Relative estimate of accuracy in orbit determination from a short tracklet

The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for orbital debris. The debris objects are discovered during systematic survey observations. In general only a short observation arc, or tracklet, is available for most of these objects. From this discovery tracklet a first orbit determination is computed in order to be able to find the object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In this paper, the accuracy of the initial orbit determination is analyzed. This depends on a number of factors: tracklet length, number of observations, type of orbit, astrometric error, and observation geometry. The latter is characterized by both the position of the object along its orbit and the location of the observing station. Different positions involve different distances from the target object and a different observing angle with respect to its orbital plane and trajectory. The present analysis aims at optimizing the geometry of the discovery observation is depending on the considered orbit.

A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

Kelvin-Helmholtz instabilities at the magnetic cavity boundary of comet 67P/Churyumov-Gerasimenko

We investigate the plasma environment of comet 67P/Churyumov-Gerasimenko, the target of the European Space Agency's Rosetta mission. Rosetta will rendezvous with the comet in 2014 at almost 3.5 AU and follow it all the way to and past perihelion at 1.3 AU. During its journey towards the inner solar system the comet's environment will significantly change. The interaction of the solar wind with a well developed neutral coma leads to the formation of an upstream bow shock and, closer to the comet, the inner shock separating the solar wind, with cometary pick-up ions mass-loaded, from the inner cometary ions which are dragged outward through abundant collisions and charge exchange with the expanding neutral gas. As a consequence the interplanetary magnetic field is prevented from penetrating the innermost region of the comet, the so-called magnetic cavity. We use our magnetohydrodynamics model BATSRUS (Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme) to simulate the solar wind - comet interaction. The model includes photoionization, ion-electron recombination, and charge exchange. Under certain conditions our model predicts an unstable plasma flow at the inner shock. We show that the plasma shear flow around the magnetic cavity can lead to Kelvin-Helmholtz instabilities. We investigate the onset of this phenomenon with change of heliocentric distance and furthermore show that a previously stable magnetic cavity boundary can become unstable when the neutral gas is predominately released from the dayside of the comet.

Narrow dust jets in a diffuse gas coma: a natural product of small active regions on comets

Comets often display narrow dust jets but more diffuse gas comae when their eccentric orbits bring them into the inner solar system and sunlight sublimates the ice on the nucleus. Comets are also understood to have one or more active areas covering only a fraction of the total surface active with sublimating volatile ices. Calculations of the gas and dust distribution from a small active area on a comet’s nucleus show that as the gas moves out radially into the vacuum of space it expands tangentially, filling much of the hemisphere centered on the active region. The dust dragged by the gas remains more concentrated over the active area. This explains some puzzling appearances of comets having collimated dust jets but more diffuse gaseous atmospheres. Our test case is 67P/Churyumov–Gerasimenko, the Rosetta mission target comet, whose activity is dominated by a single area covering only 4% of its surface.

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659−677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ∼30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241−248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.

Inventory of the volatiles on comet 67P/Churyumov-Gerasimenko from Rosetta/ROSINA

Context. The ESA Rosetta spacecraft (S/C) is tracking comet 67P/Churyumov-Gerasimenko in close vicinity. This prolonged encounter enables studying the evolution of the volatile coma composition. Aims. Our work aims at comparing the diversity of the coma of 67P/Churyumov-Gerasimenko at large heliocentric distance to study the evolution of the comet during its passage around the Sun and at trying to classify it relative to other comets. Methods. We used the Double Focussing Mass Spectrometer (DFMS) of the ROSINA experiment on ESA’s Rosetta mission to determine relative abundances of major and minor volatile species. This study is restricted to species that have previously been detected elsewhere. Results. We detect almost all species currently known to be present in cometary coma with ROSINA DFMS. As DFMS measured the composition locally, we cannot derive a global abundance, but we compare measurements from the summer and the winter hemisphere with known abundances from other comets. Differences between relative abundances between summer and winter hemispheres are large, which points to a possible evolution of the cometary surface. This comet appears to be very rich in CO2 and ethane. Heavy oxygenated compounds such as ethylene glycol are underabundant at 3 AU, probably due to their high sublimation temperatures, but nevertheless, their presence proves that Kuiper belt comets also contain complex organic molecules.

Photometric monitoring of non-resolved space debris and databases of optical light curves.

The population of space debris increased drastically during the last years. Collisions involving massive objects may produce large number of fragments leading to significantly growth of the space debris population. An effective remediation measure in order to stabilize the population in LEO, is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period and spin axis orientation. If we observe a rotating object, the observer sees different surface areas of the object which leads to changes in the measured intensity. Rotating objects will produce periodic brightness vari ations with frequencies which are related to the spin periods. Photometric monitoring is the real tool for remote diagnostics of the satellite rotation around its center of mass. This information is also useful, for example, in case of contingency. Moreover, it is also important to take into account the orientation of non-spherical body (e.g. space debris) in the numerical integration of its motion when a close approach with the another spacecr aft is predicted. We introduce the two databases of light curves: the AIUB data base, which contains about a thousand light curves of LEO, MEO and high-altitude debris objects (including a few functional objects) obtained over more than seven years, and the data base of the Astronomical Observatory of Odessa University (Ukraine), which contains the results of more than 10 years of photometric monitoring of functioning satellites and large space debris objects in low Earth orbit. AIUB used its 1m ZIMLAT telescope for all light curves. For tracking low-orbit satellites, the Astronomical Observatory of Odessa used the KT-50 telescope, which has an alt-azimuth mount and allows tracking objects moving at a high angular velocity. The diameter of the KT-50 main mirror is 0.5 m, and the focal length is 3 m. The Odessa's Atlas of light curves includes almost 5,5 thousand light curves for ~500 correlated objects from a time period of 2005-2014. The processing of light curves and the determination of the rotation period in the inertial frame is challenging. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for confirmation, will be presented. The rotation of the Envisat satellite after its sudden failure will be analyzed. The deceleration of its rotation rate within 3 years is studied together with the attempt to determine the orientation of the rotation axis.

CODE rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland;Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context a rapid solution series is generated considering all active GPS and GLONASS satellites. It contains 24 hours of observed orbits and published at the day after the observations.

The CODE MGEX orbit and clock solution

The Center for Orbit Determination in Europe (CODE) is contributing as a global Analysis center to the International GNSS Service (IGS) since many years. The processing of GPS and GLONASS data is well established in CODE’s ultra-rapid, rapid, and final product lines. With the introduction of new signals for the established and new GNSS, new challenges and opportunities are arising for the GNSS data management and processing. The IGS started the Multi-GNSS-EXperiment (MGEX) in 2012 in order to gain first experience with the new data formats and to develop new strategies for making optimal use of these additional measurements. CODE has started to contribute to IGS MGEX with a consistent, rigorously combined triple-system orbit solution (GPS, GLONASS, and Galileo). SLR residuals for the computed Galileo satellite orbits are of the order of 10 cm. Furthermore CODE established a GPS and Galileo clock solution. A quality assessment shows that these experimental orbit and clock products allow even a Galileo-only precise point positioning (PPP) with accuracies on the decimeter- (static PPP) to meter-level (kinematic PPP) for selected stations.

Impact of the arc length on GNSS analysis results

Homogeneously reprocessed combined GPS/GLONASS 1- and 3-day solutions from 1994 to 2013, generated by the Center for Orbit Determination in Europe (CODE) in the frame of the second reprocessing campaign REPRO-2 of the International GNSS Service, as well as GPS- and GLONASS-only 1- and 3-day solutions for the years 2009 to 2011 are analyzed to assess the impact of the arc length on the estimated Earth Orientation Parameters (EOP, namely polar motion and length of day), on the geocenter, and on the orbits. The conventional CODE 3-day solutions assume continuity of orbits, polar motion components, and of other parameters at the day boundaries. An experimental 3-day solution, which assumes continuity of the orbits, but independence from day to day for all other parameters, as well as a non-overlapping 3-day solution, is included into our analysis. The time series of EOPs, geocenter coordinates, and orbit misclosures, are analyzed. The long-arc solutions were found to be superior to the 1-day solutions: the RMS values of EOP and geocenter series are typically reduced between 10 and 40 %, except for the polar motion rates, where RMS reductions by factors of 2–3 with respect to the 1-day solutions are achieved for the overlapping and the non-overlapping 3-day solutions. In the low-frequency part of the spectrum, the reduction is even more important. The better performance of the orbits of 3-day solutions with respect to 1-day solutions is also confirmed by the validation with satellite laser ranging.

Search for satellites near comet 67P/Churyumov-Gerasimenko using Rosetta/OSIRIS images

Context. The European Space Agency Rosetta mission reached and started escorting its main target, the Jupiter-family comet 67P/Churyumov-Gerasimenko, at the beginning of August 2014. Within the context of solar system small bodies, satellite searches from approaching spacecraft were extensively used in the past to study the nature of the visited bodies and their collisional environment. Aims. During the approaching phase to the comet in July 2014, the OSIRIS instrument onboard Rosetta performed a campaign aimed at detecting objects in the vicinity of the comet nucleus and at measuring these objects' possible bound orbits. In addition to the scientific purpose, the search also focused on spacecraft security to avoid hazardous material in the comet's environment. Methods. Images in the red spectral domain were acquired with the OSIRIS Narrow Angle Camera, when the spacecraft was at a distance between 5785 km and 5463 km to the comet, following an observational strategy tailored to maximize the scientific outcome. From the acquired images, sources were extracted and displayed to search for plausible displacements of all sources from image to image. After stars were identified, the remaining sources were thoroughly analyzed. To place constraints on the expected displacements of a potential satellite, we performed Monte Carlo simulations on the apparent motion of potential satellites within the Hill sphere. Results. We found no unambiguous detections of objects larger than similar to 6 m within similar to 20 km and larger than similar to 1 m between similar to 20 km and similar to 110 km from the nucleus, using images with an exposure time of 0.14 s and 1.36 s, respectively. Our conclusions are consistent with independent works on dust grains in the comet coma and on boulders counting on the nucleus surface. Moreover, our analysis shows that the comet outburst detected at the end of April 2014 was not strong enough to eject large objects and to place them into a stable orbit around the nucleus. Our findings underline that it is highly unlikely that large objects survive for a long time around cometary nuclei.

Orbital elements of the material surrounding comet 67P/Churyumov-Gerasimenko

Context. We investigate the dust coma within the Hill sphere of comet 67P/Churyumov-Gerasimenko. Aims. We aim to determine osculating orbital elements for individual distinguishable but unresolved slow-moving grains in the vicinity of the nucleus. In addition, we perform photometry and constrain grain sizes. Methods. We performed astrometry and photometry using images acquired by the OSIRIS Wide Angle Camera on the European Space Agency spacecraft Rosetta. Based on these measurements, we employed standard orbit determination and orbit improvement techniques. Results. Orbital elements and effective diameters of four grains were constrained, but we were unable to uniquely determine them. Two of the grains have light curves that indicate grain rotation. Conclusions. The four grains have diameters nominally in the range 0.14-0.50 m. For three of the grains, we found elliptic orbits, which is consistent with a cloud of bound particles around the nucleus. However, hyperbolic escape trajectories cannot be excluded for any of the grains, and for one grain this is the only known option. One grain may have originated from the surface shortly before observation. These results have possible implications for the understanding of the dispersal of the cloud of bound debris around comet nuclei, as well as for understanding the ejection of large grains far from the Sun.

Regional surface morphology of comet 67P/Churyumov-Gerasimenko from Rosetta/OSIRIS images

Aims. The OSIRIS camera onboard the Rosetta spacecraft has been acquiring images of the comet 67P/Churyumov-Gerasimenko (67P)'s nucleus at spatial resolutions down to similar to 0.17 m/px ever since Aug. 2014. These images have yielded unprecedented insight into the morphological diversity of the comet's surface. This paper presents an overview of the regional morphology of comet 67P. Methods. We used the images that were acquired at orbits similar to 20-30 km from the center of the comet to distinguish different regions on the surface and introduce the basic regional nomenclature adopted by all papers in this Rosetta special feature that address the comet's morphology and surface processes. We used anaglyphs to detect subtle regional and topographical boundaries and images from close orbit (similar to 10 km from the comet's center) to investigate the fine texture of the surface. Results. Nineteen regions have currently been defined on the nucleus based on morphological and/or structural boundaries, and they can be grouped into distinctive region types. Consolidated, fractured regions are the most common region type. Some of these regions enclose smooth units that appear to settle in gravitational sinks or topographically low areas. Both comet lobes have a significant portion of their surface covered by a dusty coating that appears to be recently placed and shows signs of mobilization by aeolian-like processes. The dusty coatings cover most of the regions on the surface but are notably absent from a couple of irregular large depressions that show sharp contacts with their surroundings and talus-like deposits in their interiors, which suggests that short-term explosive activity may play a significant role in shaping the comet's surface in addition to long-term sublimation loss. Finally, the presence of layered brittle units showing signs of mechanical failure predominantly in one of the comet's lobes can indicate a compositional heterogeneity between the two lobes.

Insolation, erosion, and morphology of comet 67P/Churyumov-Gerasimenko

Context. The complex shape of comet 67P and its oblique rotation axis cause pronounced seasonal effects. Irradiation and hence activity vary strongly. Aims. We investigate the insolation of the cometary surface in order to predict the sublimation of water ice. The strongly varying erosion levels are correlated with the topography and morphology of the present cometary surface and its evolution. Methods. The insolation as a function of heliocentric distance and diurnal (spin dependent) variation is calculated using >10(5) facets of a detailed digital terrain model. Shading, but also illumination and thermal radiation by facets in the field of view of a specific facet are iteratively taken into account. We use a two-layer model of a thin porous dust cover above an icy surface to calculate the water sublimation, presuming steady state and a uniform surface. Our second model, which includes the history of warming and cooling due to thermal inertia, is restricted to a much simpler shape model but allows us to test various distributions of active areas. Results. Sublimation from a dirty ice surface yields maximum erosion. A thin dust cover of 50 pm yields similar rates at perihelion. Only about 6% of the surface needs to be active to match the observed water production rates at perihelion. A dust layer of 1 mm thickness suppresses the activity by a factor of 4 to 5. Erosion on the south side can reach more than 10 m per orbit at active spots. The energy input to the concave neck area (Hapi) during northern summer is enhanced by about 50% owing to self-illumination. Here surface temperatures reach maximum values along the foot of the Hathor wall. Integrated over the whole orbit this area receives the least energy input. Based on the detailed shape model, the simulations identify "hot spots" in depressions and larger pits in good correlation with observed dust activity. Three-quarters of the total sublimation is produced while the sub-solar latitude is south, resulting in a distinct dichotomy in activity and morphology. Conclusions. The northern areas display a much rougher morphology than what is seen on Imhotep, an area at the equator that will be fully illuminated when 67P is closer to the Sun. Self-illumination in concave regions enhance the energy input and hence erosion. This explains the early activity observed at Hapi. Cliffs are more prone to erosion than horizontal, often dust covered, areas, which leads to surface planation. Local activity can only persist if the forming cliff walls are eroding. Comet 67P has two lobes and also two distinct sides. Transport of material from the south to the north is probable. The morphology of the Imhotep plain should be typical for the terrains of the yet unseen southern hemisphere.