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Physics question

A space probe, with its engines shut down, orbits Mars at a constant distance of 3500km above the centre of the planet in a time of 110 minutes.
(i) Calculate the speed of the space probe.
(ii) Show that the mass of Mars is about 6x10^23kg
I've done part (i) although now sure if i have the correct answer, if someone could post the correct answer please do. But what I posted this thread for is, how would I go about working the mass of Mars. Thanks.
Reply 1
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Olibert
11
What was your answer for i) then?
Reply 2
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Olibert
11
For part ii) I used two equations.

F = -GMm/r^2 and F = mv^2/r

Equate them, cancel the m's and then solve to get an answer of about 5.8 x 10^-23 as long as your speed is ok.
Reply 3
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Olibert
11
[br]F=−GMmr2[br]F = \frac {-GMm}{r^2}

And

[br]F=mv2r[br]F = \frac {mv^2}{r}

Equate
−GMmr2=mv2r\frac {-GMm}{r^2} = \frac {mv^2}{r}

Divide each side by m
−GMr2=v2r\frac {-GM}{r^2} = \frac {v^2}{r}

Cancel an r on each side
−GMr=v2\frac {-GM}{r} = {v^2}

Multiply the final r onto the RHS, and divide each side by G. Leaving M which is the mass of Mars
M=rv2G M = \frac{rv^2}{G}
Thanks, I got the same answer by following your steps so my speed should be correct :p:

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