Rich Purnell maneuver in The Martian (**spoilers**)

I have a physics question about the Rich Purnell maneuver in The Martian. This has MAJOR spoilers for the book and presumably the movie, so be warned. It might be a better GQ question, but I figured CS was safer considering the spoiler-y content.

The maneuver is started when the ship is approaching Earth en route from Mars, and involves a slingshot around Earth to redirect them back to Mars. There is then a Mars fly-by and presumably another slingshot using Mars to redirect to Earth. The details of the maneuver aren’t explained, but based on the duration, I don’t think it can include using any other planets. It is a “brilliant” maneuver requiring weeks of calculations by a genius.

During the Mars fly-by, the crew is forced to use steering jets to reposition the ship by ~70 km from the original course, and then use a rapid depressurization to accelerate by 29 m/s.

My question: how precise would a course like this be? Is 70 km and 29 m/s within an acceptable margin of error, or did this completely throw off all the calculations and they are now screwed?

Vogel and Beck were pretty specific about the margin of error they needed to complete the rendezvous at Mars. So was Martinez about docking with the supply ship around Earth.

But, for story purposes, all you really need to know is Lewis’ transmission “Houston, be advised that Rich Purnell is a steely-eyed missile man.” And watch the movie with Matt Damon as Watney, coming out in October.

For the Mars rendezvous, the margin of error was about grabbing Watney, unrelated to their course back to Earth. I’ll have to look back at what Martinez said during the supply ship docking, but I think it was again about the margins for docking, not the course.

And whatever the answer is, it will in no way diminish my enjoyment of the book or prevent me from seeing the movie opening night.

Buzz Aldrin has written at length about the concept of “cycling spacecraft” orbiting back and forth from Earth to Mars. Maybe the idea there was to slide into that kind of trajectory and then out of it once they’d done what they needed to do.