Question

Phobos orbits Mars in 27,553 s at a distance of 9.378 × 106 m. What is the mass of Mars? 2.58 × 1011 kg 2.05 × 1023 kg 6.43 × 1023 kg 1.09 × 1030 kg

Answer 1

Answer:

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

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

$G$ is the Gravitational constant, $M$ is the mass of Mars, $m$ is the mass of Phobos, $v$ is the velocity of Phobos, $r$ is the Radius of orbit, $T$ is the Time period.

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

∴ Mass of Mars = $6.439\times10^{23}\text{ }kg$

       

Answer 2

Answer:

Answer is C. I just took it E2020

Explanation: