Astronomers plot the square of the orbital period (vertical axis) versus the cube of…

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

Astronomers plot the square of the orbital period

T^{2}

(vertical axis) versus the cube of the orbital radius

R^{3}

(horizontal axis) for several moons orbiting the same planet. The slope of their best-fit line is

4.0\times10^{-14}\,\text{s}^{2}\!\cdot\!\text{m}^{-3}

. Using

G = 6.67\times10^{-11}\,\text{N}\,\text{m}^{2}\,\text{kg}^{-2}

, determine the mass of the planet.