If a small part separates from an orbiting satellite, the part will

When the small part separates from the satellite, it starts moving with the same velocity as that of the satellite. Also due to the gravitational force of attraction of the earth on the small part, the radially inward (Centripetal) acceleration of the small part is the same as that of the satellite. Therefore the small part will continue to move at the same speed along with the satellite in the same orbit.