Question

A planet has an average distance to the sun of 0.66 AU.In two or more complete sentences explain how to calculate the orbital period of the planet and calculate it

Answer 1

Answer:

Orbital period of the planet is 0.537 years.

Explanation:

Given that,

A planet has an average distance to the sun of 0.66 AU, $a=0.66\ AU=9.87\times 10^{10}\ m$

The orbital period of the planet is determined using Kepler's law of planetary motion. Mathematically, the Kepler's law is given by :

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

$T^2=\dfrac{4\pi^2}{6.67\times 10^{-11}\times 1.98\times 10^{30}}\times (9.87\times 10^{10})^3$

$T=\sqrt{2.87\times 10^{14}}\ s$

T = 16941074.34 s

or

T = 0.537 years

So, the orbital period of the planet is 0.537 years. Hence, this is the required solution.

Answer 2

T² = (4π²/GM)a³; where T is in Earth years, a is distance from sun in AU, M is the solar mass (1 for the sun), G is the gravitational constant.
In the given units, 4π²/G = 1
T² = 0.66³
T = 0.536 Earth years = 195.71 Earth days