Exercise:
The most northerly star of the
Southern Cross, γ Crucis, has
declination -57°.
At what latitude will it just be visible?
The star is at S (just on the
horizon), 57° from the equator.
So at this place, it must be
33° from the equator to the zenith.
So it must be 57°
from the zenith to the north celestial pole.
So it must be 33°
from the pole to the northern horizon.
But the altitude of the
north celestial pole is the latitude of the place.
So the latitude
is 33°N.
So any observer north of latitude 33°N is unable
to see the Southern Cross.
At
what latitude will it pass directly overhead?
The star is at Z, the
zenith.
It is 57° from there to the equator,
so at this
place it must be 33° from the equator to the horizon.
So P is
57° below the northern horizon.
So the latitude is 57°S.
Note:
as a general rule, if a star of declination x° passes
overhead,
then the place has latitude x°.
At
what latitudes will it never set?
Suppose the star is at S, just
on the southern horizon.
It is 57° from S down to the
equator
so it must be 33° from S up to the south celestial
pole.
If the SCP is 33° above the southern horizon,
then
the NCP must be 33° below the northern horizon.
So the
latitude here is -33°, or 33°S.
The star will never set
(it will be circumpolar)
for any observer south of 33°S.
Back to "the HA-dec system".