Speed of Light Problem

Question

There is a problem where I believe the answer interestingly comes to the value of the speed of light. Imagine you had an object which travels in one day the distance that the moon travels in a thousand years of its lunar orbit within a geocentric inertial frame of reference, causing the system for which the calculations are made to be infinitely away from anything of influence such as stars. Is it possible for this object to be any faster and if not give reasons for your conclusion.

Assume the day is 1 Earth day outside of gravitational fields and that the length of the lunar orbit is as such likewise.