Innovative methods of correlation and orbit determination for space debris

We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the $J_2$ effect.Comment: 18 page

A Test of Gravitational Theories Including Torsion with the BepiColombo Radio Science Experiment

Within the framework of the relativity experiment of the ESA/JAXA BepiColombo mission to Mercury, which was launched at the end of 2018, we describe how a test of alternative theories of gravity, including torsion can be set up. Following March et al. (2011), the effects of a non-vanishing spacetime torsion have been parameterized by three torsion parameters, t(1), t(2), and t(3). These parameters can be estimated within a global least squares fit, together with a number of parameters of interest, such as post-Newtonian parameters gamma and beta, and the orbits of Mercury and the Earth. The simulations have been performed by means of the ORBIT14 orbit determination software, which was developed by the Celestial Mechanics Group of the University of Pisa for the analysis of the BepiColombo radio science experiment. We claim that the torsion parameters can be determined by means of the relativity experiment of BepiColombo at the level of some parts in 10(-4), which is a significant result for constraining gravitational theories that allow spacetime torsion

Orbit determination of space objects based on sparse optical data

While building up a catalog of Earth orbiting objects, if the available optical observations are sparse, not deliberate follow ups of specific objects, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper we tested two different algorithms (and the related prototype software) recently developed to solve the correlation problem for objects in geostationary orbit (GEO), including the accurate orbit determination by full least squares solutions with all six orbital elements. Because of the presence in the GEO region of a significant subpopulation of high area to mass objects, strongly affected by non-gravitational perturbations, it was actually necessary to solve also for dynamical parameters describing these effects, that is to fit between 6 and 8 free parameters for each orbit. The validation was based upon a set of real data, acquired from the ESA Space Debris Telescope (ESASDT) at the Teide observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits, starting from a sparse time distribution of observations, which would be compatible with a survey capable of covering the region of interest in the sky just once per night. This could result in a significant reduction of the requirements for a future telescope network, with respect to what would have been required with the previously known algorithm for correlation and orbit determination.Comment: 20 pages, 8 figure

Multiple solutions for asteroid orbits: Computational procedure and applications

We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a ``weak'' direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method. In particular, we show that multiple solutions can be used effectively for potential impact monitoring, preliminary orbit determination, asteroid identification, and for the recovery of lost asteroids

The BepiColombo MORE gravimetry and rotation experiments with the ORBIT14 software

The BepiColombomission to Mercury is an ESA/JAXAcornerstone mission, consisting of two spacecraft in orbit around Mercury addressing several scientific issues. One spacecraft is the Mercury Planetary Orbiter, with full instrumentation to perform radio science experiments. Very precise radio tracking from Earth, on-board accelerometer and optical measurements will provide large data sets. From these it will be possible to study the global gravity field of Mercury and its tidal variations, its rotation state and the orbit of its centre of mass. With the gravity field and rotation state, it is possible to constrain the internal structure of the planet. With the orbit of Mercury, it is possible to constrain relativistic theories of gravitation. In order to assess that all the scientific goals are achievable with the required level of accuracy, full cycle numerical simulations of the radio science experiment have been performed. Simulated tracking, accelerometer and optical camera data have been generated, and a long list of variables including the spacecraft initial conditions, the accelerometer calibrations and the gravity field coefficients have been determined by a least-squares fit. The simulation results are encouraging: The experiments are feasible at the required level of accuracy provided that some critical terms in the accelerometer error are moderated. We will show that BepiColombo will be able to provide at least an order of magnitude improvement in the knowledge of Love number k2, libration amplitudes and obliquity, along with a gravity field determination up to degree 25 with a signal-to-noise ratio of 10

Correlation and orbit determination of space objects based on sparse optical data

While building up a catalogue of Earth-orbiting objects, the available optical observations are typically sparse. In this case, no orbit determination is possible without previous correlation of observations obtained at different times. This correlation step is the most computationally intensive, and becomes more and more difficult as the number of objects to be discovered increases. In this paper, we tested two different algorithms, and the related prototype software, recently developed to solve the correlation problem for objects in geostationary orbit (GEO). The algorithms allow the accurate orbit determination by full least-squares solutions with all six orbital elements. The presence of a significant subpopulation of high area-to-mass ratio objects in the GEO region, strongly affected by non-gravitational perturbations, required to solve also for dynamical parameters describing these effects, that is to fit between six and eight free parameters for each orbit. The validation was based upon a set of real data, acquired from the European Space Agency (ESA) Space Debris Telescope (ESASDT) at the Teide Observatory (Canary Islands). We proved that it is possible to assemble a set of sparse observations into a set of objects with orbits. This would allow a survey strategy covering the region of interest in the sky just once per night. As a result, it would be possible to significantly reduce the requirements for a future telescope network, with respect to what would have been required with the previously known algorithms for correlation and orbit determinatio

The radio science experiment with BepiColombo mission to Mercury

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radio science Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. Using radio observables (range and range-rate) performed with very accurate tracking from ground stations, together with optical observations from the on-board high resolution camera (SIMBIO-SYS) and accelerometer readings from the on-board accelerometer (ISA), MORE will be able to measure with unprecedented accuracy the global gravity field of Mercury and the rotation state of the planet. In this work we present the results of a numerical full-cycle simulation of the gravimetry and rotation experiments of MORE: we discuss the accuracies which can be achieved, focussing in particular on the possible benefits from the use of optical observations in support to the tracking measurements

Digital transcriptome profiling of normal and glioblastoma-derived neural stem cells identifies genes associated with patient survival.

BACKGROUND: Glioblastoma multiforme, the most common type of primary brain tumor in adults, is driven by cells with neural stem (NS) cell characteristics. Using derivation methods developed for NS cells, it is possible to expand tumorigenic stem cells continuously in vitro. Although these glioblastoma-derived neural stem (GNS) cells are highly similar to normal NS cells, they harbor mutations typical of gliomas and initiate authentic tumors following orthotopic xenotransplantation. Here, we analyzed GNS and NS cell transcriptomes to identify gene expression alterations underlying the disease phenotype. METHODS: Sensitive measurements of gene expression were obtained by high-throughput sequencing of transcript tags (Tag-seq) on adherent GNS cell lines from three glioblastoma cases and two normal NS cell lines. Validation by quantitative real-time PCR was performed on 82 differentially expressed genes across a panel of 16 GNS and 6 NS cell lines. The molecular basis and prognostic relevance of expression differences were investigated by genetic characterization of GNS cells and comparison with public data for 867 glioma biopsies. RESULTS: Transcriptome analysis revealed major differences correlated with glioma histological grade, and identified misregulated genes of known significance in glioblastoma as well as novel candidates, including genes associated with other malignancies or glioma-related pathways. This analysis further detected several long non-coding RNAs with expression profiles similar to neighboring genes implicated in cancer. Quantitative PCR validation showed excellent agreement with Tag-seq data (median Pearson r = 0.91) and discerned a gene set robustly distinguishing GNS from NS cells across the 22 lines. These expression alterations include oncogene and tumor suppressor changes not detected by microarray profiling of tumor tissue samples, and facilitated the identification of a GNS expression signature strongly associated with patient survival (P = 1e-6, Cox model). CONCLUSIONS: These results support the utility of GNS cell cultures as a model system for studying the molecular processes driving glioblastoma and the use of NS cells as reference controls. The association between a GNS expression signature and survival is consistent with the hypothesis that a cancer stem cell component drives tumor growth. We anticipate that analysis of normal and malignant stem cells will be an important complement to large-scale profiling of primary tumors.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Light-time computations for the BepiColombo radioscience experiment

The radioscience experiment is one of the on board experiment of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian (PN) parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.Comment: 14 pages, 7 figures, corrected reference

Orbit Determination with the two-body Integrals. II

The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for this problem, that we can solve using the powerful tools of computational Algebra. An algorithm to decide if the linkage of two short arcs is successful, i.e. if they belong to the same observed body, is proposed and tested numerically. In this paper we continue the research started in [Gronchi, Dimare, Milani, 'Orbit determination with the two-body intergrals', CMDA (2010) 107/3, 299-318], where the angular momentum and the energy integrals were used. A suitable component of the Laplace-Lenz vector in place of the energy turns out to be convenient, in fact the degree of the resulting system is reduced to less than half.Comment: 15 pages, 4 figure