Question Bank NAT • 2 Marks Section 2: Classical Mechanics Central force problem

QB_PH_032: Central force problem

Question Statement

A planet orbits a star with an orbital period of $8\text{ years}$. If a second planet orbits at twice the semi-major axis, what is its period in years (rounded to one decimal place)?
Correct Answer
22.4, 22.8
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $T_2 = T_1 (a_2/a_1)^{3/2} = 8 \times 2^{3/2} = 8 \times 2.8284 \approx 22.63\text{ years}$.
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