Question

Suppose you read in the newspaper that a new planet has been found. Its average speed in its orbit is 33 kilometers per second (km/s). When it is closest to its star, it moves at 31 km/s, and when it is farthest from its star, it moves at 35 km/s. This story is in error because

Choose one:
A. Kepler's third law says the planet has to sweep out equal areas in equal times, so
the speed of the planet cannot change.
B. the average speed is too fast.
C. using these numbers, the square of the orbital period will not be equal to
the cube of the semimajor axis.
D. planets stay at a constant distance from their stars; they don't move closer or farther away.
E. Kepler's second law says the planet must move fastest when it is closest, not
when it is farthest away.
E. Kepler's second law says the planet must move fastest when it is closest, not
when it is farthest away.

Answer 1

E. Kepler's second law says the planet must move fastest when it is closest, not when it is farthest away.

Step-by-step explanation:

We can answer this question by using Kepler's second law of planetary motion, which states that:

"A line connecting the center of the Sun with the center of each planet sweeps out equal areas in equal intervals of time"

This means that when a planet is further away from the Sun, it will move slower (because the line is longer, so it must move slower), while when the planet is closer to the Sun, it will move faster (because the line is shorter, so it must move faster).

In the text of this problem, it is written that the planet moves at 31 km/s when is close to the star and 35 km/s when it is farthest: this is in disagreement with what we said above, therefore the correct option is

E. Kepler's second law says the planet must move fastest when it is closest, not when it is farthest away.