Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest.

We have an inverse square law with distance for the force, so then the force of gravity between Earth and the spaceship is lower when the spaceship is far away from Earth.

Th formula is given by:

[tex] F = G \frac{m_{Earth} m_{Spaceship}}{r^2}[/tex]

Where G is a constant [tex] G = 6.674 x10^{-11} m^2/ (ks s^2)[/tex]

[tex] m_{Earth}[/tex] represent the mass for the earth

[tex] m_{spaceship}[/tex] represent the mass for the spaceship

[tex] r[/tex] represent the radius between the earth and the spaceship

For this reason when the distance between the Earth and the Spaceship increases the Force of gravity needs to decrease since are inversely proportional the force and the radius, and for the other case when the Earth and the spaceship are near then the radius decrease and the Force increase.

Based on this case we can create the following rank:

[tex] F_5 >F_4>F_1 >F_2>F_3[/tex]

Where [tex] F_i[/tex] represent the force for each of the 5 cases [tex]i -1,2,3,4,5[/tex] presented on the figure attached.