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Gary, you asked:
"If I understand you correctly you will get the altitude of the satellite by
calculating or measuring the altitude of a star that it passes
nearby......Why not just use the altitude of the star in the first place,
kinda like normal celestial navigation?"

No measured altitudes. You watch the satellite crossing the sky with
binoculars (and the binoculars are not really necessary, but we may as well
use a tool that's probably available). As it glides along, it will pass very
close to at least one 2nd or 3rd magnitude star. When it does, you draw a
quick little sketch of the star pattern and mark it "Sat X passed less than
0.1 degrees from this star," for example. Then you call up some satellite
prediction software on your computer. You let it calculate the path of
satellite X among the stars for various locations around your estimated
position. Modern satellite prediction software will usually draw in the star
patterns so you could do this visually and get an immediate result. You find
any pair of points where the predicted motion matches what you saw. Draw a
line through those two points and you get a line of position as good as a
sextant sight but without using a sextant. One could even dispense with the
binoculars under many conditions. You observe a second satellite for a
second LOP, or if you have exact GMT and fast fingers on a stopwatch, you
could record the instant when "Sat X" passed near that star. Then you get a
position from a single observation.

This method of position-finding would have worked even thirty years ago,
when navigators might still have had some practical use for it. The
calculations would have required a programmable calculator, but the ones
just becoming available back then would have been fully capable of running
predictions. The plotting would have required a star atlas showing stars
down to about sixth magnitude (there were several good ones available back
then). But the real problem was acquiring satellite orbital elements. Today
they're online. But back then, satellite observers published orbital
elements in newsletters distributed by postal mail, and very few people knew
about them.

 -FER


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