Chapter 12, Problem 83GP

The astronomical unit AU is defined as the mean distance from the Sun to the Earth (1 AU = 1.50 × 10¹¹ m). Apply Kepler’s third law (Equation 12-7) to the solar system, and show that it can be written as

  $T=C{r}^{3/2}$

In this expression, the period T is measured in years, the distance r is measured in astronomical units, and the constant C has a magnitude that you must determine.