Kepler's second law states that the line joining the Sun to a planet

Question

BlackTom AI · Accepted Answer

Contextualizing the question helps: Kepler's second law, also known as the law of equal areas, describes how a planet sweeps out areas at a constant rate as it orbits the Sun.
Option 1: 'moves more slowly the nearer it is to the Sun.' This describes a variation in orbital speed but not the fundamental statement of equal-area sweeping; in fact, when closer to the Sun (perihelion) it moves faster, not slower, to sweep out areas in equal times. Therefore this is inaccurate.
Option 2: 'None of the choices given here is correct.' Given that the standard formulation is present among the options, this statement would be false once we identify the correct option.
Option 3: 'has constant length.' The distance between the Sun and the planet changes along the elliptical orbit, so the line segment does not have constant length; this contradicts the nature of elliptical orbits and the second law’s geometric interpretation, making this incorrect.
Option 4: 'covers an area equal to the cube of its length.' This introduces a non-physical relation between area swept and distance, which is not part of Kepler’s second law and misstates the mathematical description, so it is incorrect.
Option 5: 'sweeps out equal areas in equal times.' This is the canonical statement of Kepler's second law: the line from the Sun to the planet sweeps equal areas in equal time intervals, reflecting a constant areal velocity. This directly matches the established law and is the correct choice.
In summary, the only option that accurately captures Kepler's second law is the statement that the planet sweeps out equal areas in equal times, while all other options mischaracterize the orbital dynamics or introduce incorrect relationships.

Kepler's second law states that the line joining the Sun to a planetSingle choice

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Kepler's second law states that the line joining the Sun to a planetSingle choice

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