Gary, It is quite easily explained in both a-centric and geo-centric cosmologies the only difference between the two is the "origin" of the motion not the results of the motions or mat involved in predicting. This is because both must account for the same observed effects. The math for those assumed motions is easily obtained even on a-centric web sites. Aha, we don?t accept a-centric cosmologies, true, but the math that describes the relative velocities of the objects in the sky are only different from geocentric cosmologies in the origin of motion not their effects, this given the assumed distances, which I believe to be relatively accurate. Otherwise, I?m not sure what is in question. Allen Gary Shelton <garylshelton@xxxxxxxxxxx> wrote: "The math that would explain this is non-existent as of yet, at least that's my experience." This only make the point you don?t understand it does not proves nor does it disprove anything, except we don?t know everything. However, the faster relative speed of the sun in relationship to the moon is what is OBSERVED not theorized, as in A centric mechanics. Allen [Gary writes:] No, you're right about not understanding it. I don't. My point was that no one else has exhibited their knowledge of the shadow phenomenon from a geocentric viewpoint yet either. Yes, of course the faster relative speed of the sun versus the moon is what is seen, but this in no way explains the shadow phenomenon. It is inadequate to do so, at least given the accepted distances from the earth to the sun and the earth to the moon. The sun only gains 1/2 degree per hour on the moon. Without the moon being much closer to the sun (to gain a huge "sweeping" speed of the shadow) I don't see how it can be made to explain the shadow's 1000 mph eastwardly motion upon the earth. But again, you're right. It doesn't make it impossible just because Gary Shelton can't explain it. I'm adamant only that no one else has explained it either. Gary