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Feb 29 at 9:16 comment added mlk If the goal is to abandon the shuttle anyway and not a resupply as in the report, you could try to meet half way and add whatever delta-v is left in the shuttle, e.g. whatever fuel is reserved for the deorbit burn. If you are willing to litter the orbit even further you could even think about dismantling the shuttle to decrease weight. Realistically this might still not be enough, but a group of astronauts in partially improvised space suits, strapped to a crudely detached aft part of the shuttle would definitely make an interesting scene for a science fiction movie.
Feb 28 at 21:45 comment added Mark @Joshua, an extreme dogleg like that is still a very expensive maneuver. You need to get up to a substantial fraction of orbital velocity just to get the 10-degree range.
Feb 28 at 21:21 comment added Joshua For 10 degrees it's seems like it might be better to launch at a very steep south angle and correct after traveling 10 degrees south at a much lower velocity. It's still a boatload of fuel that a Soyuz doesn't have.
Feb 28 at 20:21 comment added Ilmari Karonen (For inclination changes of about 49° of more, it's actually more efficient to boost to a highly eccentric orbit, do the inclination change at apogee where velocity is negligible, and then circularize again at the new inclination. If you can aerobrake to circularize, the threshold drops to about 24°.)
Feb 28 at 20:08 comment added Ilmari Karonen @OldManJohn: Yes, inclination changes are expensive. Changing the inclination of a circular orbit by $\theta$ requires delta-v equal to $2\sin(\frac12\theta)$ times the orbital velocity. For $\theta = 7°$ that's about 12% of the total orbital velocity.
Feb 28 at 16:27 vote accept Old Man John
Feb 28 at 16:21 history edited Organic Marble CC BY-SA 4.0
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Feb 28 at 16:17 comment added Organic Marble @OldManJohn Yes it's very expensive in terms of propellant. As to "why" that's an orbital mechanics question and not in my wheelhouse, I just accept it as a given. There are hundreds of questions about inclination changes on this site.
Feb 28 at 16:10 comment added Organic Marble @StevePemberton I think this paragraph was included in the CAIB report just to cover "Frequently Asked Questions" not to indicate that anyone involved thought they were serious possibilities. "Resupply" was just asked about a lot by the general public.
Feb 28 at 15:32 comment added Steve Pemberton An additional problem with Ariane resupply in that timeframe is how would the consumables be accessed by the Columbia crew? The Ariane upper stage presumably would have had a makeshift attachment for a supply container which could be accessed by astronauts on an (untethered) EVA. That might work for LiOH canisters, which was the immediate need, but there would be no way in that scenario to replenish the cryogenic oxygen and hydrogen, which if I understand correctly was right behind LiOH in terms of being a limiting consumable for Columbia beyond 30 days.
Feb 28 at 15:18 comment added Old Man John Why is it so difficult to change the orbital inclination? Would it require insane amounts of fuel to change it from 46° (Baikonur's latitude) to 39°?
Feb 28 at 15:10 history edited Organic Marble CC BY-SA 4.0
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Feb 28 at 15:03 history edited Organic Marble CC BY-SA 4.0
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Feb 28 at 13:58 history edited Organic Marble CC BY-SA 4.0
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Feb 28 at 13:43 history answered Organic Marble CC BY-SA 4.0