The outer surface is not a sphere, but an oblate spheroid that touches the inner surface at the poles of the rotation axis, where the colatitude ? equals 0 or ?; its radius is defined by the formula
12.
To determine absolute declinations or polar distances, it was necessary to determine the observatory's colatitude, or distance of the celestial pole from the zenith, by observing the upper and lower culmination of a number of circumpolar stars.
13.
For example, if Alpha Centauri is seen with a latitude of 72?north ( 108?south ) and its declination is known ( 60�S ), then it can be determined that the observer's colatitude is ( i . e . their latitude is ).
14.
:: : Just to confirm, you're right : the angle between the axis and a line from the south pole to a point is half of its colatitude, for the usual reasons of being Tardis 16 : 40, 4 December 2006 ( UTC)
15.
The same constant appears in the colatitude equation, where larger values of m 2 tend to decrease the magnitude of P ( \ theta ), and values of m greater than the azimuthal quantum number \ ell do not permit any solution for P ( \ theta ).
16.
Due to the cos 2 ? term in the square root, this outer surface resembles a flattened sphere that touches the inner surface at the poles of the rotation axis, where the colatitude ? equals 0 or ?; the space between these two surfaces is called the ergosphere.
17.
In my searches, I've found that not many people include a detailed explanation of the math behind the differential equation involved in the colatitude ( \ theta ) part; most textbooks or informational sources that I've found have simply said something along the lines of, " This is a very hard differential equation.
18.
For example, Alpha Centauri will always be visible at night from Perth, Western Australia because the colatitude is, and 60?is greater than 58? on the other hand, the star will never rise in Juneau because its declination of " 60?is less than " 32?( the negation of Juneau's colatitude ).
19.
For example, Alpha Centauri will always be visible at night from Perth, Western Australia because the colatitude is, and 60?is greater than 58? on the other hand, the star will never rise in Juneau because its declination of " 60?is less than " 32?( the negation of Juneau's colatitude ).
20.
Since the gnomon's style must be parallel to the Earth's axis, it always " points " true North and its angle with the horizontal will equal the sundial's geographical latitude; on a direct south dial, its angle with the vertical face of the dial will equal the colatitude, or 90?minus the latitude.
