One problem, or not, is that Alec isn't from Earth even though he's spent a lot of time there. So Earth stars wouldn't look very familiar to him in general. Even if they were on Earth, he might not be in the same time period as people would expect the stars to look like now.

Then he sees the moon...

Welp.

That made it easy.

"So, where are we? It's not Earth. I don't know its stars, but I do know what its moon looks like. And that's not Earth's moon."