Biology: Aplanet 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: hands onexplanation:...

Aplanet has an average distance to the sun of 3.36 - id3364571967, isaiaspineda09pe6ljq

corrineikerd

15.01.2022

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.

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