An astronaut wants to test a pendulum clock and takes it on a trip orbiting the earth. What do you expect him to find out?

We anticipate him to figure out that a pendulum clock in a weightless world (like orbiting the Earth) does not work at all.

Where the weight is W = m (g-a) in which the mass is m, the momentum is g and the acceleration is.

Weightless' indicates g = a. It doesn't mean g = 0, When g was zero you'd stop spinning and go off running in a straight line.