Angles and Range: Initial Orbital Determination with the Air Force Space Surveillance Telescope (AFSST)
Abstract : The institution of a robust, comprehensive program of Space Situational Awareness (SSA) necessarily includes observations by ground-based optical and infrared (OIR) telescopes. The Air Force Space Surveillance Telescope (AFSST) has been proposed as a system of telescopes designed to address the ground-based component of comprehensive SSA. A hallmark of our definition of AFSST is that it be composed of inexpensive, replicable telescopes programmed to accomplish multiple surveillance programs, but designed to achieve the difficult design-driving task of accomplishing an uncued search for small objects in Low Earth Orbit (LEO). We discuss the configuration of AFSST and describe one technique by which AFSST simultaneously acquires angle and range data for accurate real-time determination of LEO orbital elements, even upon first detection of the object.
GPU-accelerated Faint Streak Detection for Uncued Surveillance of LEO
By astronomical standards, small objects (<10cm) in LEO illuminated by the Sun under terminator conditions are quite bright, depositing 100’s to 1000’s of photons per second into small telescope apertures (< 1m diameter). The challenge in discovering these objects with no a priori knowledge of their orbit (i.e. uncued surveillance) is that their relative motion with respect to a ground-based telescope makes them appear to have large angular rates of motion, up to and exceeding 1 degree per second. Thus in even a short exposure, the signal from the object is smeared out in a streak with low signal-to-noise per pixel. Go Green Termite (GGT), Inc. of Gilroy, CA, in collaboration with the University of New Mexico (UNM), is building two proof-of-concept wide-field imaging systems to test, develop and prove a novel streak detection technique. The imaging systems are built from off-the-shelf optics and detectors resulting in a 350mm aperture and a 6 square degree field of view. For streak detection, field of view is of critical importance because the maximum exposure time on the object is limited by its crossing time. In this way, wider fields of view impact surveys for LEO objects both by increasing the survey volume and increasing sensitivity. Using our newly GPU-accelerated detection scheme, the proof-of-concept systems are expected to be able to detect objects fainter than 12 th magnitude moving at 1 degree per second and possibly as faint as 13 th magnitude for slower moving objects. Meter-class optical systems using these techniques should be able to detect objects fainter than 14 th magnitude, which is roughly equivalent to a golf ball at 1000km altitude. The goal of this work is to demonstrate a scalable system for near real time detection of fast moving objects that can be then handed off to other instruments capable of tracking and characterizing them. The two proof-of-concept systems, separated by ~30km, work together by taking simultaneous images of the same volume to constrain the orbits of detected objects using parallax measurements. These detections will then be followed-up by photometric observations taken at UNM to independently assess the objects and the quality of the derived orbits. We believe this will demonstrate the potential of small telescope arrays for detecting and cataloguing heretofore unknown LEO objects. 1. FINDING AND TRACKING LEO OBJECTS WITH OPTICAL TELESCOPES SSA of LEO has to date been the domain of radar, especially in the case of uncued surveys for LEO objects, whereas optical surveys have been more suited to GEO. Optical techniques are not likely to supplant radar , but can supplement it, taking advantage of some of the strengths of optical techniques while accommodating shortcomings. The biggest shortcomings of optical techniques compared to radar for uncued LEO surveys are that optical telescopes must contend with weather and observe during terminator conditions. If we approximate the average terminator illumination duration as 1.5 hours after dusk civil twilight and 1.5 hours before dawn twilight, this leads to a 1/8 factor in coverage of the LEO volume accessible to radar deployed at the same place. Weather will further reduce this (conservatively) by 50%, leading to a total effective coverage of roughly 6% that of radar simply from sky and illumination conditions. The comparative strengths of optical SSA of LEO is that it is passive, using the Sun as the illuminator rather than having to project that power. Optical telescopes are also relatively inexpensive, making them easily deployed around the world, assuming that one can detect sufficiently small objects in the LEO volume with small telescopes. We hope to be able to show over the course of this ongoing work that small telescopes (by which we mean meter-class or smaller) can contribute in exactly this way. The work presented here was conducted as a SBIR Phase I study, so the results shown are based on models and simulations of telescope and detector performance. To the best of our ability we have tried to create these simulations so that they reproduce real data where we have it. Where there are unknowns, we make pessimistic estimates. The second phase of this project where these techniques will be demonstrated with real data has recently begun. In the next section, we will examine the challenges of observing objects in LEO orbits with ground-based optical sensors. Section 3 details the hardware we will use to make detections along with the deployment and operational parameters that are key to making our techniques effective. Section 4 describes the detection algorithm and how implementation on GPUs makes it practical and inexpensive. Section 5 concludes with some possible ways that arrays of small optical telescopes could be deployed to address LEO SSA. 2. SIGNAL-TO-NOISE OF FAST MOVING OBJECTS Objects in LEO under terminator conditions are actually quite bright by astronomical standards. Ackermann et al. 2003 [1] demonstrate the radiometry of LEO objects illuminated by the Sun at 90 degrees to the observer. Figure 1 shows the apparent magnitude of a golf ball (4.2cm diameter, 7 cm 2 projected area illuminated) at various distances above sea level. At 1000 km, the golf ball is a bit brighter than 14 th magnitude in V, an intensity that would deposit hundreds if not thousands of photons per second into a small telescope. If an object this bright can be tracked, it is relatively easy to detect and measure. This brightness estimate does not take into account the typical albedo of objects in space, which is about two magnitudes fainter (13%) than the white of a typical golf ball. Making this correction, 14 th magnitude corresponds to a softball-sized object at 1000 km. Figure 1This figure (from Ackermann et al. 2003 [1]) shows the estimate brightness of canonical targets, one a 95% reflective golf ball (4.2cm diameter) and another a 5% reflective basketball ( diameter) at various orbit altitudes under 90 degree phase (i.e. terminator) illumination. The challenge with uncued observations of LEO objects is that their relative motion is fast enough in relation to their distance that they appear to move at a high angular rate. Figure 2 shows the apparent angular rate for objects in circular orbits as they appear when they pass through the zenith. For objects in the LEO regime from 500 2000 km altitude, the rates range from 0.2 – 1 degree per second. Thus even if those objects deposit thousands of photons into the aperture of a telescope, the light spread out across the detector in a streak that may be over a thousand pixels long, where the signal-to-noise per pixel is much lower than in the tracked case, rendering the object undetectable to most detection algorithms. Figure 2 This figure (from McGraw et al. 2003 [2]) shows the apparent angular rate of objects in circular orbits as viewed passing through the local zenith as a function of orbit altitude. This figure demonstrates the typical angular rates we expect for LEO objects. In the uncued case, there is no a priori knowledge of streak direction or length, other than some constraints on the minimum and maximum rates for LEO objects. To render an observation useful, a few more constraints need to be applied. Simply finding a streak is not in itself very meaningful if the object traversed the entire field of view during the observation; the object could have entered and left at any time and also has an uncertainty in which way along the streak it went (the train track problem). If the object traverses half or less of the field of view during an exposure time, then it will leave endpoints in at least one image for most trajectories across the field of view. Preceding and subsequent images can break the along track direction degeneracy and measuring the endpoints constrains the velocity. Much like traditional astronomical surveys, this puts a premium on field of view, both because it limits the useful integration time and it ultimately sets how much of the LEO volume can be surveyed. Until exposures are fully sky noise limited, meaning the number of sky counts per pixel is much greater than the variance of the read noise, the signal-to-noise of a streak continues to grow, asymptotically reaching the sky noise limit. This differs from the case of point source astronomy where the background contribution to the noise variance grows linearly with time.
Philip Roth’s Great Books: A Reading of The Human Stain
Philip Roth belongs to the first generation of American novelists for whom a university education in the liberal arts was the norm. This essay charts Roth’s developing acquaintance with classical literature, the starting point for Great Books courses in the 1950s, and the implications for his fiction of his understanding of the difference in scope and purpose between the two representative classical genres. It focuses on The Human Stain (2000), the novel in which he reflects most directly upon what tragedy and epic once did, and what might happen to novels if they became more like the one or the other.