Weightlessness

Thus, if a baseball were fired side-by-side with the cannonball they would "fall" side-by-side around the earth.  In fact, if the cannonball were hollow and had a baseball and a penny inside the baseball and penny would orbit with the cannonball without pushing against the inside of the ball.  They would seem weightless.  But are they truly weightless?  To answer this, recall that we define weight as the force of gravity, and the force of gravity is the force that keeps the cannonball, baseball, and penny from going off into space.  Thus, according to our definition of weight, objects in orbit are not truly weightless.

An astronaut in orbit around the earth is "falling," in the same sense that the cannonball is "falling."  She seems to float weightlessly around in the orbiting ship.  She is not, however, beyond the pull of gravity and is therefore not truly weightless.  We should call her condition one of apparent weightlessness.