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Physics · GRAVITATION
हिन्दीThe quotient \( Q = \frac{T^2}{a^3} \) for planetary orbits in the Solar System is approximately \( 3.0 \times 10^{-34}\text{ y}^2\text{ m}^{-3} \). If a newly discovered dwarf planet has an orbital period of \( 64\text{ years} \), its semi-major axis is approximately:
Correct answer · Option 4
\( 2.4 \times 10^{12}\text{ m} \)
Explanation
\( a^3 = \frac{T^2}{Q} = \frac{64^2}{3.0 \times 10^{-34}} = \frac{4096}{3.0 \times 10^{-34}} \approx 1.365 \times 10^{37}\text{ m}^3 \). Taking the cube root gives \( a \approx 2.4 \times 10^{12}\text{ m} \).
