The question of mass gets a little hairy:
Infinite: If the Garveys’ lightship has any inertial mass and attains light-speed, its relativistic mass becomes infinite. It’s open to speculation what the effects might be of the ship’s gravitational wake on planet Earth. The practical problem is keeping the lightship in orbit rather than letting it fly off into outer space.
Zero: Such would be the case of a photon or any massless particle. Thus, the Garveys and their ship might be a television image.
Negative: Exceedingly unlikely but theoretically possible. The primary of the orbiting lightship, e.g. Earth, would have positive mass, and the presence of an object of negative mass would cause opposites to repel rather than attract each other. Therefore the Earth would have to exert a “push” or some extra centrifugal force on the lightship in order to attract it and keep it in orbit.