An adaptive optics aided differential optical positioning for passive orbit determination of the space debris at the geostationary orbit
ABSTRACT
Proliferation of space debris presents an imminent threat to all space assets. The problem is especially severe for the geostationary band of orbits (GEO) because the GEO objects never leave their orbit and, at the same time, are difficult to observe and operate due to large distance from the Earth. Under the influence of tidal forces, even passive GEO objects achieve high local velocities without vacating GEO positions, which may potentially lead to devastating collisions. Our ability to predict collisions in GEO is limited by the scarcity of the accurate orbital data, especially about the small and passive objects. The efforts to address this omission strongly rely on the ground-based optical sensors and, consequently, on the efficient space object detection and tracking techniques. In this paper we propose a passive differential optical debris tracking technique combining adaptive optics and a high accuracy astrometric references resulting in a significant improvement in the GEO object positioning accuracy. The achievable accuracy is estimated via detailed numerical simulations of two telescopes in different locations.
INTRODUCTION
The ever-growing number of space debris is a global and imminent threat affecting nearly all the assets located in space. The problem is even more severe for the Geostationary band of orbits (GEO), arguably the most precious part of the Earth's neighborhood because of its unique properties and dense population. The rate of accumulation of space debris on GEO is higher because unlike the lower orbits which decay with time the GEO objects stay there forever. As it is pointed out in Ref. [1], despite the quite low collision probability estimate for GEO objects based on the current incomplete data about the GEO population is quite low, taking into consideration the (mostly unknown at present) small objects of the size in 10 cm - 1 m range may well increase the collision probability significantly. Our ability to predict collisions in GEO is limited by the accuracy of the orbital data available, especially for the debris which are smaller than the operational satellites and thus have low brightness. The deficiency of the space debris tracking information drives the need for additional ground-based measurement facilities such as the International Scientific Optical Network [2] or the prospective European Space Surveillance System [3].
Passive optical sensors appear to be the only reliable means for the purpose because of long distance to the GEO objects. Their performance is fundamentally limited by three factors: the photon flux reflected from the Sun-illuminated objects, atmospheric seeing and positioning errors of the telescope mount. The first limit can be pushed by the use of larger ground-based telescopes and by longer observations, the second one by the use of Adaptive Optics (AO) [6] and other turbulence compensation techniques such as Speckle Interferometry [7,8], the third one by switching from a telescope mount as an angular measurement reference to highly accurate astrometric references whose appearance is anticipated in the nearest future.
In this paper we propose a passive differential optical tracking technique for the GEO objects combining AO and an extremely accurate astrometric references provided by the GAIA mission [9]. We prove through the numerical simulations the capability to achieve 40 milliarcsecond (mas) accuracy on GEO objects as deem as 15th visible magnitude for the 1.8-meter EOS telescope at Mount Stromlo Observatory (MSO) in Australia (relatively high 35∘ latitude) with AO, and roughly the same accuracy at 19th magnitude for the 3.8-meter UKIRT telescope [10] at Mauna Kea Observatory (MKO) in Hawaii (19∘ latitude) without AO.
In what follows we are going to present the theory of optical differential debris positioning and the factors driving its feasibility (Section 2). Section 3 describes the prospective laser guide star (LGS) AO system to be installed on the 1.8-meter telescope at MSO and expected to play a prominent role in the high-accuracy debris tracking. Section 4 describes in detail the positioning algorithms used in our analysis. Section 5 presents the results of the end-to-end simulations of the optical positioning system working in two significantly different but equally favorable sets of conditions: 1) a small telescope equipped with the efficient AO system operating in bad atmospheric turbulence conditions and 2) a large telescope without AO operating in exceptionally low turbulence. A value of the AO turbulence correction impact on the optical tracking accuracy is also estimated as a side product of our investigation.
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