Computing Apparent Planetary Magnitudes for The Astronomical Almanac

TL;DR

This paper presents improved equations for calculating planetary magnitudes across various bands, incorporating new terms and extensive statistical analysis, to enhance the accuracy of astronomical observations and ephemerides.

Contribution

The paper introduces novel formulas for planetary magnitudes that include additional physical parameters and provides comprehensive data and source code for practical application.

Findings

Mean, variation, and extreme magnitudes for each planet are reported.

Equations incorporate rotation, revolution, and secular time dependence.

Supplementary equations extend phase angle calculations beyond geocentric limits.

Abstract

Improved equations for computing planetary magnitudes are reported. These formulas model V-band observations acquired from the time of the earliest filter photometry in the 1950s up to the present era. The new equations incorporate several terms that have not previously been used for generating physical ephemerides. These include the rotation and revolution angles of Mars, the sub-solar and sub-Earth latitudes of Uranus, and the secular time dependence of Neptune. Formulas for use in The Astronomical Almanac cover the planetary phase angles visible from Earth. Supplementary equations cover those phase angles beyond the geocentric limits. Geocentric magnitudes were computed over a span of at least 50 years and the results were statistically analyzed. The mean, variation and extreme magnitudes for each planet are reported. Other bands besides V on the Johnson-Cousins and Sloan photometric systems are briefly discussed. The planetary magnitude data products available from the U.S. Naval Observatory are also listed. An appendix describes source code and test data sets that are available on-line for computing planetary magnitudes according to the equations and circumstances given in this paper. The files are posted as supplementary material for this paper. They are also available at SourceForge under project https://sourceforge.net/projects/planetary-magnitudes/ under the 'Files' tab in the folder 'Ap_Mag_Current_Version'.