Find mass of mars given period of moon orbit and radius of orbit

AI Thread Summary
To find the mass of Mars using the moon's orbital period and radius, the relevant gravitational equations were applied. The moon's orbital period is 459 minutes, and its orbit radius is 9.4x10^6 m. Initially, the gravitational force and mass of the moon were needed, but the user derived the velocity using v = √(GM/r) and v = ωr. Ultimately, the calculated mass of Mars is 6.5x10^23 kg. This solution demonstrates the application of gravitational physics in celestial mechanics.
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Homework Statement



Given data: A moon of Mars orbits with a period of 459 minutes. The radius of the moon's orbit is 9.4x10^6 m. What is the mass of mars?



Homework Equations





The Attempt at a Solution



The only relevant equation I could find was Fmars on moon= (G*m1*m2)/(r2)

I have the radius, but to solve I would need the mass of the moon and the gravitational force. Could I use F=mv2/r ? Or how about v= \sqrt{}GM/r ?
 
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Alright, I actually figured it out myself.

v= \sqrt{}Gm/r and v=\omega*r

so the mass of Mars is 6.5*10^23 kg!
 
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