Let us suppose that the apparent coordinates of a star are needed for a date (t + t) years after the epoch that they are referred, where t is the year of the observation that t the fraction of the year (in years) until the desired day.

    First of all the mean coordinates are calculated for t years after they epoch, these coordinates (a₁, d₁) can be derived by a Taylor expansion from the standard epoch. Keeping only the first two terms we have:

a₁ = a₀ + [da/dt]₀ ´ t

d₁ = d₀ + [dd/dt]₀ ´ t

    The subscript 0 on the derivate means that this one should be calculated regarding to the initial epoch. They expressions are:

[da/dt]₀ = m + 1/15 ´ n ´ sin(a₀)tan(d₀) + m_a

[dd/dt]₀ = n ´ cos(a₀) + m_d

    where:    m_a and m_d are respectively the components on right ascension and declination of the Star's Proper Motion.

                m and n are two quantities that have little variations during the time and are associated to the general precession. They expressions are:

m = 3^s.07496 + 0^s.00186T

n = 1^s.33621 - 0^s.00057T

n = 20’’.0431 - 0’’.0085T

    where T is the time measured in centuries since 2000.0.