Mean Position

The mean position of a star is the position (coordinates) on the celestial sphere corresponding to the true, or geometric, direction to the star and referred to the mean celestial pole and mean vernal equinox—that is, expressed in mean celestial coordinates. The mean positions of stars in mean coordinates determined for a particular epoch are published in star catalogs and astronomical yearbooks; the epoch is usually the beginning of a year—for example, 1900.0,1950.0, or 1976.0.

After corrections are performed for instrumental error and allowance is made for the effect of atmospheric refraction and a number of other factors that alter the position of heavenly bodies on the celestial sphere, astronomical observations are used to determine a direction that differs from the true direction to the star by an angle depending on the total influence of annual and daily aberration (seeABERRATION OF LIGHT). Corresponding to this direction is a point on the celestial sphere whose position (coordinates) in the true system of celestial coordinates (referred to the true [instantaneous] celestial pole and the true vernal equinox) is called the apparent position of the star. The true position of the star is the position on the celestial sphere corresponding to the true direction to the star in the system of true coordinates.

The true position can be calculated from the apparent position obtained from observations by correcting for annual and daily aberration. True positions can be converted to mean positions by rotating the coordinate system through angles corresponding to (1) the displacement due to nutation at the time of observation and (2) precession during the time interval between the epoch chosen for the mean coordinates and the time of observation (seePOLES, GEOGRAPHIC).

The concepts of mean position and true position are also valid for artificial earth satellites. Because, however, the motion of earth satellites relative to the observer lacks a component equal to the velocity of the earth in its orbital motion around the sun (this velocity is responsible for annual aberration), it is not meaningful to apply the term “apparent position” to earth satellites.