Three tables of data are presented for Charon. These tables, when used together, enable the observer to compute the position of Charon at any point in its orbit throughout the year.
In determining the position of Charon on the plane of the sky near Pluto, there are five angles to consider. The first two angles, P and P0 are associated with the orientation of Pluto's North polar axis with respect to the semiminor axis of Charon's apparent orbit as observed at the geocenter. The angle P is measured in degrees between Pluto's North polar axis and the position of Charon's apparent semiminor axis at the time of Opposition. The angle P0, also measured in degrees, is an arbitrary fixed integer amount that is chosen close to the value of P. The other three angles are denoted as p1, p2, and p'. The angle p' is the position angle in degrees of Charon as measured to the observer's east from Pluto's North polar axis. The position angle p' = p1 + p2, where p1 is the angle between Charon's position at Opposition and a chosen point in it's apparent orbit around Pluto that starts with the first Northern elongation after Opposition, and p2 is the difference P - P0.
Values of p2 and a/Δ at 0.0 hours UT are presented in the first table (found using the Satellite Offsets link) for selected days of a particular year. The quantity a/Δ, expressed in arcseconds, is the ratio of Charon's semimajor axis length at unit distance (arcseconds/AU) divided by the distance between Earth and Pluto at the time of interest (in AU). The second table (also found using the Satellite Offsets link) gives the value of p1 for Charon at equally spaced times over the course of the orbit that begins with the first Northern elongation after the time of Opposition. At each interval within one orbital period, a ratio F is also computed, where F is a scaling factor for the specific orbit chosen. It is the apparent size of Charon's semimajor axis at that time in the chosen orbit, expressed in arcseconds, divided by a/Δ.
To summarize, the first table serves to give positional information for the satellite with respect to the planet at the beginning of each chosen day; the second table gives the positional information of the satellite within one orbital period. The position angle at any time in Charon's orbit is p' = p1 + p2.
Data for Nix and Hydra are not included here due to the dimness of those satellites.