A planet travels in its orbit close to apogee, and in 2 years, its radius vector sweeps out an area of 3 A. How long will it take the planet’s radius vector to sweep an area of 3 A when it is close to perigee?(1 point) Responses
A. the same amount of time
B. a smaller time because the planet’s orbital speed will increase
C. a larger time because the planet’s orbital speed will increase
D a smaller time because the planet’s orbital speed will decrease
B. a smaller time because the planet’s orbital speed will increase
wrong again!
Review Kepler's Laws
B. a smaller time because the planet’s orbital speed will increase
To answer this question, we need to understand the relationship between a planet's orbital speed and the time it takes for its radius vector to sweep out a certain area.
When a planet is closer to apogee (the furthest point in its orbit from the central body it is orbiting), it moves more slowly. This means that it takes longer for its radius vector to sweep out a given area. On the other hand, when the planet is closer to perigee (the closest point in its orbit to the central body), it moves faster, so it takes less time for its radius vector to sweep out the same area.
Therefore, the correct answer is B. A smaller time because the planet's orbital speed will increase.