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?
A. the time the planet takes to sweep out the areas
B. the distance from the sun to the planet while it sweeps out the areas
C. the planet's speed as it sweeps out the areas
D. the energy required to sweep out the areas
A. the time the planet takes to sweep out the areas
The correct answer is B. the distance from the sun to the planet while 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, we can evaluate each option:
A. The time the planet takes to sweep out the areas:
This is not the correct answer because as the planet moves along its elliptical orbit, the time it takes to sweep out a particular area will vary. The closer the planet is to the sun, the faster it moves, and vice versa.
B. The distance from the sun to the planet while it sweeps out the areas:
This is also not the correct answer because as the planet orbits the sun, its distance from the sun continuously changes. Therefore, the distance from the planet to the sun will not remain constant.
C. The planet's speed as it sweeps out the areas:
This is the correct answer. According to Kepler's second law of planetary motion, a line that connects a planet to the sun sweeps out equal areas in equal periods of time. This means that as the planet moves along its orbit, it will sweep out equal areas in equal intervals of time. Hence, the planet's speed remains constant.
D. The energy required to sweep out the areas:
This is not the correct answer because the energy required to sweep out a particular area depends on the mass of the planet and its velocity, which can both change as it orbits the sun.
Therefore, 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 (option C).