The direction of the Earth's rotation axis it's not really fixed in space, during the time he have a slightly movement - precession - very similar to a spinning top (see Nutation). This effect it's mainly due to the attraction produced by the Sun and the Moon.

    Due to the precession, the Celestial North Pole (placed near the star a Ursula Minoris, or Polaris) it's hanging around the Ecliptic's North Pole with a period of about 26000 years. As a consequence the Vernal Equinox (the intersection of the equator with the ecliptic), is late in about 50'' per year over the ecliptic.

    Even the plane of the ecliptic is also not fixed in space, due to the force devoted by the planets on the Earth this plane spin around the "line of the nodes", being the present value for this rotation of 47'' per century.

    The plane of the ecliptic, the one of the equator and the Vernal equinox are fundamental and the origin of two systems of coordinates over the celestial sphere: the ecliptic coordinates (longitude l and latitude b) and the equatorials coordinates (right ascension a and declination d). So, due to precession the "fixed" star coordinates are always being changed.

    In this section the main objective is to determinate a procedure to convert the right ascension a and the declination d of a star given a certain epoch and equinox to the values referred to another epoch and equinox. I. e., we are going to determinate the Mean Position of the star taking the effects of precession and proper motion into account.

    The following formulas can be used in the calculation of the annual precession in right ascension and declination:

Da = m + n ´ sin(a)tan(d) + m_a

Dd = n ´ cos(a) + m_d

    To the calculation of Da the value used to n should be expressed in seconds of time (^s).