Answer to Question #112866 in Mechanics | Relativity for Clara

Question

Saturn has a mass of 1.57x1027kg and its moon Titan has an orbital period of 15.945 Earth-days. What is the radius of Titan’s orbit in meters, assuming a circular orbit? (note: it's not, but it's eccentricity is only about 0.03)

Answer 1

$$T=2\pi \sqrt{\frac{R^3}{GM}}$$

Where

R = radius of orbit

G = gravitational constant

M = mass of Saturn

T = time period

Putting all values

We get

$$15.945\times 24\times60\times60= 2\times3.14\sqrt{\frac{R^3}{6.673\times10^{-11}\times{1.57\times10^{27}}}}$$

$$4.81\times10^{10}\times6.673\times1.57\times10^{16}=R^3\\or\\R^3=5.04\times10^{27}\\=1.71\times10^9\ m$$