This song is kindof a take on 50s and 60s dance hits (do the ostrich) and Astro was apparently the name of one of his dogs at the time
Here are some interview quotes to explain

Jack: “The Astro is whatever you do in secret that nobody knows about. Everybody does the Astro. Jimmy does the Astro.”

Jack: “Actually for awhile there, right before we recorded the album, that song Astro was just an instrumental-I was just mouthing syllables, I didn’t say anything, I didn’t write lyrics to that until just a few minutes before we recorded it. And that ended up becoming about something I had been thinking about. It’s about the things that people do in secret-I called that the Astro cause it just had a ring to it, but the things people do, like I guess the clue to that was ‘Thomas Edison is AC/DC.’ He was only into direct current, he didn’t believe in alternating current, and that was supposedly his downfall of delivering electrical power to people. But maybe he secretly knew that was the right way to do things. That was my only attempt at trying to do a meaningless one. I had another dog I said that Astro – Astro’s something people do in secret – things people maybe do in secret – I said maybe jasper does the Astro – that was my other dog – but uh I never wrote a song about Elroy though.”