A line between a planet and the sun sweeps out two equal areas at different places as it moves along its orbit. Which factor remains constant as this happens?

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1 point
the time the planet takes to sweep out the areas
the distance from the sun to the planet while it sweeps out the areas
the planet’s speed as it sweeps out the areas
the energy required to sweep out the areas

The correct answer is "the planet's speed as it sweeps out the areas." This is because the equal areas swept out by the planet in equal time intervals implies that the planet's speed remains constant.

The factor that remains constant as the line between the planet and the sun sweeps out two equal areas at different places is the planet's speed as it sweeps out the areas.

To determine which factor remains constant as the line between a planet and the sun sweeps out two equal areas at different places along its orbit, let's analyze the given options:

1. The time the planet takes to sweep out the areas: As the line between the planet and the sun sweeps out equal areas at different places, the time taken to sweep out these areas will vary. Therefore, this factor does not remain constant.

2. The distance from the sun to the planet while it sweeps out the areas: The distance from the sun to the planet will change as the planet moves along its orbit. Therefore, this factor does not remain constant either.

3. The planet's speed as it sweeps out the areas: The planet's speed, defined as the rate of change of the distance traveled with respect to time, will vary as it moves along its elliptical orbit. Hence, this factor also does not remain constant.

4. The energy required to sweep out the areas: The energy required to sweep out the areas is proportional to the distance traveled by the planet. Since the distance changes as the planet moves along its orbit, the energy required will not remain constant.

Based on the analysis above, none of the given options remain constant as the line between the planet and the sun sweeps out two equal areas at different places along its orbit.