Modeling Using Variation · Exercise 46

Use Kepler’s Law, which states that the square of the time, $T,$ required for a planet to orbit the Sun varies directly with the cube of the mean distance, $a,$ that the planet is from the Sun.

Using the Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating $T$ and $a.$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Precalculus 2e · §3.9 Modeling Using Variation · Exercise 46