Question

kepler’s third law states that the square of a planet’s orbital period is related to the cube of its average distance from the star. based on this law, which statement is correct? (1 point) planets closer to the star always move slower than planets farther away. planets that are farther from the star take longer to complete an orbit. all planets, no matter their distance, take the same amount of time to orbit their star. the speed of a planet is the same whether it is near or far from its star.

Explanation:

Kepler's Third Law is \( T^{2} \propto a^{3} \) (where \( T \) is orbital period and \( a \) is average distance from the star). This means as \( a \) (distance) increases, \( T \) (period, time to orbit) increases.

• First option: Closer planets have smaller \( a \), so smaller \( T \) and actually move faster (shorter period means higher orbital speed), so this is wrong.
• Second option: Farther planets have larger \( a \), so larger \( T \) (take longer to orbit), which matches the law.
• Third option: The law shows period depends on distance, so periods aren't the same, wrong.
• Fourth option: Orbital speed depends on distance (closer planets move faster), so speed isn't the same, wrong.

Answer:

B. Planets that are farther from the star take longer to complete an orbit.