Question

can you explain why B is the correct answer and show the work used to get to that answer

Planet X s only moon travels in an elliptical orbit with eccentricity 0.64 and semi-major axis 5x 107 m. It takes 25 hr to complete one orbit. Calculate the mass of Planet X (A) 1.54 x 1013 kg (B)9.13 x 1024 kg (C) 1.18 x 1032 kg (D) 5.85 x 1024 kg (E) 2.39 x 1024 kg

Answer 1

The time period is given by

The time period is given by T = 2 pi squareroot a^3/GM Where T is the time period, a is the semi major axis, G is the gravitational constant M is the mass. = > M = 4 pi^2 a^3/GT^2 = 4 pi^2 * (5 * 10^7)^3/6.67 * 10^-11 * (25 * 3600)^2 = 9.134 * 10^24 kg

Where T is the time period, a is the semi major axis, G is the gravitational constant M is the mass.

$\Rightarrow M = 4\pi^2 \frac{a^3}{GT^2} = \frac{4\pi^2 *(5*10^7)^3}{6.67*10^{-11}*(25*3600)^2} = 9.134*10^{24} kg$