Physics

Problem

Astronomers plot the square of the orbital period (

T^{2}

) of various satellites against the cube of their orbital radii (

r^{3}

). The resulting graph is a straight line passing through the origin. If the slope of this line is

10^{-13}\,\text{s}^{2}/\text{m}^{3}

, determine the mass

M

of the central planet. (Take

G = 6.67 \times 10^{-11}

SI units and

\pi^{2} = 10