Question

A planet has an average distance to the sun of 3.36 AU. In two or more complete sentences, explain how to calculate the the orbital period of the planet and calculate it.

Answer 1

You can check this calculation by setting the masses to 1 Sun and 1 Earth, and the distance to 1 astronomical unit (AU), which is the distance between the Earth and the Sun. You will see an orbital period close to the familiar 1 year.

Step-by-step explanation:

Answer 2

The orbital period of the planet is 6.16 years.

Step-by-step explanation:

A planet has an average distance to the sun of 3.36 AU i.e. a = 3.36 AU

`1\ AU=1.496* 10^(11)\ m`

or
`3.36\ AU=3.36* 1.496* 10^(11)\ m`

i.e. average distance,
`a=5.02* 10^(11)\ m`

If we want to calculate the orbital period of the planet, it can be calculated using Kepler's third law as :

`T^2\propto a^3`

`T^2=(4\pi^2)/(GM)a^3`

Where

M = mass of sun

G = universal gravitational constant

`T^2=(4\pi^2)/(6.67* 10^(-11)* 1.98* 10^(30))* (5.02* 10^(11))^3`

`T=\sqrt{(3.78* 10^(16))}`

T = 194422220.952 seconds

Since,
`1\ Year=3.2* 10^7\ seconds`

So, T = 194422220.952 seconds = 6.16 years

Hence, the orbital period of the planet is 6.16 years.