You are a space explorer who is on an expedition of scientific discovery to another galaxy. Unfortunately , your space ship was damaged by an asteroid and needs to make an emergency landing Quick reveal three possible planets your ship could land on. Based on the information in the table below, how do you convince your shipmates of the planet that would have a force of gravity which is most similar to Earth's?
Ares Twice the radius, Half the mass
Borros: Half the Radius, one fourth the mass
Caeto: One third of the radius, Nine times as much mass

1) We should go to Ares. Since it has twice the radius , the gravity would be stronger , but since it only has half the mass , the changes balance out and gravity would be the same as on Earth ."
2) "We should go to Borros . Since it has half the radius , the gravity would be stronger , but since it is only one fourth the mass , the changes balance out and the gravity will be the same as on Earth ."
3) "We should go to Caeto Since it has three times the radius , the gravity would be weaker , but since it is nine times as much mass , the changes balance out and the gravity will be the same as on Earth

In order to have a planet that has a force of gravity similar to that of the earth, the space ship must land in Borros whose radius is half of the earth's radius and has one - fourth of the earth's mass.

The force of gravity is obtained from;

F = Gm1m2/r^2 It is an example of an inverse square law.

For another planet, Borros, the radius is half of that of the earth and the mass is one - fourth of that of the earth, hence;

F = 1/4Gm1m2/(r/2)^2

F = 1/4Gm1m2/r^2/4

F = Gm1m2/r^2

Therefore, the planet that is most similar to the earth is Borros because, the gravity would be stronger , but since it is only one fourth the mass , the changes balance out and the gravity will be the same as on Earth.

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