GURPS Space - assistance

[Anthony]

Originally Posted by Whill

Which brings me to an astronomical question. Before I get back to system generation questions, what would it be like at the barycenter?

Uninteresting; you won't get star motion due to orbiting, but that's not human-visible to start with.

Originally Posted by Whill

If you could park your ship there (not moving with respect to the Thanatos-Astra system), would it just be completely weightless with no gravitational forces pulling in either direction?

No, you want lagrange points.