Satellite Optical Brightness

Abstract

The apparent brightness of satellites is calculated as a function of satellite position as seen by a ground-based observer in darkness. Both direct illumination of the satellite by the Sun as well as indirect illumination due to reflection from the Earth are included. The reflecting properties of the satellite components and of the Earth must first be estimated (the Bidirectional Reflectance Distribution Function, or BRDF). The reflecting properties of the satellite components can be found directly using lab measurements or accurately inferred from multiple observations of a satellite at various solar angles. Integrating over all scattering surfaces leads to the angular pattern of flux from the satellite. Finally, the apparent brightness of the satellite as seen by an observer at a given location is calculated as a function of satellite position. We develop an improved model for reflection of light from Earth’s surface using aircraft data. We find that indirectly reflected light from Earth’s surface contributes significant increases in apparent satellite brightness. This effect is particularly strong during civil twilight. We validate our approach by comparing our calculations to multiple observations of selected Starlink satellites and show significant improvement on previous satellite brightness models. Similar methodology for predicting satellite brightness has already informed mitigation strategies for next-generation Starlink satellites. Measurements of satellite brightness over a variety of solar angles widens the effectiveness of our approach to virtually all satellites. We demonstrate that an empirical model in which reflecting functions of the chassis and the solar panels are fit to observed satellite data performs very well. This work finds application in satellite design and operations, and in planning observatory data acquisition and analysis.

Expected Impact of Glints from Space Debris in the LSST

“…An average albedo of 0.1 is meant to cover a range of debris. In reality, most centimeter-scale debris are expected to be dominated by specular flat surfaces with albedos approaching 1, tumbling on a range of timescales (Fankhauser et al 2023). Thus a broad distribution of glint duration is expected, extending up to second-timescale flares (Vestrand et al 2022).…”

“…LEO satellite brightness, including flares in brightness, is possible to model accurately given full knowledge of the bidirectional reflectance distribution function (BRDF) of all satellite components (Fankhauser et al 2023). However, we do not have this capability for space debris.…”

“…We point out that the model of a uniformly diffuse debris object with an albedo maximum of 1 can be incorrect for mirror-like surfaces such as shards of multilayer insulation, and even small debris objects will often have a combination of diffuse and reflective surfaces. The BRDF of specular surfaces can have a sharp peak reaching 100 over 1 deg angular range (Fankhauser et al 2023). Conveniently for LSST, lab measurements show a significant minimum at LSST filter wavelengths for various spacecraft materials (Bowers et al 2011).…”

BRDF-Based Photometric Modeling of LEO Constellation Satellite from Massive Observations

“…Additionally, the integrated satellite BRDF model must be corrected for the blocking effect of the chassis on the incident and reflected light from the solar array. The modeling of the external light source considers both direct sunlight and sunlight reflected from the Earth's surface (earthshine) [18,21]. Finally, the photometric prediction model is established by converting the flux given by the BRDF model to astronomical magnitude based on the apparent magnitude of the Sun.…”

“…However, the model does not consider earthshine contributions, which may result in reduced fidelity in the observation geometry dominated by earthshine. The BRDF models of the Starlink V1.5 satellite were established based on laboratory measurements and astronomical observations [21]. The observational best-fit model also includes reflections from the chassis and solar array, and accounts for the earthshine effects of the chassis in the model.…”