Term: altitude, vertical circle
Here at CSB/SJU the north celestial pole
sits about 45° directly above the north point on the horizon.
Thus the altitude of the north celestial pole is
about 45°. Altitude describes
the angle between the nearest part of the horizon and a star.
Zenith has an altitude of 90° above every part of the horizon.
The "line" (really part of a great circle) that goes straight
down from the star to the horizon, and straight up through zenith
and back down to the other horizon, is called a vertical circle.
Vertical circles rise perpendicular to the horizon.
Technically altitude is the angle along the vertical circle between
the horizon and the star.