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
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Use $T \propto r^{3/2}$ for quick calculations in orbital problems.
Updated On: May 1, 2026
- $81$ years
- $27$ years
- $729$ years
- $\sqrt[3]{81}$ years
- $9$ years
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The Correct Option is B
Solution and Explanation
Concept:
Kepler’s third law: \[ T^2 \propto r^3 \]
Step 1: Take ratio.
\[ \left(\frac{T_S}{T_E}\right)^2 = \left(\frac{r_S}{r_E}\right)^3 \]
Step 2: Substitute values.
\[ = 9^3 = 729 \]
Step 3: Solve.
\[ \frac{T_S}{T_E} = \sqrt{729} = 27 \]
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