Determination of the Brightness Temperature of Planet Mercury by Employing Magnitude - Time Graphs on Stellarium

Abstract

This study presents a novel approach to estimating the brightness temperature of Planet Mercury by employing magnitude–time graphs generated via the Stellarium astronomical simulation software. Brightness temperature, a measure of the effective temperature of a celestial body based on its radiative output, provides insight into the planet’s thermal properties and surface conditions. Stellarium was employed to generate magnitude–time datasets for Mercury across selected observation periods, accounting for its orbital position, phase angle, and distance from Earth. The magnitude–time graphs were constructed to identify peak and minimum brightness values, which were subsequently converted into flux densities using standard photometric relations using Pogson’s equation. A modified form of the Stefan–Boltzmann law, adapted to account for Mercury’s phase angle and emissivity variations, was applied to model the planet’s thermal emission. The analysis integrates the concept of radiative equilibrium to reconcile observed brightness with theoretical temperature predictions, considering Mercury’s lack of a substantial atmosphere and its extreme diurnal temperature variations. Results demonstrate that the combined use of Stellarium-based photometry and the adapted mathematical model yields brightness temperature estimates, ranging from 445 ± 15 K during dim phases to 698 ± 20 K at peak illumination. These results prove to be consistent with established observational data, while offering a computationally accessible method for planetary thermal characterization. This methodology has potential applications in educational settings, amateur astronomy, and preliminary planetary science research. Future work could refine accuracy by incorporating atmospheric seeing effects, albedo variations, and multi-wavelength magnitude data to better approximate Mercury’s true surface temperature distribution.