Question

the figure shows the path of a planet orbiting the sun. the three areas shaded in gray have equal areas.

according to keplers second law, which conclusion is supported by the data?

• the time intervals from a to b, c to d, and e to f are all equal.
• the time interval from a to b is twice the interval from e to f.
• the time intervals from a to b, c to d, and e to f combine to be equal to one half of a full orbit.
• the time intervals from c to d and from e to f combine to be equal to the time interval from a to b.

Explanation:

Kepler's second law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. Since the three gray - shaded areas are equal, the time intervals taken to sweep out these areas (from A to B, C to D, and E to F) should be equal.

Let's analyze each option:

• Option 1: If the areas swept are equal (as given, the three gray areas are equal), according to Kepler's second law, the time intervals to sweep equal areas are equal. So the time intervals from A to B, C to D, and E to F being all equal is supported.
• Option 2: There is no basis from Kepler's second law or the given equal - area information to conclude that the time interval from A to B is twice that from E to F.
• Option 3: There's no reason to believe that the sum of these three time intervals equals half of a full orbit. The equal - area condition doesn't imply this.
• Option 4: The equal - area condition (and Kepler's second law) doesn't support that the sum of the time intervals from C to D and E to F equals that from A to B. If the areas are equal, their time intervals should be equal, not that the sum of two equals the third.

Answer:

The time intervals from A to B, C to D, and E to F are all equal.