The changes due to precession are then applied. These can be found from the formula

where A dp is the change in position angle due to precession a is the right ascension of the star.

This is an approximate formula, however, and should not be used for stars that are close to the pole. A rigorous formula, according to Green1, is given by tan(0- 0O) =

sin(a- ZA)sin cos S cos 0A + sin S sin 0A cos(a- zA)

where 0 is the position angle referred to the equator and equinox of date and 0O is the position angle referred to the standard equator and equinox (i.e. Adp = 0 -0O). dA and zA are precessional angles which, for the standard epoch of J2000, are given by

6a= 0°5567530T + 0°0001185T2 + 0°0000116T3 where T is the interval (t - t0)expressed in Julian centuries of 365,25 days.

In terms of the precessional angles, the approximate formula could be written as

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