Question:
The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to
The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to
Updated On: Apr 19, 2025
- 81 years
- 27 years
- 729 years
- $\sqrt[3]{81}$ years
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The Correct Option is B
Solution and Explanation
Given,
Semi-major axis of the orbit of saturn $=g r_{E}$
Where, $r_{E}=$ semi major axis of earth
According to Kepler's law,
$T^{2} \propto r^{3}$
Let the time period of revolution of saturn around the sun is $T_{s}$
$\therefore \frac{T_{S}^{2}}{T_{E}^{2}}=\left(\frac{9 r_{E}}{r_{E}}\right)^{3} $
$T_{S}^{2} =T_{E}^{2}(9)^{3} $
$T_{S} =\sqrt{T_{E}^{2}(9)^{3}} $
$=9^{3 / 2} \times 1 $ year
$\approx 27$ 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