Kepler’s second law holds that a line segment connecting an orbiting planet to its sun sweeps out equal areas in equal periods of time: In the diagram above, if the time intervals t are equal, then so are the areas A.

If gravity were turned off, would this still be true?

(Below Picture) Yes. The planet would pass into space in a straight line, and each time interval would define a triangle with height h and base t. Since a triangle’s area is half the product of its height and base, they’re all equal.