Question

which statement describes the area swept out by a line between a planet and the sun at equal times as the planet moves along its orbit? (1 point)
○ it changes shape but always remains constant.
○ it decreases as the planet moves closer to the sun.
○ it is proportional to the distance between the sun and the planet.
○ it increases as the planet moves closer to the sun.

Explanation:

This question is about Kepler's Second Law (Law of Equal Areas), which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. As a planet moves along its elliptical orbit, when it is closer to the Sun, it moves faster, and when farther, slower. But the area swept in equal times remains constant (though the shape of the swept area may change, like a triangle or a sector with different dimensions, the area is the same for equal time intervals).

• The option "It decreases as the planet moves closer to the sun" is wrong because when closer, the planet moves faster, so the area swept in equal time should stay constant, not decrease.
• "It is proportional to the distance between the sun and the planet" is incorrect as the area is constant for equal times, not proportional to distance.
• "It increases as the planet moves closer to the sun" is wrong for the same reason as the first wrong option—speed increases near the Sun to keep the area swept in equal times constant, not increase the area.
• The correct option is "It changes shape but always remains constant" because the area (from the Sun - planet line) over equal time periods is constant, even if the shape (like the triangle or sector) of the swept region changes due to the planet's varying speed and distance.

Answer:

A. It changes shape but always remains constant.