Question

a student says, \at perigee, a planets orbital speed is the greatest since it is closest to the sun. so, the planets radius vector sweeps a larger area in a week than it does when the planet is at apogee.\ which of the following statements is accurate? (1 point)

the student is incorrect. the orbital speed of the planet is constant. so, the radius vector will sweep out the same area for the same time interval.

the student is correct that the greatest orbital speed occurs at perigee; also, since the planet is traveling faster, it will sweep out a larger area.

the student is correct that the orbital speed is greatest at perigee, but keplers second law says that the area swept by the radius vector must be equal for the same time interval regardless of where the planet is in its orbit.

the student is incorrect. the planets orbital speed is least at perigee and it will sweep the smallest area due to the low speed.

Explanation:

Kepler's Second Law states that a planet's radius vector sweeps out equal areas in equal time intervals. While the orbital speed is greatest at perigee (closest to the Sun) and least at apogee (farthest from the Sun), the area swept by the radius vector in a given time interval (like a week) is the same regardless of the planet's position in its orbit. The first option is wrong because orbital speed is not constant. The second option is wrong as the area swept is not larger at perigee. The fourth option is wrong because orbital speed is greatest at perigee, not least.

Answer:

The student is correct that the orbital speed is greatest at perigee, but Kepler’s Second Law says that the area swept by the radius vector must be equal for the same time interval regardless of where the planet is in its orbit.