2024 UPDATED!!! Phobos orbits Mars in 27,553 s at a distance of 9.378 × 106 m. What is the mass of Mars?

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Phobos orbits Mars in 27,553 s at a distance of 9.378 × 106 m. What is the mass of Mars?

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6.43 times $textbf {10} ^ textbf {23}$ KG

Explanation:

Phobos orbit Mars in a circular path. Therefore, some force must act as a centripetal force to maintain the circular path. A gravitational force due to mars assumes this role of the Centripetal Force.

So Gravitational Force = Central Force

$dfrac {GMm} {r ^ {2}} = dfrac {mv ^ {2}} {r}$

the Gravitational constant, is the mass of Mars, is the mass of Phobos, is the velocity of Phobos, is the radius of the orbit, the Time period.

$v = dfrac {Circumference} {Time text {} Period} = dfrac {2 pi r} {T} \\ dfrac {GMm} {r ^ {2}} = dfrac {m times ( frac {2 pi r} {T}) ^ {2}} {r} \\ dfrac {GM} {r} = dfrac {4 pi ^ {2} r ^ {2}} {T ^ {2}} \\ G = 6.67 times10 ^ {- 11} text {} m ^ {3} kg ^ {- 1} s ^ {- 2}, text {} r = 9.378 times10 ^ {6} text {} m, text {} T = 27533 text {} sec \ M = dfrac {4 pi ^ {2} times (9.378 times10 ^ {6}) ^ {3}} {(27533) ^ {2} fold (6.67 times10 ^ {- 11})} = 6.439 times10 ^ {23} text {} kg$

Mars Mass $6.439 times10 ^ {23} text {} kg$

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