# . If a planet’s closest distance to the Sun is 1.00 AU, and its furthest distance from the sun is 9.00 AU, what would its orbital period be?

## How do I solve this?

Feb 7, 2018

The planet takes 11.2 earth years to complete one orbit.

#### Explanation:

The orbit described here is highly elliptical as opposed to being nearly circular. If we add the distance of nearest approach to the sun and the greatest of greatest separation, we get what is called the major axis of the ellipse that describes the orbit.

To solve this problem, we will use Kepler's third law:

${T}^{2} = k {r}^{3}$

but it is convenient to know that $r$ in this equation, although often referred to as the average radius of the orbit, is better stated a one-half of the major axis (also called the semi-major axis).

In this case, the semi-major axis is 5 AU.

Because the distances are in AU, we can set the constant $k$ equal to one. This will yield an answer for the period that is in earth years.

Here goes:

${T}^{2} = \left(1\right) {\left(5\right)}^{3}$

${T}^{2} = 91.125$

$T = \sqrt{125} = 11.2$ Earth years.