Planet X Gravitation Question

[Yosty22]

"Planet X" Gravitation Question

Homework Statement

Planet X is a planet that has two spherical moons in circular orbits. The table summarizes the hypothetical data about the moons. Both moons have low axial spin rates. (G=6.67*10^-11 Nm²/kg²).

Moon A: Mass=4.0*10²⁰ kg. Radius - Data not provided. Moon orbit radius (center-to-center=2.0*10⁸. Orbital period=4.0*10⁶ s.

Moon B: Mass=1.5*10²⁰ kg. Radius=2.0*10⁵m. Moon orbit radius (center-to-center)=3.0*10⁸ m. Orbital period - Data not provided.

a). Determine the acceleration due to gravity that you would expect on the surface of Moon B in m/s².
b). What is the mass of planet X in kg?

Homework Equations

F_g=[tex]\frac{GMm}{r^2}[/tex]

The Attempt at a Solution

For part a, I have no idea where to even start. For part b, all I could think of doing was to solve for the velocity of moon A in its orbit around Planet X. To do this, I did V_A=[tex]\frac{2 \pi R}{T}[/tex] and solved. I got that the velocity of Moon A around Planet X is 314.159 m/s. However, I don't know what to do from there.

Any help would be greatly appreciated.

 

[mfb]

I would expect that this is not the first problem of that type, and you can use known equations for it.
Otherwise, it is possible to calculate it from scratch. Focus on the first moon: which force acts on it? What is required to keep it in a circular orbit?

For part a, I have no idea where to even start.

How are gravitational acceleration and gravitational force related?