Except the sun hasn't moved the 2.13 degrees in those 8 minutes - it's still in the same place! So even thought the light is 8 minutes old, the light is still coming from the same place as it was 8 minutes ago because the sun is in the same place it was 8 minutes ago.
Please just answer this one question: If the earth were turning at the rate of 180 degrees per 8.5 minutes, how far lagged would the sun's optical image be from its real position?
Thanks,
-Jesse
180 degrees off. Just think of the timing a sniper would need to shoot a laser pulse at someone on the earth, 180 degrees or 8.5 minutes of lead time.
Or conversely think of it this way. At dawn the sun would be at 90 degrees and at sunset 8.5 minutes later it would be at 270 degrees from the perspective of someone on the earth. So if the Sun got turned on just before dawn the observer on the earth wouldn't see the sun until just before sunset, exactly 180 degrees off.
LeGrande has said that the lag would be 180 degrees. Thus it would be nighttime on the face of the Earth pointing to the Sun, and daytime on the face pointing away from the Sun. Now, let's consider the moon.
Unlike LeGrande's Sun, the moon really does orbit the Earth, but its orbital velocity is very small (1 km/s) compared to the speed of light. So the real, non-LeGrandean lag is exceedingly small and can be ignored. The LeGrandean lag is not so small though. In this example the Earth rotates with a period of 17 minutes or 1020 seconds. The moon is 4/3 light-seconds away. So the moon's optical image is lagged by 4/3 seconds. How many degrees is that? It is about 0.47 degrees. This is not really negligible. The moon's apparent diameter is about half of a degree, so, if we were living in the LeGrandean universe, we would have to keep in mind that the real moon is one moon-diameter off from the moon we see.
Now, where would we put the moon to cause a solar eclipse? We can't put the moon between the Earth and the Sun, because it's nighttime on the side of the Earth facing the Sun, and how can a solar eclipse happen at night? We must put the moon somewhere on the other side of the Earth, the daytime side, which is facing away from the Sun. But, it makes not much sense to say we have to put the moon between the apparent Sun and the Earth, because the apparent's Sun doesn't exist. So, perhaps we must place the moon in such a way so that it's lagged optical image coincides with the lagged optical image of the Sun. That is to say, we must put the actual moon on the other side of the Earth, about 0.47 degrees from the apparent Sun.
So you see, in the Legrandean universe, you put the Earth in between the Sun and the moon to cause a solar eclipse.