>>1 here, just adding that Ad Astra does not use Newtonian physics, and so it's easy to bring your ship to a complete halt by simply reducing your drive output to zero. This is much the same as in Elite and Oolite (and in fact most space sims I've seen). Unlike those two games, however, in Ad Astra you can not only fly forwards, but backwards as well, which presumably allows for much fancier maneuvering once you've gotten used to the controls. I haven't yet. (´・ω・`)
Having played a bit more Ad Astra, I can say it's quite a fun game, but because of the default controls where pitch and roll are mouse-controlled, aiming tends to be a bit of a bitch. When I try to assist police ships in taking down a pirate, I almost inevitably end up accidentally firing at a cop, and being promptly blown apart as soon as the pirate ship has stopped being a police concern and begun its new life as a salvage target. I have yet to try its joystick control options.
Can I mention the obvious: EVE Online?
I have never played it, but what I've read on Wikipedia does not suggest too obvious similarities.
First and foremost, Elite is a single-player game played without an internet connection. All ships other than your own are computer-controlled. Eve Online is a massively-multiplayer online game, with all the social interaction, collaboration and competition between players this implies.
No trading, but if you like general space simulation/exploration then Noctis is pretty fun.
Evochron Mercenary. It's part of a series, and can be played single player or multi (LAN or online).
The version on Steam was bugged - you should look for the trial version or patched version and run that instead (after entering the CD key that was presented by Steam.)