Question

The Martian satellite Phobos travels in an approximately circular orbit of radius `9.4 * 10^6` `m` with a period of `7` `h` `39` `min`. What is the mass of Mars?

Answer 1

`M_(mars)=6.479xx10^23` kg (I used Google calculator so you may get a slightly different number if you approximate `pi`).

Explanation:

The equation that relates the mass of Mars with the orbital information provided about Phobos is the following:

`T^2/R^3=(4pi^2)/(G*M_(mars))`

T is the period. Let's express that in seconds:

`7*3600+39*60=25200+2340=27540` seconds

Let's plug in and solve for M:

`M=4pi^2R^3/(T^2G)=4pi^2(9.4xx10^6)^3/((27540)^2*6.673xx10^-11)`

`M=6.479xx10^23` kg (I used Google calculator so you may get a slightly different number if you approximate `pi`).

A quick check of "the internet" tells me that the actual number for the mass of Mars is `6.39xx10^23` kg, so we're pretty close.

Thanks to the following link for the equation: http://www.physicsclassroom.com/class/circles/Lesson-4/Mathematics-of-Satellite-Motion