A planet in our solar system whose orbital semi-major axis is larger than that of the Earth's will have an orbital period, compared to the Earth, which is

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The question asks about how the orbital period P of a planet relates to its orbital semi-major axis a, via the context of our solar system.
Option 1: 'shorter' — This is inconsistent with Kepler's third law, which states that, all else being equal, larger semi-major axis leads to longer orbital periods, not shorter.
Option 2: 'longer' — This matches the core idea of Kepler's third law (P^2 ∝ a^3): as a increases, P increases as well. For bodies orbiting the Sun, the period grows with the size of the orbit because the gravitational dependence scales with distance, and taking a larger orbit takes more time to complete a revolution.
Option 3: 'variable' — While orbital speed varies along an elliptical path (faster near perihelion, slower near aphelion), the period itself is not variable with respect to the instantaneous position; for a given semi-major axis, the period is fixed (to a good approximation) by Kepler's law. Therefore labeling the period as variable due to eccentricity is misguided in this two-body approximation.
Option 4: 'equal' — This would imply no change in period with changing a, which contradicts the proportional relation P ∝ a^(3/2). A larger a does not yield the same period as Earth; it yields a longer one.
Option 5: 'impossible to calculate if the eccentricity is unknown' — In the standard two-body model with a known central mass, the orbital period depends primarily on the semi-major axis, and eccentricity does not prevent estimation of P from a (eccentricity affects the shape but not the average time to complete one orbit in the idealized model). Thus, the period is still calculable from a and the central mass, even if eccentricity is not specified.

ASTRON 2140 AU2025 (23428) Final - 2025 Dec 12

A planet in our solar system whose orbital semi-major axis is larger than that of the Earth's will have an orbital period, compared to the Earth, which is

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