no, ames. The moon has gravity just like any other object, so the astronaut will be drawn back to its surface. Just with less acceleration than on planet Earth.
P.S. I think my solution to your riddle should be acceptable too, providing that you replace “Mars” with a planet that has a lower gravitational pull. Falling 210 feet would not create a dangerous velocity if we assume that the gravitational pull is sufficiently low.
SJS or Dr. Pepper should be able to reverse engineer the maximum acceleration that would allow such jump to be safe.