What Is the Orbital Period of a Satellite Between Earth and Mars?

[sarahhhh]

Homework Statement

What would be the period of a satellite moving around the sun between the orbits of the Earth adn Mars at a mean distance of 2.00 x 10^11 m?

Homework Equations

R^3/T^2 = 3.35 x 10^18 m^3/s^2 for all objects orbiting the sun.

The Attempt at a Solution

I am so confused how to solve this problem. I set it up like this so far but I am really not sure what to do next/how to start solving the problem. http://img65.imageshack.us/img65/8821/keplerslawas4.png

 

[sarahhhh]

please help me! :(

 

[mgb_phys]

I think you are slightly over reading the question.

Keplers (3rd) law just says that R^3 is proportional to T^2

We know for earth. R = 149.6 million km (you have to look this up)
T = 1 year or 365 days or 31 million seconds

so R_earth^3 / T_earth^2 = R_sat^3 / T_sat^2
Rearrange for T_sat and put the numbers in.

The bit about Mars just says that the satelite is between Earth and mars.
You can also do the above equation for Mars if you happen to know the radius of mar's orbit and the length of it's year.

If you want to split hairs it's the semi-major axis of the orbit so you would also have to know the ellipticity of the satelite.