Astronomic gravitation problems

[philadelphia]

1. If the INternational space station has an orbital velocity of 9,000 m/s. find the time (in minutes) it takes to make one complete orbit.

Relevant equations
F = mv²/ R = m4[pi]²R / T²

The attempt at a solution
Is this the way to solve for T?
Do I use Earth mass and Earth R b/c that all the question says?


2. A martian day is 1.03 Earth days. At what altitude above Mars should a communications satelite be placed such that it always stay over the same spot above the surface of Mars (answer in units of miles. 1000m = 0.62 miles

Relevant equations
F = ma = m4[pi]²R / T²
a= GM/R²

The attempt at a solution
I know how to solve the problem but what kinda threw me off are the martian days given...
Is T 354.36 days that is 365/1.03
If it is, can i find "a" after the "m" cancel, than solve for R which is (mar's radius + Mars altitude)


3. find the lagrange Point between the sun and Jupiter. In between what two planets will you find this point?

Jupiter:
mass: 1.9x10²⁷ kg

Sun:
mass: 1.99x10³⁰

distance betwwen sun and Jupiter: 778x10⁶ km

Relevant equations
Im really not sure what is lagrange point equation, is it... GM_sunm_jupiter/ r
r is the distance of Jupiter- sun ?

 

[LowlyPion]

You have the velocity and and hence you have

mv²/r = Gravitational force = GMm/r²

This yields v² = GM/r

What you don't know from that equation is r. But you want to calculate it, because v/r = ω

and ω = 2πf = 2π/T or

T = 2π/ω = 2πr/v

 

[LowlyPion]

For Lagrange Points:
http://en.wikipedia.org/wiki/Lagrangian_point

Specifically the answer to your question is where the Trojan Asteroids are orbiting the sun.
http://en.wikipedia.org/wiki/Trojan_asteroids

Though they are located at the L4/L5 points, and your question is asking about the L1 point.