Question

Maskbyte is the furthest star from earth. It has a mass of 0.123 times the mass of planet Mekaverse. Calculate the orbital radius and velocity of a planet which has a measured orbital period of 20.4 days!

Answer 1

$M_{earth} = 5.972 × 10^{24} kg$

$M_p = 0.123M_{earth}$

$T = 20.4 \space days = 20.4 * 86400 s$

$M = \frac{4}{3}\pi R^3\to R = \sqrt[3]{\large\frac{3M}{4\pi}}=\sqrt[3]{\large\frac{3 * 0.123*5.972*10^{24}}{4*3.14}} = 6*10^7m$

$v = \frac{2\pi R}{T}=\frac{2\pi \sqrt[3]{\large\frac{3M}{4\pi}}}{T} = \frac{2*3.14*\sqrt[3]{\large\frac{3 * 0.123*5.972*10^{24}}{4*3.14}}}{20.4*864000}=200 m/c$