I've got to fill in some physics in a short story, MARTIAN CHRONICLES, that I wrote for Jonathan Strahan's forthcoming young adult Mars anthology, LIFE ON MARS. I could try to do the orbital mechanics myself, but chances are I'll screw 'em up. So I turn them over to you! Here's the relevant passage:
Here's how you get to Mars: first, you boost for $A days at $F gees, which gets your ship really *moving*. Since there's nothing in space to stop it — except a few stray hydrogen atoms and the odd gust of solar wind — it'll just coast Marswards pretty much forever. So you switch the engines off and ride your momentum ever and ever Marsward. If you've timed it all correctly, Mars should also be moving toward *you*, swinging around the Sun at $B km/h and closing fast.
Once you're closer to Mars than you are to Earth, you flip the ship over, so that your main antenna array is pointed at the red planet, and reboot the ship's computers, bringing them back online running a Mars-compliant OS that runs on Martian time. Then, $C days later, you turn the engines back and boost *away* from Mars for $D days, because $B km/h and closing fast is *fast* — fast enough to turn your rocket into a cloud of atoms and a giant shockwave if you run *into* Mars instead of going into a gentle orbit around Phobos Base for transfer to a ground-shuttle.
We were almost at turnaround, which meant that we were nearly equidistant from Mars and the Earth. That meant that almost no one was playing the game anymore, because it was at $E seconds of latency, meaning that a message sent to Earth took $E/2 seconds to get there and $E seconds to get back.
Here are the narrative parameters:
* the whole trip needs to take 90 days
* they have to stop boosting after an initial thrust, coast, reverse, and thrust again
* g-stresses from thrust can't exceed healthy limits for juvenile civilians
Given those parameters, what's the right answer for $A, $B, $C, $D, $E and $F above?
First correct answer will win, um, a signed copy of any of my novels (you choose), inscribed and posted to the address of your choosing (to be sent after I get back from holidays in the second week of September).
Update: In response to several commenters: you can put Earth and Mars in any plausible starting position that is justifiable from the point of view of a space-launch where the date can be picked far (a decade, say) in advance.
Also updated to make thrust a variable as well. Any thrust is OK, provided that it won't harm a ship full of baseline civilians, including juveniles.
We have winners!
Thanks, everyone, for a fascinating discussion! There were so many great answers, I couldn't pick just one, so I've picked out two! Winners, please expect an email around Jan 11 on my return to get your details for your prizes.
Grand prize: Remus Shepherd
First runner up: astroeph
(Image: Mars the Red Planet, a Creative Commons Attribution photo from jasonb42882's photostream)