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?
O the distance the planet moves along its orbit while it sweeps out the area
O the distance from the sun to the planet while it sweeps out the areas
O the planet's speed as it sweeps out the areas
O the time required to sweep out the areas
The factor that remains constant as the line between a planet and the sun sweeps out two equal areas at different places is the planet's speed as it sweeps out the areas.
The factor that remains constant as the line between a planet and the sun sweeps out two equal areas at different places along its orbit is the planet's speed.
To answer this question, we need to understand Kepler's Second Law of Planetary Motion. According to this law, an imaginary line connecting a planet to the sun sweeps out equal areas in equal periods of time as the planet moves along its elliptical orbit.
Now, let's consider the different factors mentioned in the options:
- The distance the planet moves along its orbit while it sweeps out the area: This distance changes as the planet moves along its elliptical orbit. Therefore, this factor is not constant.
- The distance from the sun to the planet while it sweeps out the areas: The distance between the sun and the planet changes as the planet moves in its elliptical orbit. Therefore, this factor is not constant.
- The planet's speed as it sweeps out the areas: According to Kepler's Second Law, the planet's speed changes as it moves along its elliptical orbit. Hence, this factor is not constant.
- The time required to sweep out the areas: Based on Kepler's Second Law, the time required to sweep out equal areas is constant for a given planet. The planet will take equal amounts of time to cover a particular area, regardless of its location in its orbit. Therefore, this factor remains constant.
Thus, the correct answer is: O the time required to sweep out the areas.