If a hypothetical planet is twice as far from the sun as the earth, it should have a time period of 1032 days.
In the early 17th century, Johannes Kepler observed planetary motions and researched them to give three laws known as Kepler’s Laws.
These laws are:
(1) Law of orbits
(2) Law of Areas
(3) Law of Periods
According to the third law, the square of the time period of revolution of a planet around the sun is proportional to the cube of the distance between the sun and the planet, represented by the following formula
T^2 = r^3
Let T1 be the time period of the revolution of Earth and T2 be the time period of the revolution of the hypothetical planet.
Let r1 be the distance between Earth and the sun and r2 be the distance between the hypothetical planet and the sun.
From the above equation
T1^2 = r1^3
T2^2 = r2^3
Dividing the above equations,
(T1/T2)^2 = (r1/r2)^3
We are given that,
r2 = 2 x r1
And T1 = 365 days
So,
(365/T2)^2 = (r1/2r1)^3
Solving the above equation,
T2 comes out to be 1032 days.
Hence, if a hypothetical planet is twice as far from the sun as the earth, it should have a time period of 1032 days.
To know more about "Kepler's Laws", refer to the following link:
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