Last week I thought of a potential way to deorbit satellites that should be enormously cheaper, because it only involves suborbital sounding rockets which could easily be made re-usable. The idea is to put a long cylinder of gas in the path of the satellite, as if the Earth's atmosphere raised up. A possible way to do that is have the upper stage of the sounding rocket orient its axis along the flight path of the debris, then fire its engine to put out an expanding plume of gas along the satellite's track, so the satellite will have to fly through it.
My rough calculations assumed a 2 degree cone angle on the plume and showed you could put out perhaps 1000 kg of gas with a Merlin engine in a cone a couple hundred meters wide at the far end and 10 or so kilometers in length (as the Merlin's exhaust velocity is about 3 km/sec). If the upper stage had two engines aimed away from each other (one facing forward, one back) you'd have a double cone.
Then I estimated the gas density, the frontal area of the debris, and the mass of gas it would encounter at hypersonic velocities. Hypersonic flow is Newtonian, so it's really just a mass on mass collision that lets you calculate the deceleration rate, contact time, and resulting delta V. To deorbit most of this debris in one pass should take a change anywhere from 50 to 100 m/sec, and that's about what I was getting from my spreadsheet.
I'll have to dig deeper into plume behavior in a vacuum, perhaps looking at
this paper and others, to see if it's really feasible.
