Determination of Planetocentric Coordinates of the Center of the Illuminated Part of the Spherical Planet's Visible Disk

Exact formulas are derived for calculating the correction for phase to the central meridian longitude and the latitude of the center of the illuminated part of the visible disk of a spherical planet in projection onto the plane of the sky. The range of possible values of the phase correction to the central meridian longitude is determined. The proposed formulas are valid for any planet's orientation with respect to the Earth and Sun and allow a transition, in planetocentric coordinates, from the center of the geometric disk of a spherical planet to the center of the illuminated part of the planet's visible disk. The reduction formulas are derived for direct and inverse transitions between the two aforementioned points of the planetary disk in geocentric equatorial coordinates. The examples of special cases of illumination of visible disks of planets in specific ephemeris are given.