That will be the first and simplest prob, since Luna shares basically the same orbit. If I were casting such a horoscope, my first assumption would be that one should assign the traditional Lunar influence to Earth, and otherwisse proceed as traditionally as possible.
Other planets become more problematic. From Mrs or Venus orbits, both Earth and Moon can be seen separately, but is the seperation far enough to put them far enough apart to be significant. A competent technician in astronomy could tell, but I don't know. Should they be treated as separate entities, or simply as Luna? And what becomes the relevance of one's birth planet, which is not in the chart? One possibility is that the influence is transferred to Earth. All these hypothesis woulod have to be tested until enough data was accumulated to determine the accuracy of the predictions (As the Chaldeans doubtless did with the surviving Atlantean supercomputers
Mrs will also give us our first opportunity to figure out the effects of other moons. What are the significance of Demos and Phobus? The problem will be immense on on satellite of Saturn of Jupiter, with thirty or forty "planets" to chart, and extra solar planets are literally off the charts. How will the houses and signs match to different constellations? If astrology is valid, some new personality types may be revealed among the starborn.
By the way, is Pluto still considered an "astrological" planet? How about the rest of the plutonic type bodies?
As I said, it may be hogwash, but I would love for us to have a real opportunity to worry about it.
One last consideration. The rotation of Luna is slow enough planets would remain in a particular aspect for days, rather than hours, and on Venus, the motion of the planets would be likelier to move them from house and sign quicker than rotation would.
Thankyou for asking a question I have been wanting to answer since I was twelve.