. What is the gravitational force of attraction between the satellite and the moon? (Ganymede has a mass of 1.48x1023 kg and a radius of 2631 km.)

Answer 1

Answer:

3.36m or 1680 N

Explanation:

Given:

Mass of the satellite =m

Mass of the moon Ganymede, M = 1.48 × 10²³ kg

Radius of Ganymede, R = 2631 km

Distance of satellite above the surface of the moon, d = 300 km

According to Universal Gravitational law:

$F=\frac{GMm}{(R+d)^2}$

where, G is the gravitational constant, M and m are mass of the objects and (R+d) is the distance between the centers of the objects.

Substitute the values:

$F=\frac{6.67\times 10^{-11}\times 1.48 \times 10^{23} m}{(2.931\times 10^6)^2}=3.36m$

If we consider mass of a satellite to be about 500 kg, the gravitational force between the moon and the satellite would be:

$F = 3.36\times 500 = 1680 N$