In the present time frame the moons domain has been minutely surveyed by optical, radar, and spacecraft, both manned and unmanned. Data, probably amounting to many hundreds of terabytes and being collected at a prodigious rate by multiple nations in on going programs, has failed to find a satellite of Luna. But, in the late 1800's scientists were theorizing and working to prove or disprove the hypothesis.
I have included three pertinent articles. The first is from the 1892, "American Illustrated - Vol. IX ". The second is E.E. Barnard's article and the third is a part of an article by F.R. Moulton, from a June 1899 "Popular Astronomy - Vol. VII". This is a calculation on the distance that a Lunar Satellite could survive in orbit based on the gravitational influences of other bodies.
(Click on article to read)
Clear Sky - Rich