|Pathologically Eclectic Rubbish Lister|
On the basis of those numbers it looks pretty damning. The high absolute speeds involved make it sound implausible, but you have to consider the relative speeds. When a shuttle docs with ISS, they are both travelling at over 27,000 kph, but their relative closing speed is sub 1 meter per minute.
I understand the shrapel issue, but again it sounds dramatic because of the high absolute speeds involved. Once you start considering that for the deflector to be in (roughly) the same orbit as the debris, it has to be travelling at approximately the same speed, then the relative speeds involved become much less. (Or much more if they were orbiting in opposite directions. :) It's this aspect, maneouvering to match the direction and altitude that is the likely downfall of the idea. Unless you can pre-compute an efficient sequence of transfers from one debrise encounter to the other.
However, the Hohmann Transfer Orbit is a one-shot, circular to circular transfer. I suspect, but cannot prove, that rather than attempting to deaccelerate the debris to initiate a direct transfer from a circular LEO orbit into a atmosphere scrapping lower circular orbit in one hit, chanhging it from circular to elliptical may be enough and require less deacceleration.
Changing it's orbit from circular to elliptical, with a atmosphere scraping pericentre that occurs 180 degrees away from the collision (ie. on the other side of the earth half an orbit later), would (I think) require less deacceleration. And then you get the atmospheric drag and gravity working for you. Ie. Most orbits aren't actually circular but elliptical. If you can arrange the collision on the 'out-bound leg' of the orbit, when gravity is working with you, I think that the effect of the deacceleration you obtain from the collision is hieghtened?
There is some tantalising stuff in the section "low -thrust transfer" on the page you linked. And a little more in the next section "Therefore, relatively small amounts of thrust at either end of the trip are all that are needed to arrange the transfer.". Mars orbitors tend to enter mars orbit in highly elliptical orbits initially, because it requires less deacceleration, as the planets gravity tends to aid the manoeuver. They then use apocentre burns, when the vehicle is travelling at it's slowest due to having been fighting the planets gravity for half an orbit, to slowly circularise the orbits. Of course they are also usually transfering into polar orbits at the same time, so the maths gets way too complicated for me to understand.
I'll say it again. I've not enough knowledge to understand how far off base I really am. I kind of wish Mr. NASA (or Mr. ESA or Mr RKA), would pop by and simply say: It won't work. Then I could stop thinking about it. Of course, I'd still like to hear why it wouldn't, but the chances are I wouldn't understand the math :(
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