Question

If a small planet is located eight times as far from the sun as Earth (`1.5 * 10^11` `m`), how many years would it take the planet to orbit the sun?

Answer 1

It takes this planet 22.6 Earth years to orbit the sun.

Explanation:

Problems involving the period of revolution of an orbiting body are generally done using Kepler's third law:

`T^2 = kr^3`

If the information given is in units of Earth years (for T) and astronomical units (multiples of the mean radius of the Earth's orbit), the value of `k` will be unity (1).

Because this is the case here, we can write Kepler's law as:

`T^2 = (1) (8^3)`

and we avoid using `1.5xx10^11` m as the radius.

Finishing the calculation, we get

`T^2 = 512`

`T= 22.6` Earth years