The Rich Purnell Maneuver was a trajectory course for the Hermes proposed and calculated by astrodynamicist Rich Purnell. Using the Earth's gravity as a slingshot, it sent the Hermes back to Mars to save Mark Watney before returning home to Earth once more. The meeting in which it was proposed and discussed was known as 'Project Elrond'.
Statistics of the Maneuver
The maneuver started as Hermes approached Earth. Instead of Hermes executing its planned month-long deceleration to enter low Earth orbit (LEO), Hermes instead began accelerating again using its ion engines to increase its momentum further to perform a flyby of Earth, using Earth's gravity to perform a gravity assist and increase its momentum further. As Hermes flew by Earth, it then resupplied for the extended voyage to Mars from a supply craft launched using the Chinese rocket booster originally intended for the Taiyang Shen.
Hermes then spent 322 days enroute to Mars. As Hermes approached Mars, unable to enter orbit due to lack of available propellant, it instead performed a high-speed flyby; during the flyby, Mark Watney then used the heavily-moodified Ares IV MAV to launch on an escape trajectory intercepting that of Hermes's. The remaining Ares III crew on Hermes then retrieved him.
Hermes, still on a flyby trajectory, then used Mars's gravity to perform a second gravity assist to put the spacecraft on a trajectory back to Earth lasting 221 days. As Hermes approached Earth for the second time in the Ares III mission, the spacecraft used its ion engines once more to slow down and enter LEO, allowing its crew to return home via a crew shuttle.
The Rich Purnell Maneuver added 533 days to the Ares III mission, making it the longest Ares mission at a total of over 1,000 days in space and making its crew the only humans to fly to Mars twice in a single mission.