Question

Planet Mars has two moons, phobos and delmos. Phobos has a period of 7 hours 39 minutes and orbital radius of 9.4 × 10³ km. Calculate the mass of Mars. (G = 6.67 × 10^-11 Nm²-kg^-2)

Answer 1

We have,

T² = \(\frac{4\pi^2}{GMm}R^3\)

or M_m = \(\frac{4\pi^2}{G}.\frac{R^3}{T^2}\)

\(\therefore\) M_m = \(\frac{4\times(3.15)^2\times(9.4\times10^3)^3}{6.67\times10^{-11}\times(459\times60)^2}\)

= 6.48 x 10²³ kg