How high is an airspace?

I was wondering: how high is an airspace? Is it infinite? Does it stop where… air stops? If a satellite flies over North Korea could Kim Jong say the US are invading and cause a WW3?

In 1960, Francis Gary Powers’ U2 spy plane was shot down by the Soviets at 70,000 feet, described as “the edge of the stratosphere”. The Soviets had no aircraft that could fly that high and fast, so fired rockets to bring down the plane.

The highest FAA airspace, Class A, goes up to 60,000’. Above that it supposedly reverts to Class E, so you could say it’s infinite.

According to some books, Eisenhower deliberately sabotaged the progress of the U.S. space program because he didn’t want the U.S.S.R. to be able to claim that American satellites were spying on Russia and he was afraid they’d discover that he was already using balloons (and later spy planes) to do so.

I don’t know of any direct proof of this, and the evidence can be debated either way. The official announcement of the U.S. program was made as early as 1955, when a launch was planned in the International Geophysical Year, scheduled for January 1957 to June 1958. (Yep, an 18-month year. The Pogo cartoon had endless fun with that.) The Soviets announced their program the next day. Presumably the cover of peaceful science was sufficient. Anyway, the point is that people really did worry about this at one time but when the reality came they retreated to more reasonable official definitions of airspace.

As to where “space” begins:

Wiki

…SpaceShipOne, a spacecraft designed by Burt Rutan and financed by Paul Allen, co-founder and former CEO of Microsoft. On that Space Ship, Melvill broke the 100-kilometer (62.5 mi) mark, the internationally recognized as the boundary of outer space…

/wiki

As to satellites: I suspect it comes down to who can shoot down what, and if the other side could retaliate - we might be in the point of “yes, we all spy on each other - I’m put up with yours if you tolerate mine”. For the big players.
For DPRK, they can only be pissed - they’re not close to being able hit anything.

The treaties governing jurisdiction over airspace (which is what North Korea would be relying on in making any objection to overflights) don’t actually define an upper limit to what constitutes “airspace”. But the word alone suggests what, at a height at which no atmosphere is detectible, you’re no longer in airspace. And of course the Outer Space Treaty - to which North Korea is a party - provides that outer space is not subject to claims of national sovereignty.

It’s as high or low as a country can launch an interceptor aircraft/missile. If you can’t enforce ownership, airspace is pretty meaningless.

So during the time when Neil and Buzz were standing on the moon, how many countries’ air space did they violate?

The Master speaks: Can I declare a no-fly zone over my house?