Which statement is true?
1. the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas in equal amounts of time.
2. the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas, but in a shorter time period the closer the planet is to the sun.
3. the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out different amounts of space in equal amounts of time.
4. the law of equal areas suggests that the imaginary line connecting the sun to a planet sweeps out equal areas, but in a faster time period the closer the planet is to the sun.

1. The law of equal areas suggests that the imaginary line connecting the Sun to a planet sweeps out equal areas in equal amounts of time.

Explanation:

This statement correctly describes Kepler's 2nd law of planetary motion. The three Kepler laws of planetary motion are:

1st law: the orbits of the planets around the Sun are ellipses, with the Sun at one of the two focii

2nd law: an imaginary line connecting the Sun to a planet sweeps out equal areas in equal amounts of time

3rd law: the cube of the average distance of a planet from the Sun is proportional to the square of the orbital period of the planet

As we can see, the 2nd law corresponds to the first statement described in the question. Also, a result of this law is that the speed of a planet decreases as the planet moves farther from the Sun, while its speed is higher when the planet is close to the Sun.