# Notes on Uranian Satellite Offsets and Elongation Times

Three tables of data are presented for each of the Uranian satellites. These tables, when used together, enable the observer to compute the position of a given satellite at any point in its orbit throughout the year.

The first table (found using the Satellite Offsets link) gives the angular separation, position angle, and a/Δ values for each satellite at 0.0 hours UT for each day of a particular year. The time is expressed as a Julian date. The angular separation is given in arcseconds and is the distance from the center of Uranus to the center of the Uranian satellite of interest as viewed from the geocenter. The position angle, given in degrees, is measured to the observer's East from an axis that points towards the Celestial North Pole with origin at the center of the apparent disk of Uranus. The last quantity, a/Δ, expressed in arcseconds, is the ratio of the satellite's semimajor axis length at unit distance (arcseconds/AU) divided by the distance between Earth and Uranus at the time of interest (in AU).

The second table (also found using the Satellite Offsets link) gives the position of each satellite at equally spaced times over the course of one orbit. That orbit is the one that starts at the first northern elongation after opposition. At each interval within one orbital period, a ratio F and a position angle p' are computed. F is a scaling factor for the specific orbit chosen. It is the apparent size of the satellite's semimajor axis at that time in the chosen orbit, expressed in arcseconds, divided by a/Δ. The position angle, p', is that of the given satellite at that moment in time in the chosen orbit. Due to the observed orientation of the Uranian system, rapid changes in the position angle can occur when the satellites cross the polar axis of Uranus.

The third table (found under the Satellite Elongation Times link) is the table of elongation times; it gives the time of each northern elongation throughout the year.

To summarize, the first table serves to give positional information for the satellite with respect to the planet at the beginning of each day; the second table gives the positional information of the satellite within one orbital period; the third table gives the time of each new orbital period.

The Astronomical Almanac Online! 2020