Daniel Dombrowski, Air Force Institute of Technology; Robert Bettinger, Air Force Institute of Technology
Keywords: Orbit Determination, Satellite Transit, SSA, Space based mirrors
Abstract:
A novel method of preliminary satellite orbit determination is presented utilizing a union of the techniques used in astronomical occultation analysis, short arc orbit determination techniques integral to asteroid orbit determination, and satellite optical tracking. Departing from the convention of employing ground- and/or space-based radar to obtain angle and position data for near-Earth orbit determination, such information is instead obtained by using a combination of ground or space-based visual light sensor and a space-based mirror. In this new method, the space-based mirror reflects light towards the Earth and the resultant illumination disk is observed for the transit of satellites or other resident space objects (RSO). The sensor observes the passing shadow of the satellite or RSO and directly computes the relative position of the object casting the shadow to the space-based mirror.
Traditionally, the problem of orbit determination based on azimuth and elevation data has been handled using classical angles-only orbit determination techniques, such as Laplaces or Gausss Method. The proposed system creates a novel orbit determination technique using the known geometry of the space-based reflector, illumination disk optical data, and a linearized orbit model. The accuracy of this novel method will be compared with traditional orbit determination techniques for accuracy and to determine applicability for different orbital regimes. This method would meld the advances made in the astronomy field with that of near-Earth orbit determination and could provide particular benefit to spacecraft lost after initial orbit insertion.
Large space-based reflectors have been researched extensively in the past for use in reflecting solar energy back to Earth for a variety of uses including illumination of large urban areas, emergency operations, farming, and enhancing photosynthesis. Should a reasonably large nadir pointing solar reflector be placed into orbit, it would act as a point light source. This would cause anything that passes through its cone of reflected light to cast a shadow onto the Earth with a negligible penumbra creating shadows with well-defined edges. This fact allows for a novel reverse occultation problem. Historically, stellar occultations have been used to determine the shape parameters of objects as far as the Kuiper Belt. In this novel occultation problem, the shadow from a resident space object (RSO) is observed and a translational orbit model is derived using the inertial position and velocity vectors. One of the benefits of this method is that all three components of the inertial position vector can be calculated simultaneously, as opposed to angular data and rates as is common in optical tracking techniques or range and range rates as is common in satellite laser ranging.
In further detail, the satellite or RSO passes through the illumination cone provided by the reflected light from the space-based mirror. The resultant shadow is then observed. Using basic trigonometry, a relative position vector from the space-based mirror to the transiting object is then created utilizing the position of the centroid of the observed shadow and trigonometric data. This relative position vector in the space-based mirrors body reference frame is then converted to the Earth-centered inertial frame. The relative position vector is then added to the position vector of the space-based mirror to result in the position vector of the RSO. Using a linearized model and a high frequency optical sensor the velocity vector of the spacecraft or RSO can then be derived. Having computed an Earth-based inertial position and velocity vector, the RSOs classic two body orbit is then fully determined and can be propagated both forward and backward in time.
An astrodynamicaly accurate software simulation has been developed to create a video upon which to test this technique. This program takes inputs of the space-based mirrors and RSOs classical orbital elements (COEs) and optical sensor parameters and outputs a video simulation and the propagated position data of the space-based mirror. These outputs are then fed into a second software program to analyze the video using the novel orbit determination technique developed herein and outputs the COEs of the RSO. The results from this software will then be compared to show the efficacy of this novel orbit determination technique. Circumstances under which this novel method may prove particularly advantageous will be discussed.
The method proposed is deterministic in nature. In order to increase the efficacy of this model, the research in occultation solutions and short arc orbit determination must be melded. In recent years, short arc orbit determination methods have seen significant research in the realm of asteroid orbit determination as well as satellite optical tracking. This research could prove invaluable to this technique. For the scope of this paper, however, the deterministic model will be applied and tested to gain initial quantitative data for this novel initial orbit determination (IOD) method. It has been shown that accurate orbit determination can be performed with dense observational data (several hundred observations per pass). This is ideally suited to this IOD method. Using either modest frame rate cameras or luminosity sensors hundreds of dense observations can be gathered quickly.
Date of Conference: September 14-17, 2021
Track: Astrodynamics