Jovan Skuljan, Defence Technology Agency
Keywords: Photometry, light-curve modelling, GEO satellites
Abstract:
A comprehensive three-dimensional photometric model was developed at the Defence Technology Agency (DTA) to study the light curves of satellites in geostationary orbit (GEO). The model treats a satellite as a collection of small flat facets, where each facet has its own light-reflection properties. A complete three-dimensional lighting geometry was considered, including the direct sunlight, moonlight and earthshine (the sunlight reflected from the Earth). The reflection of light was modelled based on the Ashikhmin-Shirley anisotropic bidirectional reflectance distribution function (BRDF), which ensures energy conservation, while allowing for both the diffuse and specular components of the reflection. Special attention was placed on the earthshine component of the lighting model, as this was found to be the predominant source of illumination at large solar phase angles. The illuminated part of the Earth was modelled as an extended source of light, while taking into account both the geographic and seasonal variations of the surface albedo across the globe. This was based on the data from the Global Ozone Monitoring Experiment (GOME), an instrument aboard the European Space Agencys (ESA) Second European Remote Sensing Satellite (ERS-2).
The software implementation of the model was written in Delphi. The application has a built-in module for the orbital positions of the Sun, Earth and Moon, based on the Jet Propulsion Laboratory’s (JPL) solar system ephemeris DE441 (with an option for a different ephemeris file to be selected instead). All coordinate transformations are performed using the International Astronomical Union’s (IAU) Standards of Fundamental Astronomy (SOFA) library, in combination with the current values for the Earth orientation parameters (EOP). In addition, the built-in SGP4 propagator converts the TLE parameters into a state vector, to complete the viewing geometry. This allows the program to generate the apparent magnitudes for any observer over the specified time interval.
The DTA photometric model was tested using a number of observations of GEO satellites over the Pacific, collected from the DTA Space Domain Awareness (SDA) Observatory at Whangaparaoa Peninsula near Auckland, New Zealand. An 11-inch (279-mm) Celestron Edge HD Cassegrain telescope on a Paramount MEII robotic mount was used, equipped with a Finger Lakes Instrumentation (FLI) ML-11002 CCD camera. All observations were reduced using StarView, an SDA image analysis tool developed at DTA for astrometric, photometric and polarimetric measurements of satellite observations. The second data release (DR-2) of the ESA’s GAIA catalogue, limited down to magnitude 16, was used for data calibration. A typical photometric calibration based on the GAIA G-band produced an RMS error of about 0.1 magnitudes, mainly caused by stellar colours. At the same time, the random measurement errors in the aperture photometry were about 0.02, over a wide range of apparent magnitudes.
A number of light curves of selected objects in the GEO belt were collected and compared with the model predictions, for a broad range of input parameters, such as the satellite’s overall shape and size, as well as the reflectivity properties of the individual facets. It was demonstrated that inexpensive small-aperture optical equipment can be successfully used to examine the photometric properties of satellites in GEO regime and collect important information for space domain awareness.
Date of Conference: September 14-17, 2021
Track: Non-Resolved Object Characterization