Question:
The earth revolves around the sun in one year. If distance between them becomes double, the new time period of revolution will be
The earth revolves around the sun in one year. If distance between them becomes double, the new time period of revolution will be
Updated On: Sep 20, 2024
- $4 \sqrt 2 $ years
- $2 \sqrt 2 $ years
- 4 years
- 8 years
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The Correct Option is B
Solution and Explanation
Given : $T_1 = 1\, year, R_1 = R, R_2 = 2R $
According to Kepler's third law of planetary motion
$\hspace40mm T^2 \propto R^3$
where R is the distance between earth and sun.
$\therefore \hspace20mm \bigg(\frac{T_1}{T_2}\bigg)^2 = \bigg(\frac{R_1}{R_2}\bigg)^3 $
$\hspace35mm = \bigg(\frac{R}{2R}\bigg)^3 = \frac{1}{8}$
$\Rightarrow \hspace25mm \frac{T_1}{T_2} = \frac{1}{2 \sqrt 2}$
$\Rightarrow \hspace25mm T_2 = 2 \sqrt 2 T_1 $
$\hspace35mm = 2 \sqrt 2 \, years$
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Concepts Used:
Keplers Laws
Kepler’s laws of planetary motion are three laws describing the motion of planets around the sun.
Kepler First law – The Law of Orbits
All the planets revolve around the sun in elliptical orbits having the sun at one of the foci.
Kepler’s Second Law – The Law of Equal Areas
It states that the radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
Kepler’s Third Law – The Law of Periods
It states that the square of the time period of revolution of a planet is directly proportional to the cube of its semi-major axis.
T2 ∝ a3