Question

The masses of the two moons are determined to be 2M2M for Moon AA and MM for Moon BB . It is observed that the distance between Moon BB and the planet is two times that of the distance between Moon AA and the planet. How does force exerted from the planet on Moon AA compare to the force exerted from the planet on Moon BB

Answer 1

F_A = 8 F_B

Step-by-step explanation:

The force exerted by the planet on each moon is given by the law of universal gravitation

F =

where M is the mass of the planet, m the mass of the moon and r the distance between its centers

let's apply this equation to our case

Moon A

the distance between the planet and the moon A is r and the mass of the moon is 2m

F_A = G \frac{2m M}{r^{2} }

Moon B

F_B = G \frac{m M}{(2r)^{2} }

F_B = G \frac{m M}{4 r^{2} }

the relationship between these forces is

F_B / F_A = = 1/8

F_A = 8 F_B

Answer 2

F_A = 8 F_B

Step-by-step explanation:

The force exerted by the planet on each moon is given by the law of universal gravitation

F =
`G (m M)/(r^(2) )`

where M is the mass of the planet, m the mass of the moon and r the distance between its centers

let's apply this equation to our case

Moon A

the distance between the planet and the moon A is r and the mass of the moon is 2m

F_A = G \frac{2m M}{r^{2} }

Moon B

F_B = G \frac{m M}{(2r)^{2} }

F_B = G \frac{m M}{4 r^{2} }

the relationship between these forces is

F_B / F_A =
`(1)/(2 \ 4 )` = 1/8

F_A = 8 F_B