For instance, Harness has Eratosthenes recognizing that the "other planets" go around the Sun just as the Earth does. Since he is told by the alien that the Earth goes around the sun, I am willing to believe that Eratosthenes could handle this idea. However, he would never have thought this was consequently true of the "other planets". The ancient Greeks did not think of Earth as one of the planets. In fact, the word "planet" itself derives from the fact that they thought of planets as wandering stars and had no way to think of them being in any way like the thing we live on. Similarly, there is no reason to expect that he would be able to conclude from this that the sun is just a star which we are close to...this is not really a logical consequence of a heliocentric solar system.

Moreover, the mathematics he consults does not sound believable to me. This story takes place long before the decimal numbering system that we are familiar with, and before trigonometry as we know it. I could be wrong about this (please correct me if you know!) but I seriously doubt that you could have looked up a table of values of the tangent function in 160 BC.

I'm sure there are other historical innacuracies. (He has a "rabbi" there among the non-mathematical figures that Eratosthenes encounters. My understanding is that there was no rabbinic Judaism at this point in history. Again, correct me if I'm wrong.)

If none of the anachronisms or innaccuracies bother you, what about the idea that on the day after he has determined the Earth's circumference, Eratosthenes just happens to meet an alien who needs this exact piece of information to be able to return home?