damerell: NetHack. (Default)
damerell ([personal profile] damerell) wrote2015-12-03 04:21 pm

David tries to break The Martian

I thought I'd found a bug in The Martian but [personal profile] davidgillon pointed out I hadn't. This is preserved for curiosity's sake.

All figures come from here and appear to be KORECT although they are sometimes in stupid 18th-century units.

The final scenes of the book depend on the premise that the _Hermes_ is approaching Mars at a greater speed than that intended for rendezvous with the MAV, and so the MAV must have its weight drastically reduced in order to have enough delta-v to reach that speed. This doesn't quite work so there is clever improvisation etc etc.

However, the Hermes has an ion drive. This type of drive has a very high specific impulse (the amount of shove you get per kg of reaction mass) but a very _very_ low thrust to weight ratio. We are told, in fact, the Hermes can accelerate by 2 mm/s/s/.

The rendezvous is at 100km above Mars, where the orbital velocity is c. 3.5 km/s. The Hermes is arriving at 5.36km/s. Rather than the MAV getting up to that speed, can the Hermes slow down?

Normally, the idea that a space mission can find an extra 2km/s or so of delta-v is ridiculous. However, it's not so ridiculous with an ion drive where the quantity of reaction mass is small... and especially not because nearly all ion thruster designs use xenon as reaction mass and the Hermes has a fission reactor onboard which generates small quantities of stable isotopes of xenon.

(There is an assumption here that NASA built a capability into the Hermes to capture and use that xenon. However, the Hermes is meant to be by far the most capable and expensive spacecraft they ever built - and if the ship can capture the xenon it generates, it both has more flexibility for mission profile changes and NASA doesn't have to spend so much money sending up xenon to resupply it.)

The first objection I got was that if the Hermes slows down, it will delay the rescue mission long enough for Watney to die. However, I make the deceleration period 10.5 Sols and since our average speed during that period is circa 4.4km/s we need to travel for an extra 2.4 Sols at 5.36 km/s to make up the loss - of course, this isn't totally accurate because Mars doesn't stay put but it should be close enough.

So, anyone, tell me why I have not broken the Martian?

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