Mark Watney missed Ares III and died

[DaveC426913]

TL;DR Summary

Things I think of while trying to go to sleep.

SPOILERS

In the final scene of The Martian, Watney cut open his suit and used the jet of air to fly (like Ironman!) up to meet Ares III.

Ares III had braked to match velocities with Watney's HAB capsule (both of which, presumably were moving at higher than escape velocity, or Ares III couldn't have made it back home), but was still several hundred metres too high to intercept.

Watney blasted toward (i.e. upward) the Ares III with his ersatz jet. This would actually have caused him to fall behind the Hermes, even as he rose toward its path.

He really should have remembered his basic orbital mechanics, and instead blasted parallel to the Ares III's trajectory.'Out' takes you back.
'Back' takes you down.
'Down' takes you forward.
'Forward' takes you up.
https://en.wikipedia.org/wiki/The_Smoke_Ring_(novel)

 

[jedishrfu]

Another refrain for the song I fought the law and the law won.

 

[Drakkith]

Based on my experiences in Kerbal Space Program, at close ranges (less than a few hundred meters or so) you don't need to worry too much about thrusting prograde instead of thrusting directly towards your target. Your drop in speed will be very small at that range, so it doesn't take much to compensate. The difference in orbital velocity between a 200 km and a 201 km orbit around Earth is around 0.6 m/s, dropping to about 0.06 m/s for a 100 meter difference. I don't know what the velocity of a 200x201 km orbit is at apogee and perigee, but they should be close enough to their circular counterparts for this crude analysis.

Around Mars, going from a 200 km to a 201 km orbit is a difference of only 0.4 m/s. Now, neither Watney nor the Ares were in a closed orbit of Mars during their rendezvous, instead both appeared to be on a hyperbolic escape orbit, so the numbers would change a little. I don't know the numbers exactly, but since the escape velocity of Mars is only 5.03 km/s and the distance between Watney and the Ares was almost certainly less than half a km, I would guess that Watney lost less than 0.3 m/s when moving upwards to the Ares.

A 1 ft/s loss seems easily made up by his suit's air jet.

Anyone with more experience in orbital mechanics should feel free to pick apart this analysis.

 

[DaveC426913]

Mebbe true, although the target for interception in this case is less than 6 feet. They only get one shot, and they can't stop and fine tune it. Not quite analogous to spaceship docking.

 

[jedishrfu]

He could've got knocked out.

 

[DaveC426913]

He could've got knocked out.

What do you mean? How would that help?

 

[jedishrfu]

If you're knocked out from hitting the spacecraft then you can't grab ahold of anything and pull yourself in.

 

[DaveC426913]

Thanks Drak. That's good stuff you got there.

I would guess that Watney lost less than 0.3 m/s when moving upwards to the Ares.

That results in him falling behind by 18m for every minute he was in transit.

If he were in-transit for one minute, he'd have missed by 60 feet - 10 body lengths. (actually 12.5 body lengths for Matt Damon. )

 

[Drakkith]

Thanks Drak. That's good stuff you got there.That results in him falling behind by 18m for every minute he was in transit.

If he were in-transit for one minute, he'd have missed by 60 feet - 10 body lengths. (actually 12.5 body lengths for Matt Damon. )

Unless corrected for, yep.

 

[DaveC426913]

Unless corrected for, yep.

...by directing his jet to go forward...

 

[sophiecentaur]

Shock horror. They got it a bit wrong in a film. That must be a first.
In any case, Mat Damon can do anything on film and I will believe him. How did the Talented Mr Ripley get away with it?