## Related questions with answers

Question

Find the orbital radius that corresponds to a "year" of 150 days.

Solution

VerifiedStep 1

1 of 4${\large \textbf{Knowns}}$

From Kepler's third law (equation 12-7), the period of an object's orbit $\color{#c34632}T$ is proportional to the $\color{#c34632}3/2$ power of its average distance $\color{#c34632}r$ from the orbited object:

$\begin{gather*} T = \left( \dfrac{2\pi}{\sqrt{GM}} \right)\ r^{3/2} \tag{1} \end{gather*}$

Where $\color{#c34632}M$ is the mass of the orbited object.

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