A space shuttle in orbit around the earth carries its payload with its mechanical arm. suddenly, the arm malfunctions and releases the payload. part a what will happen to the payload?

The payload will continue in orbit along with the space shuttle and their relative velocities will be close to zero. However, depending up the relative orientation of the space shuttle's center of mass and the payload's center of mass, the orbits of both the shuttle and payload is likely to slowly diverge from each other. To illustrate how low the relative velocities would be, let's assume a near worse case situation happens and the center of mass of the payload and the space shuttle differs after the release by 50 meters, then the resulting orbital periods of the shuttle and the released payload would differ by about 0.06 seconds from each other.