Gravitation: Mass Ratio, Separation, and Potential Maximum

[karis]

Homework Statement

A. The mass ratio of the Earth and the moon is 81:1 and the earth-moon separation is 3.8x10⁸m. At which position between the Earth and the moon is the gravitational potential at a maximum?

B. Which of the following statement about a communication satellite in parking orbit above the Earth's surface is incorrect?
A. It is accelerating towards the centre of the Earth at all times.
B. It must be in a circular orbit above the Earth's equator
C. It is always vertically above the same place on the Earth's surface
D. It must be rotating in the same sense and with the same angular speed as the earth
E. It is at a height where its gravitational potential energy is numerically equal to its kinetic energy

C. X and Y are two planets. Each of them has a low-altitude satellite revolving in a circular orbit close to the planet. If the two satellites are observed to have the same period, then X and Y must have nearly the same
A. mass
B. average density
C. radius
D. acceleration due to gravity at the planet surface
E gravitational potential at the planet's surface

Homework Equations

The Attempt at a Solution

For A, i have absolutely no idea, I've tried to simply use ratio to get the answer n i failed.
For B, i know A,C and E are correct answers, but why B is correct too?

Thz so much :):):)

 

[cepheid]

Hello karis,

Well, you did not put anything under the "relevant equations" section. What is the expression for the gravitational potential between two bodies? Once you have that equation, you can figure out what value of the separation, r, between the two bodies, maximizes it.

 

[cepheid]

For part B, think about it this way: that satellite must have the same orbital period as the Earth's rotation period in order for it to be geosynchronous. However, in order for it to have the special geosynchronous orbit where it is always above the same point on the Earth's surface (geostationary) a further condition must be satisfied, which is that its speed relative to the ground must be zero. Different points at different latitudes on the Earth's surface rotate at different speeds...

 

[karis]

thz so much, cepheid,

i got Part B now,

as for part A
the equation is Gm/r, and what should i do with the m?
i rly don't know wt to do next :( :(:(