Local minimum declination is easy to determine if the observer knows his or her latitude. For example, if the observer is located in Washington DC, where the latitude is about 40 degrees, the minimum decination is 40-90 or -50. What this means is that a star having a declination of -50 degrees will appear exactly at the horizon. This star will never appear above the horizon. A star of -51 degrees will never appear at all. As a practical matter, the real limitation is something on the order of 15 to 20 degrees above the horizon, so a better measure of minimum declination is
Latitude-90+20, or in the case of Washington DC, -30 degrees of declination. The 20 degree factor removes the extreme distortion of the atmosphere that is present close the the horizon. Good choices for star observations usually can be made above this minimum declination level.
The above diagram illustrates minimum declination. Polaris sits at +90 degrees approximately. At any northern latitude, the angle Alpha is in fact the latitude.
Zero degrees (or the celestial equator) lies 90 degrees to the south.
The angle Beta, which represents the minimum declination is easily derived when one remembers that the north-south horizon here is represented by a line traveling from north to south. The three angles of alpha, the center right angle, and the angle beta must equal 180 degrees.
If Angle Alpha is the Latitude, and the center right angle is 90 degrees, then the minimum declination (or angle Beta) must be
Beta=180-90-Latitude, or to simplify Beta=90-Latitude.
Since angles measured south of 0 degrees declination are indicated as negative,
minimum declination=0-Beta=0-(90-Latitude) = Latitude-90
for northern observers.
