Question

the law of equal areas suggests that planets move fastest when at and slowest when at

Explanation:

The law of equal areas (from Kepler's laws of planetary motion) states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means a planet moves faster when it is closer to the Sun (at perihelion) because it needs to cover more arc length in the same time to sweep equal area, and slower when it is farther from the Sun (at aphelion) as it covers less arc length in the same time for equal area sweep.

Answer:

First blank: perihelion; Second blank: aphelion