Chapter 1.2, Problem 104E

Distance from the Earth to the Sun It follows from Kepler’s Third Law of planetary motion that the average distance from a planet to the sun (in meters) is

$d={\left(\frac{GM}{4{\pi }^2}\right)}^{1/3}{T}^{2/3}$

where M = 1.99 × 10³⁰ kg is the mass of the sun, G = 6.67 × 10⁻¹¹ N · m²/kg² is the gravitational constant, and T is the period of the planet’s orbit (in seconds). Use the fact that the period of the earth’s orbit is about 365.25 days to find the distance from the earth to the sun.