Well, there's You're So Vain by Carly Simon.

I know of a few songs about comets, especially Halley's Comet, but not much about eclipseses.

Well I hear you went up to Saratoga and your horse naturally won
Then you flew your Lear Jet up to Nova Scotia
To see the total eclipse of the sun
Well you're where you should be all the time
And when you're not you're with
Some underworld spy or the wife of a close friend
Wife of a close friend, and...

You're so vain, you probably think this song is about you
You're so vain, I'll bet you think this song is about you
Don't you? don't you? don't you?

-Joe-