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

Answer:

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.

Explanation:

Answer 2

Answer:

The orbital period of the planet is 6.16 years.

Explanation:

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

$1\ AU=1.496\times 10^{11}\ m$

or $3.36\ AU=3.36\times 1.496\times 10^{11}\ m$

i.e. average distance, $a=5.02\times 10^{11}\ m$

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

$T^2\propto a^3$

$T^2=\dfrac{4\pi^2}{GM}a^3$

Where

M = mass of sun

G = universal gravitational constant

$T^2=\dfrac{4\pi^2}{6.67\times 10^{-11}\times 1.98\times 10^{30}}\times (5.02\times 10^{11})^3$

$T=\sqrt{(3.78\times 10^{16})}$

T = 194422220.952 seconds

Since, $1\ Year=3.2\times 10^7\ seconds$

So, T = 194422220.952 seconds = 6.16 years

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