Final answer:
The gravitational force between the planet and Satellite B is 3/4 F, considering that Satellite B is three times more massive than Satellite A and orbits at twice the distance from the planet.
Step-by-step explanation:
The student is asking about the gravitational forces between a planet and two satellites, A and B, which have different masses and orbital distances. To answer this, we apply Newton's universal law of gravitation. This law states that the gravitational force (Fgravity) between two masses is directly proportional to the product of their masses (M₁ and M₂) and inversely proportional to the square of the distance (R) between them.
For Satellite A, the force can be represented as F = (G M m) / R², where G is the gravitational constant, M is the planet's mass, m is Satellite A's mass (m=M), and R is the orbital radius.
For Satellite B, which has a mass of 3M and orbits at a distance of 2R, the force would be F' = (G M (3m)) / (2R)². Simplifying this equation gives us F' = (3GMm) / (4R²), and if we divide F' by F, we get F' = (3/4)F, showing that the gravitational force between the planet and Satellite B is three-quarters that of the gravitational force between the planet and Satellite A.
The answer to the student's question is: a. 3/4 F.