Just wondering, is it possible to use a big enough mirror and just reflect sunlight to do the same thing? Though this only means satellites can only be destroyed during daytime.
Missiles are easily tracked. Your opposition will know who, how, when and where someone was taking action against them. Light pressure could just subtly push a satellite off course as it passes overhead. They have finite propellant on board to correct for it.
That said, I don't think a big mirror reflecting the sun is all that practical when a big ass laser would do the same job and be easier to manufacture and operate.
Let me get this straight, a missile is easy to track, but a giant mirror reflecting a load of sunlight that would have to be LoS to the satellite wouldn’t be? Not to mention that bombing the mirror would be a lot easier than shooting down the missile...
A missile can be viewed from many angles. A beam of light is (mostly) only visible by whoever its aimed at. Light dispersion not withstanding. Sunlight is quite bright and will mask a lot of the scattered light as well.
The effects of a beam of light strong enough to push a satellite into a rapidly decaying orbit would bloom like mad through the atmosphere, and create very detectable thermal effects. It would be detectable in a number of wavelengths for a staggering distance. You’d also have to impact the satellite so strongly that its station-keeping thrusters would be insufficient, while account for losses through the atmosphere. It would have to work quickly enough that the satellite wouldn’t fly out of range, and your weapon would only work during the day in clear weather.
The atmosphere is hardly a problem. You'd use numerous beams simultaneously, fired from all over the country. No single beam would be powerful enough to cause atmospheric breakdown. The sensible choice is to surround every power plant with lasers.
No, this won't be undetectable.
Light pressure is fine, but probably not as productive as ionizing the surface to produce thrust. With high power, atoms at the surface can become multiply ionized. They get blasted off the surface. This would be pulsed, since otherwise the resulting ions would absorb some of the beam and there would be a risk of melting the surface.
If the thrust isn't enough, for example due to a very high orbit, you can just keep going until the target is gone.
Weather isn't much of a problem. There is probably clear weather somewhere over the country. Station keeping won't last forever.
Oh, and if you don't insist on a neat and tidy removal, you can just use non-pulsed beams to melt the target.
For a rough estimate, see this: https://what-if.xkcd.com/13/