Meridian altitudes
The altitude of an object is the angle, from the point on the horizon directly below the object, up to the object. In the northern hemisphere, objects rise in the east, climb to a maximum altitude, and then descend to the west, eventually setting below the horizon. Objects reach their maximum altitude when they are directly south of the observer. At this point they are said to be 'on the meridian'. The altitude angle at this point contains crucial information.
It was by measuring this angle to bright stars, and noticing that each star's meridian altitude changed slowly over a period of centuries, that allowed ancient astronomers to deduce the precession of the earth's rotation axis. ..... Just from this angle, closely watched.
The meridian altitude of an object reveals its declination if the latitude is known.
Let us assume that you are in the northern hemisphere and have an astronomical telescope on an aligned equatorial fork mount. In the diagram below, you are standing east of your telescope, looking back at it toward the west (as shown immediately below). This scope is pointed approximately towards the celestial equator.
The heavy dot in the center of the horizon line is your scope. If you start your pointing at the zenith, then a rotation of the telescope 90 degrees to the exact south, will put the telescope's view on the southern horizon. This is altitude (ALT) = zero. I use capitalized text instead of Greek letters for the angles.
If you raise the scope to point at declination zero, then it will be pointing to the celestial equator. For me, this is about 50 degrees above the southern horizon. This angle is called the 'altitude of the equator', EQ in the diagram. Note that the angle from the northern horizon, through the zenith, to the southern horizon, is 180 degrees. This means that EQ = 180 - LATITUDE - 90, as seen in the diagram.
If you then point to a star reaching its maximum altitude (due south), the angle from the horizon to the star is the meridian altitude of the star (ALT in the diagram). This diagram also applies to stars that are north of the zenith. In that case, the star on the meridian is due north of the telescope.
The declination of the star is simply DEC = ALT - EQ.
If the object on the meridian is the Sun, much more information becomes available.
In this diagram you are standing just north of your scope, looking south, at a time when the Sun, moving from left to right, is reaching its maximum altitude above the southern horizon (local noon). EQ again is the altitude of the equator, per the previous diagram, ALT is the altitude of the Sun as it crosses the meridian, and the declination of the Sun is just DEC = ALT - EQ, as before.
Because the Earth is tilted, we can also find the right ascension of the Sun by using the spherical triangle formed by the ecliptic, equator, and dec, in the diagram above. This is a 'right' spherical triangle because of the 90-degree angle between the equator and the meridian. We thus have the DEC, the 90-degree angle, and, if we can find the angle EPS (called formally the 'obliquity' - this is just the tilt angle of the earth's axis to its orbit) then spherical geometry allows us to determine the other sides of this triangle; the ecliptic longitude (the angle from the first point of Aries to the Sun), and the right ascension (RA) of the Sun at the instant of meridian crossing. The RA and DEC of the Sun come directly from this meridian altitude measurement.
Two things are undefined; the EPS (tilt) angle of the earth to its orbit(in the second diagram), and the latitude of the telescope in the first diagram. We need both before we can obtain the RA and DEC of our objects. EPS is short for the greek letter epsilon.
You can see from this diagram that if you observe that the Sun has a DEC of zero then that means that ALT = EQ (the Sun is on the equator) and that the right ascension is zero. This is how the Sun is used to define the origin of the right ascension coordinate.