Question

which statement is true?
the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas, but in a shorter time period the closer the planet is to the sun.
the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas in equal amounts of time.
the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas, but in a faster time period the closer the planet is to the sun.
the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out different amounts of space in equal amounts of time.

Explanation:

The law of equal areas (from Kepler's laws) states that the line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time. Let's analyze each option:

• First option: Incorrect. The time period for equal areas is equal, not shorter when closer.
• Second option: Correct. Matches the definition of the law of equal areas.
• Third option: Incorrect. The time period is equal, not faster when closer.
• Fourth option: Incorrect. The law states equal areas, not different amounts of space, in equal time.

Answer:

The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out equal areas in equal amounts of time.