From time to time, readers requests information about the direction of the moon's shadow on the surface of the earth during an eclipse of the sun. The question arises from Marshall Hall's vision that the shadow of the moon conceals a proof for geocentricity. He argues that the shadow should move from west to east (as observed) in a geocentric system but from east to west in an heliocentric model. Unfortunately, that just isn't so. This paper illustrates why.

There is no difference between the geocentric and heliocentric models insofar as eclipses are concerned. Suppose for a moment that the moon and sun stood still in the sky, that is, the moon is always at new moon. It looks like the figure at the right. (Here east is at top, west at bottom, and north is coming out of the page.) According to the heliocentric view, the point A (Atlanta, Georgia?) is moving to the east (up the page) at, say, 750 miles per hour (mph). According to the geocentric view, the sun-moon-earth line is moving down the page (to the west) at 750 mph. In either case, ten minutes later A will appear above the line.

However, we know that the moon is not fixed at new but goes through phases, that is, the moon moves "up" the page, away from the line, such that whereas sunrise to sunrise is 24 hours, moonrise to moonrise is 23 hours and 8 minutes. So let’s take it that the shadow of the moon falls at A during an eclipse and let’s start the moon moving up the page so that its shadow on the earth moves up the page and away from the original sun-moon-earth line at 950 miles per hour. It is crucial to remember that the 950 miles per hour is measured from our original line, not from point A!

Now let’s look at the situation an hour later (the two figures on the right). You’ll note that in the heliocentric view point A runs up the page at 750 mph while the moon’s shadow goes up the page at 950 mph. After an hour, then, the shadow will be 200 miles east (above in the figure) at point B. So the shadow moves west-to-east, relative to its original position.

Next, consider the geocentric case (below). Here, too, the moon’s shadow travels eastward, away from the original sun-moon-earth line at 950 miles per hour. However, the original A-moon-sun line, along with the later sun-moon-B line, travel to the west, (down the page) at 750 miles per hour. After an hour, the line falls 750 miles west of (below) point A. The shadow traveled 950 miles eastward from that point and so is 200 miles east (above) point A.

What Marshall fails to grasp is that the moon orbits the center of the earth, not the surface point A. The original line is actually a sun-moon-earth’s centerline. The sun-moon-B line does not go through the earth’s center. So, in both models the shadow of the moon travels from west to east, as observed.