Question:
If a new planet is discovered rotating around sun with the orbital radius double that of the earth, then what will be its time period?
(in earth's days) (Take $\sqrt{2}=1.4$ )
If a new planet is discovered rotating around sun with the orbital radius double that of the earth, then what will be its time period?
(in earth's days) (Take $\sqrt{2}=1.4$ )
Updated On: Jul 29, 2023
- 1032
- 1023
- 1024
- 1043
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The Correct Option is A
Solution and Explanation
By Kepler's third law, $T^{2} \propto R^{3}$
$\therefore \left(\frac{ T _{2}}{365 \text { days }}\right)^{2}=\left(\frac{2 r }{ r }\right)^{3} $
$T _{2}=365 \times 2 \sqrt{2}=1032$ days
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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