Timothy Olson, Slingshot Aerospace; Clarice Reid, Slingshot Aerospace; Russ Johnson, Slingshot Aerospace; Jeff Shaddix, Slingshot Aerospace; Dylan Kesler, Slingshot Aerospace; Belinda Marchand, Slingshot Aerospace
Keywords: Earthshine, LEO, Optical Systems, Modeling, Data Analysis, Small Aperture, Wide Field of View Optical Systems, Machine Learning
Abstract:
Reflectance modeling is important for the study of object photometry and development of optical tracking systems. When estimating resident space object (RSO) brightness, it is essential to not only model solar light that is reflected directly off the RSO but also to capture significant contributions from other sources such as solar light reflected off nearby celestial bodies. The contribution of solar light that is reflected off of the Earth’s surface onto a nearby RSO is colloquially known as “earthshine”. We provide a side-by-side comparison of several existing and novel models which seek to capture the impact of earthshine on predicted RSO brightness and to compare those results to RSO brightness in several illumination conditions with analytic, numerical, and data-driven methods.
There is a significant corpus of research available for models developed on a select subsets of RSOs, but these models fall short in analyzing utility for widespread application. In this paper, we investigate and evaluate three families of earthshine models for low Earth orbit (LEO) satellite photometry, highlighting the effects on a diverse collection of RSOs spanning multiple orbits, sizes, and shapes. We expand upon prior analytical and numerical methods and present a novel data-driven approach from a data set of over 1 billion photometric observations collected on the majority of objects in LEO with optical fences and daytime-capable optical telescope systems. The models are evaluated for accuracy, run-time, and necessary compute resources across synthetic and real data collected by daytime-capable and traditional nighttime electro-optical sensor systems. Ultimately, the contribution of this work is to capture the impact of earthshine on predicted RSO brightness while addressing the question of feasible computational costs and generalizability given the ever-mounting RSO population in LEO.
Previously proposed earthshine models are compared in this work in addition to novel models. As such, we consider models in which Earth is assumed to be a diffuse sphere as has been applied in modelling earthshine for targets in geosynchronous Earth orbit (GEO), as well as more sophisticated models in which geometric illumination constraints are applied. Specular bidirectional reflectance distribution functions (BRDFs) are considered as well to capture non-diffuse reflections from the Earth and in particular bodies of water as part of this comparison via a standard Phong reflection model. We perform the analyses with real and synthetic photometric data across multiple representative satellite geometries, generating data-driven best fit approximations using real observations to estimate unknown model parameters. The predicted RSO brightnesses from these earthshine models are compared against observed illumination of RSOs in LEO outside of the sample set in an effort to demonstrate the efficacy of each model in capturing the illumination levels of each target and assess the applicability of the model to broad target sets in LEO.
The models and experiments discussed provide information about the performance of each on a diverse set of LEO RSOs. We also evaluate how applicable these models are when used in practice, exploring the pros and cons of each approach and estimating minimum necessary model complexity for useful results on a range of LEO objects and illumination conditions based on the efficacy of the model to accurately produce photometric estimates. We discuss how these results affect choices for earthshine modeling in systems and identify future research.
Date of Conference: September 16-19, 2025
Track: Satellite Characterization