Respuesta :
Planets rotate and revolve around the sun in fixed orbits and are at a specified distance from the sun. The planet's orbital period will be 4.6 years.
What is an orbital period?
The time taken by the planet to complete one revolution around the sun in their fixed orbits is called the orbital period of the planet.
The period can be determined using Kepler's third law:
[tex]\rm T^{2} = \dfrac{4\pi ^{2}}{GM}\times a^{2}[/tex]
Where,
- The orbital period of a planet (T) = ?
- Distance form sun (a) = [tex]\rm 6.28\times 10^{11} m[/tex]
- Gravitational constant (G) = [tex]\rm 6.67 \times 10^{-11} m^{3}kg^{-1}s^{-2}[/tex]
- Mass of the parent star (M) = [tex]\rm 6.96 \times 10^{30} kg[/tex]
Substituting values in the above equation:
[tex]\begin{aligned}\rm T&= \sqrt{\dfrac{4\pi ^{2}}{6.67\times 10^{-11}\times 6.96\times 10^{30}}\times (6.28\times 10^{11})^{3}} \\\\&=145,128,196\;\rm seconds\end{aligned}[/tex]
Therefore, 4.6 years is the orbital period of the planet.
Learn more about Kepler's law here:
https://brainly.com/question/12473529
