Question

Imagine a new planet is discovered with two moons of equal mass: Moon A and Moon B.



The mass of the new planet is greater than the combined mass of its moons.



Moon A is farther away from the new planet than Moon B.



What is the planet's gravitational pull on Moon A compared to the planet's gravitational pull on Moon B?

Answer 1

A.
The planet's gravity repels Moon A with a greater force than it repels Moon B, which is why Moon A is farther away.


B.
The gravitational pull on Moon B is greater than on Moon A because Moon B is farther away from the new planet than Moon A.


C.
The gravitational pull on Moon B is greater than on Moon A because Moon B is closer to the new planet than Moon A.


D.
The gravitational pull on Moon A is the same as the gravitational pull on Moon B because distance does not affect the planet's gravity.

Answer 2

If they're the same mass, then the force that attract them together would be the same IF AND ONLY IF the distance is the same, but it's not, so...

Ok, just think about this for a second, would according to this formula
\[F = \frac{ Gm_1m_2 }{ r^2 }\]

If Force is inversely proportional to distance, would being farther away mean that the force is less, or more?

After you answered that question, it's fairly obvious which answer it should be. A is obviously not the right answer because the force of gravity only attracts, not repel. We know that it's not the same because the distance between the moons and the planet is different. So only B or C would make sense. It's your job to figure out which :)