Plot hole: Rich Purnell started his calculations that required the Hermes to dock with the Tieyang Shen well before Teddy, the Director of NASA, found out about the confidential information about the Tieyang Shen even having enough fuel to be the booster.
Suggested correction: I don't think that is correct. When he first comes up with the idea to reroute the Hermes back to Mars he was thinking about/ working on the calculations for the original probe before it blew up.