Precise Orbit Determination of Low Earth Satellites at AIUB using GPS and SLR data

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite’s solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case. Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The reasons are threefold: The direct SRP is about a factor of 30–40 smaller for typical geodetic SLR satellites than for GNSS satellites, allowing it in most cases to not solve for SRP parameters (ruling out the correlation between these parameters and the geocenter coordinates); the orbital arc length of 7 days (which is typically used in SLR analysis) contains more than 50 revolutions of the LAGEOS satellites as compared to about two revolutions of GNSS satellites for the daily arcs used in GNSS analysis; the orbit geometry is not as critical for LAGEOS as for GNSS satellites, because the elevation angle of the Sun w.r.t. the orbital plane is usually significantly changing over 7 days.

Impact of loading displacements on SLR-derived parameters and on the consistency between GNSS and SLR results

Displacements of the Earth’s surface caused by tidal and non-tidal loading forces are relevant in high-precision space geodesy. Some of the corrections are recommended by the international scientific community to be applied at the observation level, e.g., ocean tidal loading (OTL) and atmospheric tidal loading (ATL). Non-tidal displacement corrections are in general recommended not to be applied in the products of the International Earth Rotation and Reference Systems Service, in particular atmospheric non-tidal loading (ANTL), oceanic and hydrological non-tidal corrections. We assess and compare the impact of OTL, ATL and ANTL on SLR-derived parameters by reprocessing 12 years of SLR data considering and ignoring individual corrections. We show that loading displacements have an influence not only on station long-term stability, but also on geocenter coordinates, Earth Rotation Parameters, and satellite orbits. Applying the loading corrections reduces the amplitudes of annual signals in the time series of geocenter and station coordinates. The general improvement of the SLR station 3D coordinate repeatability when applying OTL, ATL and ANTL corrections are 19.5 %, 0.2 % and 3.3 % respectively, w.r.t. the solutions without loading corrections. ANTL corrections play a crucial role in the combination of optical (SLR) and microwave (GNSS, VLBI, DORIS) space geodetic observation techniques, because of the so-called Blue-Sky effect: SLR measurements can be carried out only under cloudless sky conditions—typically during high air pressure conditions, when the Earth’s crust is deformed, whereas microwave observations are weather-independent. Thus, applying the loading corrections at the observation level improves SLR-derived products as well as the consistency with microwave-based results. We assess the Blue-Sky effect on SLR stations and the consistency improvement between GNSS and SLR solutions when ANTL corrections are included. The omission of ANTL corrections may lead to inconsistencies between SLR and GNSS solutions of up to 2.5 mm for inland stations. As a result, the estimated GNSS–SLR coordinate differences correspond better to the local ties at the co-located stations when applying ANTL corrections.

Time-variable gravity signal in Greenland revealed by high-low satellite-to-satellite tracking

[1] In the event of a termination of the Gravity Recovery and Climate Experiment (GRACE) mission before the launch of GRACE Follow-On (due for launch in 2017), high-low satellite-to-satellite tracking (hl-SST) will be the only dedicated observing system with global coverage available to measure the time-variable gravity field (TVG) on a monthly or even shorter time scale. Until recently, hl-SST TVG observations were of poor quality and hardly improved the performance of Satellite Laser Ranging observations. To date, they have been of only very limited usefulness to geophysical or environmental investigations. In this paper, we apply a thorough reprocessing strategy and a dedicated Kalman filter to Challenging Minisatellite Payload (CHAMP) data to demonstrate that it is possible to derive the very long-wavelength TVG features down to spatial scales of approximately 2000 km at the annual frequency and for multi-year trends. The results are validated against GRACE data and surface height changes from long-term GPS ground stations in Greenland. We find that the quality of the CHAMP solutions is sufficient to derive long-term trends and annual amplitudes of mass change over Greenland. We conclude that hl-SST is a viable source of information for TVG and can serve to some extent to bridge a possible gap between the end-of-life of GRACE and the availability of GRACE Follow-On.

Combined LARES-LAGEOS Solutions

LARES is a new spherical geodetic satellite designed for SLR observations. It is made of solid tungsten alloy covered with 92 corner cubes. Due to a very small area-to-mass ratio, the sensitivity of LARES orbits to non-gravitational forces is greatly minimized. We processed 82 weeks (Feb12-Aug13) of LARES observations from a global SLR network and we analyzed the contribution of LARES data to the current SLR products (e.g., global scale and geocenter coordinates). The quality of the combined LARES+LAGEOS-1/2 solutions is also addressed in the paper. Introduction LARES

Earth gravity field recovery using GPS, GLONASS, and SLR satellites

The time variable Earth’s gravity field provides the information about mass transport within the system Earth, i.e., the relationship of mass transport between atmosphere, oceans, and land hydrology. We recover the low-degree parameters of the time variable gravity field using microwave observations from GPS and GLONASS satellites and from SLR data to five geodetic satellites, namely LAGEOS-1/2, Starlette, Stella, and AJISAI. GPS satellites are particularly sensitive to specific coefficients of the Earth's gravity field, because of the deep 2:1 orbital resonance with Earth rotation (two revolutions of the GPS satellites per sidereal day). The resonant coefficients cause, among other, a “secular” drift (actually periodic variations of very long periods) of the semi-major axes of up to 5.3 m/day of GPS satellites. We processed 10 years of GPS and GLONASS data using the standard orbit models from the Center of Orbit Determination in Europe (CODE) with a simultaneous estimation of the Earth gravity field coefficients and other parameters, e.g., satellite orbit parameters, station coordinates, Earth rotation parameters, troposphere delays, etc. The weekly GNSS gravity solutions up to degree and order 4/4 are compared to the weekly SLR gravity field solutions. The SLR-derived geopotential coefficients are compared to monthly GRACE and CHAMP results.

SLR-derived terrestrial reference frame using the observations to LAGEOS-1/2, Starlette, Stella, and AJISAI

Currently, the contributions of Starlette, Stella, and AJISAI are not taken into account when defining the International Terrestrial Reference Frame (ITRF), despite the large amount of data collected in a long time-span. Consequently, the SLR-derived parameters and the SLR part of the ITRF are almost exclusively defined by LAGEOS-1 and LAGEOS-2. We investigate the potential of combining the observations to several SLR satellites with different orbital characteristics. Ten years of SLR data are homogeneously processed using the development version 5.3 of the Bernese GNSS Software. Special emphasis is put on orbit parameterization and the impact of LEO data on the estimation of the geocenter coordinates, Earth rotation parameters, Earth gravity field coefficients, and the station coordinates in one common adjustment procedure. We find that the parameters derived from the multi-satellite solutions are of better quality than those obtained in single satellite solutions or solutions based on the two LAGEOS satellites. A spectral analysis of the SLR network scale w.r.t. SLRF2008 shows that artifacts related to orbit perturbations in the LAGEOS-1/2 solutions, i.e., periods related to the draconitic years of the LAGEOS satellites, are greatly reduced in the combined solutions.

Safety and Efficacy of Lysergic Acid Diethylamide-Assisted Psychotherapy for Anxiety Associated With Life-threatening Diseases

A double-blind, randomized, active placebo-controlled pilot study was conducted to examine safety and efficacy of lysergic acid diethylamide (LSD)-assisted psychotherapy in 12 patients with anxiety associated with life-threatening diseases. Treatment included drug-free psychotherapy sessions supplemented by two LSD-assisted psychotherapy sessions 2 to 3 weeks apart. The participants received either 200 μg of LSD (n = 8) or 20 μg of LSD with an open-label crossover to 200 μg of LSD after the initial blinded treatment was unmasked (n = 4). At the 2-month follow-up, positive trends were found via the State-Trait Anxiety Inventory (STAI) in reductions in trait anxiety (p = 0.033) with an effect size of 1.1, and state anxiety was significantly reduced (p = 0.021) with an effect size of 1.2, with no acute or chronic adverse effects persisting beyond 1 day after treatment or treatment-related serious adverse events. STAI reductions were sustained for 12 months. These results indicate that when administered safely in a methodologically rigorous medically supervised psychotherapeutic setting, LSD can reduce anxiety, suggesting that larger controlled studies are warranted.This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License, where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially.

A Near-Real-Time Automatic Orbit Determination System for COSMIC and Its Follow-On Satellite Mission: Analysis of Orbit and Clock Errors on Radio Occultation

The COSMIC-2 mission is a follow-on mission of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) with an upgraded payload for improved radio occultation (RO) applications. The objective of this paper is to develop a near-real-time (NRT) orbit determination system, called NRT National Chiao Tung University (NCTU) system, to support COSMIC-2 in atmospheric applications and verify the orbit product of COSMIC. The system is capable of automatic determinations of the NRT GPS clocks and LEO orbit and clock. To assess the NRT (NCTU) system, we use eight days of COSMIC data (March 24-31, 2011), which contain a total of 331 GPS observation sessions and 12 393 RO observable files. The parallel scheduling for independent GPS and LEO estimations and automatic time matching improves the computational efficiency by 64% compared to the sequential scheduling. Orbit difference analyses suggest a 10-cm accuracy for the COSMIC orbits from the NRT (NCTU) system, and it is consistent as the NRT University Corporation for Atmospheric Research (URCA) system. The mean velocity accuracy from the NRT orbits of COSMIC is 0.168 mm/s, corresponding to an error of about 0.051 μrad in the bending angle. The rms differences in the NRT COSMIC clock and in GPS clocks between the NRT (NCTU) and the postprocessing products are 3.742 and 1.427 ns. The GPS clocks determined from a partial ground GPS network [from NRT (NCTU)] and a full one [from NRT (UCAR)] result in mean rms frequency stabilities of 6.1E-12 and 2.7E-12, respectively, corresponding to range fluctuations of 5.5 and 2.4 cm and bending angle errors of 3.75 and 1.66 μrad .

Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Highly accurate isotope composition measurements by a miniature laser ablation mass spectrometer designed for in situ investigations on planetary surface

An experimental procedure for precise and accurate measurements of isotope abundances by a miniature laser ablation mass spectrometer for space research is described. The measurements were conducted on different untreated NIST standards and galena samples by applying pulsed UV laser radiation (266 nm, 3 ns and 20 Hz) for ablation, atomisation, and ionisation of the sample material. Mass spectra of released ions are measured by a reflectron-type time-of-flight mass analyser. A computer controlled performance optimiser was used to operate the system at maximum ion transmission and mass resolution. At optimal experimental conditions, the best relative accuracy and precision achieved for Pb isotope compositions are at the per mill level and were obtained in a range of applied laser irradiances and a defined number of accumulated spectra. A similar relative accuracy and precision was achieved in the study of Pb isotope compositions in terrestrial galena samples. The results for the galena samples are similar to those obtained with a thermal ionisation mass spectrometer (TIMS). The studies of the isotope composition of other elements yielded relative accuracy and precision at the per mill level too, with characteristic instrument parameters for each element. The relative accuracy and precision of the measurements is degrading with lower element/isotope concentration in a sample. For the elements with abundances below 100 ppm these values drop to the percent level. Depending on the isotopic abundances of Pb in minerals, 207Pb/206Pb ages with accuracy in the range of tens of millions of years can be achieved.

The Science of Exoplanets and Their Systems

A scientific forum on “The Future Science of Exoplanets and Their Systems,” sponsored by Europlanet* and the International Space Science Institute (ISSI)† and co-organized by the Center for Space and Habitability (CSH)‡ of the University of Bern, was held during December 5 and 6, 2012, in Bern, Switzerland. It gathered 24 well-known specialists in exoplanetary, Solar System, and stellar science to discuss the future of the fast-expanding field of exoplanetary research, which now has nearly 1000 objects to analyze and compare and will develop even more quickly over the coming years. The forum discussions included a review of current observational knowledge, efforts for exoplanetary atmosphere characterization and their formation, water formation, atmospheric evolution, habitability aspects, and our understanding of how exoplanets interact with their stellar and galactic environment throughout their history. Several important and timely research areas of focus for further research efforts in the field were identified by the forum participants. These scientific topics are related to the origin and formation of water and its delivery to planetary bodies and the role of the disk in relation to planet formation, including constraints from observations as well as star-planet interaction processes and their consequences for atmosphere-magnetosphere environments, evolution, and habitability. The relevance of these research areas is outlined in this report, and possible themes for future ISSI workshops are identified that may be proposed by the international research community over the coming 2–3 years.

Planet formation models: the interplay with the planetesimal disc

Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims: We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods: We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results: We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M⊕ or above several Jupiter masses. Conclusions: To form giant planets before the dissipation of the disc, small planetesimals (~0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.