Paul Schlyter:
Second, for circumpolar objects there is no requirement that their
altitude at upper culmination should be higher than the altitude of
the celestial pole. As an extreme example, consider an observer at
89 degrees N latitude and an object at +3 degrees declination: to
that observer, the celestial pole will be 89 degrees above his
horizon, and that object at +3 degrees declination will be 4 degrees
above his horizon at upper culmination and 2 degrees above his
horizon at lower culmination (ignoring atmospheric refraction). To
him, everything north of +1 degree declination will be circumpolar,
but very few objects will appear higher in his sky than the north
celestial pole.

*****

This example is both clever and fascinating. I fear, however, that if I
were at +89 I would freeze to death before I had to time to fully grok
its elegance.

Davoud

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