Math Chat: A Weight-Loss Formula for Space

Old space station challenge

The new space station is only about 6 percent farther from the center of the earth than the earth's surface. Therefore gravity should be just about 12 percent less than on the earth's surface (by Newton's "inverse square" law of gravity, if you like). Then why will the astronauts appear weightless?

Answer

The orbiting astronauts appear weightless because the whole station is in free fall. If the station continued straight ahead, it would shoot off into space, but fortunately it is always falling back toward earth at precisely the right rate to balance that effect. As Jason Heine puts it, "An astronaut floating in the middle of a room will be falling but the room will also be falling at the same rate."

W. Cullers, Bill Hasek, and Eric Randolph give an alternative explanation in terms of the apparent "centrifugal force" pulling circling objects outward, which you feel when your car speeds around a corner. For the orbiting astronauts, centrifugal force balances gravity, and they appear weightless.

Ed Dravecky reports that the movie "Apollo 13" filmed weightless scenes in one of NASA's special KC-135 planes. When the plane is zooming upward at a 45-degree angle, power is turned off for about 15 seconds of free fall. The plane coasts upward, levels off, and falls downward in a "parabolic" path. Mike Bevan (as well as Louis Pushkarsky) points out that "you will have a very small apparent weight in the space station": astronauts in the part of the station closest to the earth will have a slight pull toward it (important to certain delicate experiments). (Other winners chosen from many correct answers: Eric Brahinsky, Joe Conrad, Kenneth Eggert, James Fahs, Russ Morales, Catherine Schmitt.)

New bridge-crossing challenge (Tiku Majumder and Conrad Weiser)

"There are four people who need to cross a river at night. There is a bridge that can only hold up to two people at a time. (It's rickety or something.) There is one flashlight that must be used when crossing. (It is extremely dark, and someone must bring the flashlight back to the others; no throwing anything, no halfway crosses, etc.). The four people take different amounts of time to cross the river. If two people cross together, they travel at the slower person's rate. The times are 10 minutes, 5 minutes, 2 minutes, and 1 minute for each of the four individuals." How fast can they complete the passage? Can they do it in 19 minutes? in 17 minutes?

* Send answers and new questions by e-mail to: Frank.Morgan@williams.edu