physics help.......Keplers laws and gravitation!!!?

Question

1.) Phobos and Deimos, the two satellites of Mars, have orbits with average radii of 9380 km and 23,500 km, respectively. The period of Phobos is 0.319 earth days. What is the period of Deimos?

2.) The moons mass is (7.3 x 10^22) kg, and the average radius of its orbit is (3.8 x 10^8 ) m. At what point could an object be placed between the earth and the moon where it would expirience no resultant force? (neglect the gravitational attractions of the sun and the other planets.)

3.) The moon circles the earth every 27.3 days in an orbit of radius *3.8 x 10^8) m, and the earth circles the sun every 365 days in an orbit of radius (1.5 x 10^11) m. From these figures, without knowing the value of G, find the ratio between the masses of the sun and the earth.

4.) Show that the period of a satellite orbiting a planet just above the surface depends only on G and the planents density p (rho). (density is mass per until volume; the volume of a sphere of radius r is 4(pi)(r)^3 / 3

Answer 1

Tyler. It would be wrong to do your homework for you, but I see no reason why we can't point you in the right direction.
For the most part, the tool you need to solve these problems is Newton's version of Kepler's third law. It has to be Newton's version, because Kepler's third law only works for the sun and a planet/asteroid/comet etc. Kepler did not develop his third law for planets and moons.
It was Newton who formulated the Universal Law of Gravity and then applied it to Kepler's law that allows you to solve all these problems.
In the first problem, you only need the basic form of Kepler's third law because you are creating a relationship in which the constants can be eliminated e.g. (P^2 of Deimos / P^2 of Phobos =a^3 of Deimos /a^3 of Phobos).
In part 2, you can use Newton's Law to set two gravitational forces equal to each other Fe=Fg and where Re+Rm=Rem.
That is to say Fe is the force of gravity from the earth at Re and Fg is the force of gravity from the moon at Rm and Re+Rm is the distance between the earth and the moon.
For part 3, you can use the same method you used in part 1 except in this case you have to use Newton's Version of Kepler's law because you are looking at the masses.
For part 4 you can simply use Newton's Law of Gravity and essentially show that since F=mg and the gravity is GMm/r^2 that the two lower case "m" represent the satellite and cancel out.

Answer 2

These are all worthwhile exercises that you should do yourself. You need one more datum to do part 2, the mass of the earth is 5.974E24 kg (You could figure that out from the moon's orbital radius, but that is an unnecessary complication.)