Question

Mimas, a moon of Saturn, has an orbital radius of 1.62 × 108 m and an orbital period of about 23.21 h. Use Newton’s version of Kepler’s third law and these data to find the mass of Saturn. Answer in units of kg.

Answer 1

Answer:

$3.60432\times 10^{26}\ kg$

Explanation:

a = Orbital radius = $1.62\times 10^8\ m$

T = Orbital period = 23.21 hours

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

From Kepler's third law we get

$M=\frac{4\pi^2a^3}{GT^2}\\\Rightarrow M=\frac{4\pi^2\times (1.62\times 10^8)^3}{6.67\times 10^{-11}\times (23.21\times 3600)^2}\\\Rightarrow M=3.60432\times 10^{26}\ kg$

From the given data the mass of Saturn is $3.60432\times 10^{26}\ kg$