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A very high-altitude balloon would float near the top of the atmosphere, collecting solar energy and using it to power a beam gun (laser / electron beam / particle beam) to fire at space junk to de-orbit it.
Floating near the top of the atmosphere means there would be little atmosphere between the
platform and the targeted space junk, which would minimize beam attenuation. The balloon's own skin would be made of a photovoltaic polymer that could harvest solar energy to power the beam gun. Furthermore the balloon could be equipped with radar, just like a radar aerostat.
DARPA High Altitude Blimp
ISIS [sanman, Apr 20 2013]
JAXA Unmanned Balloon
JAXA to launch highest unmanned balloon flight [sanman, Apr 20 2013]
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||Firing at junk from slightly below would just push it to a higher orbit. But it would not deorbit it.
||Perched near the top of the atmosphere, it can fire in a tangential vector, against orbital debris with oncoming velocities. This will help to decelerate objects and drop them out of orbit, so that they'll burn up in the atmosphere. The system would operate round-the-clock, only pausing to avoid hitting legitimate satellites.
||I'm pretty sure a decrease in orbiting velocity could only be achieved by hitting it with some kinetic energy--momentum equals mass x velocity. I don't think you can get very much mass from a 'beam gun' (whatever that means). You can probably burn it up or melt it, but it would still be orbiting just the same. And if you blew it up, some would de-orbit, but other parts would become more space junk.
||Here we need something similar, lo-tech, to get rid of the junk in streets and sidewalks.
||A laser or particle weapon can both transfer
kinetic energy. The laser isn't very much, but it's
the same theory that makes solar sails work.
Particle beams are using massive particles
(electrons, protons, or ions), so no special theory
needed for kinetic energy transfer.
||And as far as boosting objects into a higher orbit,
that's fine, as long as that's not all you do. You hit
the object at least 45 degree off radial, and you'll
subtract as much from orbital velocity as you add,
with the result being a more eccentric orbit with a
lower perigee. Repeat until the perigee is within
the atmosphere, and your object is dealt with.