Answer :
Answer:
6.43[tex]\times[/tex][tex]\textbf{10}^\textbf{23}[/tex] kg
Explanation:
Phobos orbits Mars in a circular path. So, there must some force acting as centripetal force to maintain the circular path. Gravitational force due to mars takes this role of Centripetal Force.
So, Gravitational Force = Centripetal Force
[tex]\dfrac{GMm}{r^{2}} =\dfrac{mv^{2}}{r}[/tex]
[tex]G[/tex] is the Gravitational constant, [tex]M[/tex] is the mass of Mars, [tex]m[/tex] is the mass of Phobos, [tex]v[/tex] is the velocity of Phobos, [tex]r[/tex] is the Radius of orbit, [tex]T[/tex] is the Time period.
[tex]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}\times (6.67\times10^{-11})}= 6.439\times10^{23}\text{ }kg[/tex]
∴ Mass of Mars = [tex]6.439\times10^{23}\text{ }kg[/tex]
