Question

A planet is found to orbit a distant star with an orbital period of 25 earth years. Use Keplers third law of planetary motion to find the orbital radius of this planet in kilometers

Answer 1

We will have the following:

`T^2=a^3\Rightarrow(25)^2=a^3\Rightarrow a^3=625`
`\Rightarrow a=\sqrt[3]{625}\Rightarrow a=8.549879733\ldots`
`\Rightarrow a\approx8.55AU\Rightarrow a\approx1.3\cdot10^9km`