Kepler's Third Law
Two planets have orbital radii r₁ and r₂ = 4r₁. What is the ratio of their time periods T₁/T₂?
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About This Question
- Subject
- physics
- Chapter
- gravitation
- Topic
- kepler's third law
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
1/8
- Kepler's Rule: The square of the orbital period is proportional to the cube of the semi-major axis.
- T2∝r3⟹T∝r3/2.
- Ratio Format: T2T1=(r2r1)3/2.
- Substitute r2=4r1:
- T2T1=(41)3/2.
- Simplify:
- (41)1/2=21.
- (21)3=81.
- Result: The second planet takes 8 times longer to complete an orbit.
This medium difficulty physics question is from the chapter gravitation, covering the topic of kepler's third law. It appeared in the 2025 exam.
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