Why are there few atomic/molecular collisions at LEO level?

[tomwilliam2]

The book I'm reading (Spacecraft Systems Engineering) says that there are very few atomic/molecular collisions between components of the atmosphere and spacecraft in LEO or GEO, which means that any heat exchange comes from radiation alone, and the path of the orbit can be modeled as free molecular flow.

I've been trying to work out why there aren't many collisions. Apparently, the mean free path at about 200km from the Earth's surface (as an example of a LEO level) is about 240m, which is larger than most spacecraft , so that makes sense.
However, that seems to be a remarkably sparse density at just 200km in height. Is the atmosphere really so empty up there? Or is it because we're talking about the ionosphere, and there are very few molecules or non-ionised atoms left at that height?
Thanks in advance

 

[Drakkith]

However, that seems to be a remarkably sparse density at just 200km in height. Is the atmosphere really so empty up there?

Yep. I don't know what the density of the atmosphere is at 200 km, but at 100 km the pressure is roughly 1/100,000th of what it is at sea level so I assume the density falls off in about the same amount.
See here: http://www.regentsprep.org/regents/math/algtrig/atp8b/exponentialresource.htm