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 :(

Re-read it. The Hohmann Transfer Orbit is a 2 shot circular to circular transfer. First you turn it elliptical, then you turn the elliptical circular. I discussed only doing the first shot, which would turn the circular orbit into an elliptical one. I was therefore discussing the idea of what it takes to turn a circular orbit into an elliptical one that grazes the atmosphere.

About matching speeds. With work you can match orbits very precisely. But the point I was making is that if you have, say, a 10 cm piece of metal in orbit next to your spacecraft, it is easier to take that piece of metal and store it in your spacecraft for later disposal than to suddenly knock it out of orbit.

However doing this means taking a spacecraft and maneuvering it to match the junk. Every piece of junk you try to maneuver to takes a lot of energy, energy means fuel, and fuel means cost. This is no big deal if you're going to the ISS or servicing a satellite because that docking maneuver is the whole point of the trip. However you generally don't have resources to do a whole lot of those maneuvers. And it is truly cost prohibitive to dock individually with every dropped screw that is up there.

About low thrust. First, that is relatively low thrust. But you still need just as much energy in the end. Unless you use the chaotic nature of orbit to wind up getting repeated net gravity boosts from the Moon and the Sun to move. This would potentially let you do your rendezvous much more cheaper per rendezvous, but at a cost of only picking up one piece of junk every year or two. Amortized over several decades, this might be reasonably cost effective. But to make a dent in the existing problem you would need a flotilla of these garbage satellites, and you'd need a long time. There remains the question of who would design and build these satellites, or what their incentive would be.