Session 1/2: "Scientific Achievements, Applications, and Future Requirements"

Status of ITRF Development and SLR contribution

Zuheir Altamimi

Institut Geographique National, ENSG/LAREG, France

It is expected to start preparing for a new version of the International Terrestrial Reference Frame, namely the ITRF2008. Before initiating this new solution, some conditions have to be satisfied, mainly the need of reprocessed and consistent solutions from each technique: a new reprocessed IGS solution involving the absolute PCV models, an improved reanalysis solution from IVS accounting for the mean pole tide correction and better troposphere modeling, an improved ILRS solution taking into account all range bias and other station-dependent corrections, and new DORIS solutions where improvements are expected in the frame Z translation and the scale. It is anticipated to have some of these solutions available so that some initial pre-analysis can be performed and their quality assessed. A particular emphasis will be given to the time behavior of the frame physical parameters (origin and scale). Based on the availability of reprocessed ILRS individual and combined solutions, the stability over time of the SLR origin and scale will be reassessed and quantified. Considering these expected changes, a re-evaluation of the consistency between the available local ties and space geodesy estimates becomes necessary, and in particular their impact on the ITRF datum specification.

A 33 Year Time History of the Earth Dynamic Oblateness changes from SLR data

Minkang Cheng, Byron D. Tapley

Center for Space Research, University of Texas at Austin
E-mail :

Satellite Laser Ranging (SLR) data tracked by the ILRS network have recorded the global nature of long-wavelength mass redistribution occurring within the Earth system for more than three decades. The second degree zonal harmonics of the Earth's gravity field, or the J2 coefficient is directly related to the Earth dynamic oblateness, or the dynamic shape factor, which represents how much its rounded shape flattens at the poles and widens at the equator. The variations in J2 are the results of imbalance of the climate induced mass changes between the tropical area (in the range of the north and south 35 degree latitude) and the extra tropical area.  Studying the variations in J2 has provided a clear vision of the large-scale mass redistribution with a long-term signature within the Earth system from analysis of SLR data. Early analysis of 28-year time series of monthly SLR estimates of J2 [Cheng and Tapley, 2004] has indicated that in addition to the secular, 18.6 year tidal and seasonal variations, the J2 has undergone significant interannual variations with time scales of ~4-6 years and a decadal variation with a period of ~21 years. Two large interannual variations are related to the strong El Ninio-Southern Oscillation (ENSO) events during the periods of 1986-1991 and 1996-2002. Recent analysis including an additional five years of data suggests that the Earth has undergone another 3 fluctuations cycles starting from middle of 2002.
Because of the significant aliasing effects in the GRACE data derived J2 coefficient and the J2 variations from SLR data is the most accurate measurement for the application of GRACE product to extract the signal of mass variations in ocean and hydrological. This paper presents detail analysis for the variations in J2 from analysis of multiple geodetic satellites over the period from 1976 to 2008, and a comparison with the monthly solutions from GRACE measurements.


Ignazio Ciufolini, Antonio Paolozzi, Erricos Pavlis

University of Salento, Italy

LARES (LAser RElativity Satellite) is a laser ranged satellite of the Italian Space Agency (ASI) for accurate measurement of the Earth gravitomagnetic field (Lense-Thirring effect). We descibe the status of this experiment that will be launched with the VEGA maiden flight.

Evaluation of PPN parameter Gamma as a test of General Relativity using SLR data

Ludwig Combrinck

HartRAO, South Africa
E-mail :

The Post Newtonian parameter Gamma is evaluated as a solve-for parameter utilising SLR data from LAGEOS. The effects of mis-modelling other variables are estimated. This approach is based on utilising the range component of SLR data as acceleration of the satellite due to GR primarily has a radial component. Initial results are presented, which indicate that there is merit in this approach, though not without pitfalls.

Status of the INFN Satellite/lunar laser ranging Characterization Facility (SCF)

S. Dell'Agnello, G. O. Delle Monache, D. G. Currie, R. Vittori et al

E-mail :

We describe the status of the SCF operation and the program of integrated thermal and optical test of laser retro-reflector arrays for GNSS, Space Geodesy and Fundamental Physics applications. Results presented include the "SCF-Tests" of glonass CCR prototypes, of the "GPS3" flight model and LAGEOS CCRs of a 3x3 matrix and from the NASA-GSFC "sector" prototype. Future programs and applications will also be reported.

Temporal variations of the Earth gravity field derived from SLR Data over a long period of time

Florent Deleflie, Pierre Exertier, Olivier Laurain, Dominique Feraudy, Jean-Michel Lemoine

Observatoire de la Cote d'Azur, France

We use SLR data tracked by the ILRS network since more than 20 years to derive long time series of the low wavelenghts of the Earth's gravity field. The work is based on post-fit residuals analyses, performed with the computation of orbits of geodetic satellites (LA-1 and STA in particular). Two approches are led in parallel and then combined, to decorrelate in an efficient way seasonal effects (mainly annual and semi-annual periods) from long periodic and secular ones (mainly due to the post-glacial rebound, and the 18.6 year tide). On the one hand, osculating orbital arcs are propagated over short periods of time and adjusted on tracking data. On the other hand, mean orbital arcs, containing only the long periodic effects acting on the satellite motion are propagated over the whole period where tracking data are available. With such a method, small but cumulative variations of the gravity field can be enlightened explicitly. As a result, the parameters characterizing the post glacial rebound, and the 18.6 year tide can be inserted explicitly in the corresponding normal matrices. Then normal matrices deduced from both approaches are then mixed, then inversed to perform time series of each parameter, and then analyzed: weighting of normal matrices, corresponding impact on geopotential coefficients time series, frequency analysis.

Laser Ranging Contributions to Earth Rotation Studies

Richard Gross

Jet Propulsion Laboratory, USA
E-mail :

The groundwork for a new field in the geophysical sciences - space geodesy - was laid in the 1960s with the development of satellite and lunar laser ranging systems, along with the development of very long baseline interferometry systems, for the purpose of studying crustal plate motion and deformation, the Earth's gravitational field, and Earth orientation changes. The availability of accurate, routine determinations of the Earth orientation parameters (EOPs) afforded by the launch of the LAser GEOdynamics Satellite (LAGEOS) on May 4, 1976, and the subsequent numerous studies of the LAGEOS observations, has led to a greater understanding of the causes of the observed changes in the Earth's orientation. LAGEOS observations of the EOPs now span 32 years, making it the longest available space-geodetic series of Earth orientation parameters. Such long duration homogenous series of accurate Earth orientation parameters are needed for studying long-period changes in the Earth's orientation, such as those caused by climate change. In addition, such long duration series are needed when combining Earth orientation measurements taken by different space-geodetic techniques. They provide the backbone to which shorter duration EOP series are attached, thereby ensuring homogeneity of the final combined series.

Measurment of Anomalous Angle of Deviation of Light During Satellite Laser Ranging

Yuriy V. Ignatenko, Vladimir M. Tryapitsyn, Andriy A. Makeyev, Igor Yu. Ignatenko

Crimean Laser Observatory, Katzively, Ukraine

Our station ranges satellites with laser beam with small angular divergence (about 5 arcseconds). Thus we need high pointing accuracy to receive responce signal from ranged objects. We discovered that in order to obtain strong signal we have to make an advance not only for speed aberration but also for an unknown factor comparable with speed aberration by value but as a rule different by direction. First manual mostly qualitative observations were conducted in years 2001, 2002, 2004. Seasonal dependency of the anomalous angle of deviation of light was found. Also it was proved that observed effect is not caused by heating and mechanical deformations of the telescope or disalignment of telescope and laser beam axes [Ignatenko et al. 2004].
With installation of CCD camera in mid 2007 connected with computer with proper software we increased quality and quantity of observations. This allowed us to determine more precisely anomalous deviation of light from the preset direction in the field of view of the telescope subtracting speed aberration from apparent deviation of satellite image. Maximal value of anomalous deviation is about 10-12 arcseconds, its direction is seasonally and time of day dependent.
Further processing of obtained results needed. We will make an attempt to combine a 3D-vector of anomalous deviation from its different projections onto the field of view of the telescope.
Reference: Ignatenko Yu.V., Tryapitsyn V.M., Ignatenko I.Yu. "Determination of Speed Aberration While Laser Location of Earth Artificial Satellites", Journal of Automation and Information Sciences, vol. 36, issue 4 (2004).

ICESat, GRACE, and Time Varying Gravity: SLR Contributions and Applications

S. B. Luthcke, D. D. Rowlands, F. G. Lemoine, H. J. Zwally, S. M. Klosko, D. S. Chinn, J. J. McCarthy, T. A. Williams


Temporal changes in the Earth's gravity field have a rich history of study, prediction, measurement, and with today's technologies, monitoring. Over the past 25 years, the need to improve the modeling of these effects within SLR precision orbit determination investigations and in the context of the geophysical interpretations of the results developed from SLR, has progressed significantly and added challenging complexity to SLR pursuits. Laser altimeter missions, like ICESat and DESDynI provide another component for better understanding and monitoring geodynamical systems having topographical manifestations.
The GRACE mission, launched in 2002, has now operated for approximately 6 years, producing monthly and ten-day snapshots of the variations of the gravity field of the Earth. The available solutions either from spherical harmonics or from mascons provide new monitoring capabilities for integrated surface mass flux. Through extensive validation with independent sources, GRACE derived products have been shown to be highly reliable. A wide range of independent sources of derived time gravity variations, when tested in forward modeling approaches for GRACE, have been shown to significantly reduce the variance levels seen in GRACE highly precise KBRR data analyses. This paper will review some of the comparisons which have been made comparing GRACE-derived science products with these independent sources - including ocean tides, atmospheric pressure variations, surface hydrological mass variations, and ice sheet mass changes from ICESat. We will also show the significant improvement obtainable in SLR orbit recoveries if these same forward models are applied.

Determination of the SLR station coordinates and velocities on the basis of laser observations of low satellites

P. Lejba, S. Schillak

Space Research Center of the Polish Academy of Sciences
Astrogeodynamic Observatory, Borowiec
E-mail :

The orbits of three low satellites Ajisai, Starlette and Stella have been determined on the basis of the data collected in 2001-2005 from the best 14 Satellite Laser Ranging stations. The positions and velocities of four SLR stations Graz (7839), Greenbelt (7105), Herstmonceux (7840) and Yarragadee (7090) were determined. Additionally, the station velocities were compared with the geological model NNR-NUVEL1A. All calculations have been made assuming the model of the Earth gravity field EIGEN-GRACE02S. The results presented in this work show that the data from low satellites such as Ajisai, Starlette or Stella can be successfully applied for determination of the SLR station coordinates and velocities.

International Terrestrial Reference Frame - Latest Developments

Horst Mueller

Deutsches Geodaetisches Forschunsintitut, DGFI, Germany

The publication of the newest international terrestrial reference frame, ITRF2005, has started a vital discussion on combination strategies, models and time series. Mainly the scale problem was an ambitious aim to look at and identify the difference between SLR and VLBI. As result of this process a number of effects in both techniques were identified, a new pole tide model in VLBI, range biases in SLR. Absolute instead of relative phase centre corrections in GPS will have an influence on the GPS scale and the connection of techniques at collocation sites. Correcting these effects may lead to better agreement in scale. The problem how to treat the local ties and seasonal signals is controversially discussed and still unsolved. Some efforts from the services will provide longer and homogeneously processed time series of station coordinates for the next ITRF. This includes the backward computation until 1984, especially from SLR, and include longer time series of new, mainly GPS, stations. Homogeneous models in all techniques will improve the quality of a new ITRF and facilitate the comparison of time series. A good example what can be achieved with carefully harmonized models is the GGOS-D project. The result is a global reference frame from reprocessed time series of GPS, SLR and VLBI each processed and combined by two different processing centres in Germany. Additional models, like atmospheric pressure loading, are necessary to be implemented in all processing chains to reduce the annual signals in station positions. The processing strategy, on the basis of solutions, normal equations or observation level, is an other point of investigation and discussions. The Global Geodetic Observing System (GGOS) a component of the International Association of Geodesy (IAG) is the platform to discuss all these points.

Lunar Laser Ranging - A Science Tool for Geodesy and General Relativity

Juergen Mueller

Institut für Erdmessung, Leibniz Universität, Hannover, Germany

Lunar Laser Ranging (LLR) has routinely provided observations for more than 38 years. A new site called APOLLO has just started with measurements reaching mm ranging accuracy. The main benefit of LLR is, e.g., to determine many parameters of the Earth-Moon dynamics (e.g. orbit and rotation of the Moon, a selenocentric reference frame or the secular increase of the Earth-Moon distance: 3.8 cm/year) and to test metric theories of gravity. LLR data analysis determines gravitational physics quantities such as the equivalence principle, any time variation of the gravitational constant, relativistic precessions, and several metric parameters. The gravitational physics parameters cause different spectral perturbations of the lunar orbit, which can be used to separate the various relativistic and Newtonian effects with high accuracy. We give an overview of the recent status of our LLR analysis procedure, present new results for the relativity parameters, and address potential capabilities of LLR in the near future.

Use of SLR Observations to improve Galileo GIOVE-B Orbit and Clock Determination

I. Hidalgo, A. Mozo, P. Navarro, R. Píriz, D. Navarro-Reyes

GMV, Spain
E-mail :

GIOVE-A and GIOVE-B (Galileo In Orbit Validation Elements) are experimental satellites that have been launched by ESA in order to verify some of the critical technologies of the future Galileo system, such as on-board atomic clocks and the gerneration of the navigation signal, in addition to characterising the processing of the Galileo signal by user receivers, all in the frame of the GIOVE Mission.
As a primary tool in the experimentation activities, the GIOVE Mission E-OSPF software (Experimental Orbitography and Synchronization Processing Facility) receives the navigation observations gathered by a network of dual GPS/Galileo receivers and estimates the orbit and clock offsets of the GPS and GIOVE satellites. The inclusion of GPS satellites is necessary to achieve the required level of redundancy in the clock estimation. The clock offsets are obtained every 5 minutes, and their time series is essential to characterise the behaviour of the on-board atomic clocks, both the RAFS (Rubidium Atomic Frequency Standard) and the Passive Hydrogen Maser clock (PHM) of GIOVE-B, the most stable clock ever flown in space.
The main problem in the determination of the offsets of the on-board clocks is that the radial error in orbits and the clock offsets are highly correlated, so that it is difficult to disentangle them. A good way of overcoming this effect is to have a complementary means to compute the estimated orbits, such as SLR measurements. The GIOVE satellites are equipped with laser reflectors, and dedicated campaigns of laser tracking are being carried by ILRS in coordination with ESA. The E-OSPF is able to process SLR observations together with the navigation ones. In this way, the orbit determination can be improved and decorrelated from the clock estimation.
This paper describes the process of orbit and clock determination from the navigation signal, and how the SLR measurements can be added to have better orbits and a better observability of the on-board clocks. It presents the results of the experimentation carried to characterise the behaviour of the GIOVE-B PHM, with the help of SLR measurements, and to assess the improvement obtained by using them.

Comparison and Combination of SLR Solutions Including Gravity Field Coefficients and Range Biases

N. Panafidina, M. Rothacher, D. Thaller

GeoForschungsZentrum, Germany

Within the GGOS-D project SLR solutions containing station coordinates, Earth rotation parameters (ERPs), range biases and low-degree gravity field coefficients were generated by GFZ and DGFI for the time span 1993-2007. The processing strategy, models and parameterization used by GFZ and DGFI were selected to be as consistent as possible to insure the compatibility of the solutions for future combination studies. We used these two long-term weekly solutions to study the impact of estimating different parameter sets on the solutions.
First, all gravity field coefficients were fixed to an accurate a priori gravity field model and the weekly solutions for station coordinates and ERPs were compared to individual solutions from ILRS Analysis Centers, to the combined ILRS solution and to the IERS C04 series. The influence of the estimation of range biases on the station coordinates and ERPs was considered here in detail, especially because the list of range biases used within the GGOS-D project does not correspond to the ILRS list of range biases.
In the second step gravity field coefficients of degree 1 were estimated in addition. It was found that in this case ERPs and station coordinates show systematic differences with respect to the solution where all the gravity field coefficients were kept fixed. These differences and the correlations between the various parameter types will be discussed.

The methods of converting observation data of SLR between two nearby stations

Pap V., Medvedsky M.

Main Astronomical Observatory National Academy of Sciences of Ukraine
E-mail :

There are two methods of converting observation data of satellite laser ranging from one station to another nearby station. The first method is conditionally named analytical and it consist of ordinary geometrical conversation in system of the station A - station B - satellite S. The second method we are called differential and it is based on ephemeris data of the same pass of satellite for the each station. We have converted observation data from two Ukrainian SLR station Simeiz 1873 and Katzively 1893 the distance is about 3 kilometers between them. The result of this conversation with Lageos 1 and Lageos 2 at 2004 year for both stations is present in article.

Geocenter Motion: Causes and Modeling Approaches

Erricos C. Pavlis, Magdalena Kuzmicz-Cieslak

Joint Center for Earth Systems Technology (JCET), USA

Since the first realization of the International Terrestrial Reference Frame (ITRF), its origin, defined to coincide with the geocenter, has been realized through the estimated coordinates of its defining set of positions and velocities at epoch. Satellite Laser Ranging (SLR) contributes to the ITRF realization this unique information along with that for its absolute scale, for over two decades. Over the past decade, the focus extended beyond the accuracy at epoch to include the stability of these realizations, given the increasingly more accurate observations of geophysical mass redistribution within the Earth system. Driven by numerous geophysical processes, the continuous mass redistribution within the Earth system causes concomitant changes in the long-wavelength terrestrial gravity field that result in geometric changes in the figure described by the tracking station network. The newly adopted ITRF development approach allows the simultaneous estimation of origin variations at weekly intervals through a geometric approach during the stacking step, and for the first time in the history of the ITRF accounts to some extent for these effects. Our dynamic approach has been used since the mid-90s, delivering, initially biweekly and later on, weekly variations of an "origin-to-geocenter" vector, simultaneously with an SLR-only TRF realization. Over the past year, the International Laser Ranging Service's (ILRS) Analysis Working Group adopted significant modeling improvements for the SLR data reduction of future as well as the historical SLR data. Based on this new standards, ILRS has embarked on a reanalysis of the LAGEOS 1 & 2 SLR data set up to present, to develop a uniformly consistent set of weekly variations with respect to a frame realized simultaneously by the ensemble of the data, closely approximating the current (scaled) ITRF2005. These series can complement the precise application of the ITRF when used as Cartesian offsets or the GRACE-derived monthly gravitational models, when converted to degree-1 harmonics. A simple model based on the dominant frequencies decomposition of the series can be easily used to account for the most significant part of the signal in various applications (examples).

Confirming the Frame-Dragging Effect with Satellite Laser Ranging

John C. Ries, Richard J. Eanes, Michael M. Watkins

The University of Texas at Austin, Center for Space Research, USA

The theory of General Relativity predicts several non-Newtonian effects that have been observed by experiment, but one that has proven to be challenging to directly confirm is the so-called 'frame dragging' effect. One manifestation of this effect is the Lense-Thirring precession of a satellite's orbital plane due to the Earth's rotation. While the signal is large enough to be easily observed with satellite laser ranging, the Lense-Thirring measurement uncertainty is limited by the knowledge of the even zonal harmonics of the Earth's gravity field that also produce Newtonian secular orbit precessions. In the late 1980's, it was proposed to launch the LAGEOS-3 satellite matching LAGEOS-1, except that the orbit inclination would be exactly supplementary to LAGEOS-1. This would have allowed the cancellation of the equal but opposite orbit precession due to the Earth's gravity field to reveal the Lense-Thirring precession. However, this satellite was never launched, and the orbit selected for LAGEOS-2 was not sufficiently close to the proposed LAGEOS-3 orbit specifications to support an accurate Lense-Thirring experiment with the available gravity models. However, this problem has been largely overcome with the dramatically improved models resulting from the joint NASA-DLR Gravity Recovery and Climate Experiment (GRACE) mission. Using laser ranging to LAGEOS-1 and LAGEOS-2, we demonstrate, with an error analysis based on several now-available GRACE gravity models, that the General Relativity prediction of the Lense-Thirring precession can be confirmed with an uncertainty better than 15%, in good agreement with previously published results. In addition, with extensive modeling improvements in the various models, including the terrestrial reference frame and solid earth and ocean tides, we show that a credible experiment can be conducted with just four years of SLR overlapping the GRACE mission.

Estimation of the elastic Earth parameters k2 and k3 from the SLR tecnique

Milena Rutkowska *, Marcin Jagoda **

* Space Research Centre, Polish Academy of Sciences, Poland, E-mail:
** Technical University , Koszalin, Poland, E-mail:

The global elastic parameters k2,k3 associated with the tide variations of the satellite motion are estimated from the Satellite Laser Ranging (SLR) data. The study is based on satellite observations taken by the global network of the ground stations during the period from January 1, 2005 until January 1, 2007 for monthly orbital arcs of satellites Lageos 1 and Lageos 2, separately. The observation equations, contain unknowns for orbital arcs, some constants and elastic Earth parameters which describe tide variations of the satellite motion. The adjusted values k2 equal to 0.3016 ± 0.0001 and 0.3006 ± 0.0001, k3 equal to 0.0989 ± 0.0051 and 0.0810 ± 0.0051 for LAGEOS1 and LAGEOS2 tracking data are discussed and compared with geophysical estimations of Love numbers. All computations were performed employing the NASA software GEODYN II (eddy et al. 1990).

Overview of the Science Results from ICESat

B. E. Schutz, H. J. Zwally

The University of Texas at Austin, USA

ICESat (ICE, Cloud and Land Elevation Satellite) was launched in January 2003 into a 94, 600 km altitude orbit and laser altimeter operations began one month after launch. Although laser life issues were identified after one month of operation, the adopted operation scenario has supported the creation of a time series of elevation from which elevation change has been measured. A variety of calibration/validation experiments have been executed which show that the elevation products, when fully calibrated, have an accuracy that meets the science requirements (e.g., radial orbit accuracy < 5 cm, laser spot geolocation accuracy < 5 meters). The elevation products from ICESat use GPS-derived orbits, but the SLR measurements collected through the ILRS are critical to verify the radial orbit accuracy. Results obtained from ICESat for elevation change correlate well with mass change results obtained from GRACE over the same time interval. This presentation will summarize the science results obtained from ICESat.

Planetary Laser Altimetry; Past and Present

David E. Smith, Maria T. Zuber

E-mail: David.E.Smith@nasa,gov

After Apollo, laser altimetry in NASA began with Mars Observer (MOLA-1), launched in 1992 but lost on approach to Mars, and re-flown on Mars global Surveyor (MOLA-2) in 1996. In Jan 1994 the Clementine mission to the Moon carried the second laser altimeter into space that provided the first global shape of the Moon. In 1996 the NEAR spacecraft carrying the NEAR Laser Ranger (NLR) was launched to the asteroid 433 Eros, and in 2004 a laser altimeter was launched on the MESSENGER spacecraft to Mercury and is currently in cruise to the planet. Early next year the LRO spacecraft carrying LOLA will be launched to the Moon. Japan launched the SELENE spacecraft in 2007 carrying the LALT laser altimeter followed by Chang'E by China. Soon India will launch Chandrayaan carrying a laser altimeter. In nearly all the missions todate laser altimeters have been used for mapping of planetary bodies with remarkable success and played major roles in preparing for subsequent lander missions. All of the these missions and their laser instruments have helped make advances in the use of lasers for planetary science and helped convince skeptical space agencies that these kinds of instruments could be used with confidence and reliability on long planetary missions in some harsh environments. Laser altimetry is now accepted, albeit not with the same level of confidence as microwave instruments, and laser tracking of planetary spacecraft will be next challenge.

Preparing the Bernese GPS Software for the analysis of SLR observations to geodetic satellites

D. Thaller, M. Mareyen, R. Dach, W. Gurtner, G. Beutler, B. Richter, J. Ihde

Astronomical Institute, University of Bern, Switzerland

Abstract: CODE (Center for Orbit Determination in Europe) is an associated analysis center of the ILRS performing quicklook analyses on a daily basis using SLR measurements to GNSS satellites (two GPS and three of the GLONASS satellites) with the Bernese GPS software. In cooperation with BKG the Bernese GPS software is being generalized to analyze SLR observations to Laser satellites, like Lageos and Etalon. The analysis includes initially the estimation of station coordinates, Earth orientation parameters, and satellite orbits based on SLR measurements.
The software developments are validated using the data set of the ILRS benchmark project, i.e., of 28 days in October/November 1999. We compute orbits of different lengths (e.g., 7 days, 14 days, 28 days) using data sets shifted by one day. This allows us to perform repeatability studies from the overlapping days of adjacent orbital arcs.
Our estimates are validated externally using the solutions provided by the ILRS analysis centers within the ILRS benchmark project, in particular with solutions generated by BKG using the UTOPIA software (developed at CSR, University of Texas).

Orbit Determination of LRO at the Moon

David E. Smith, Maria T. Zuber, Frank G. Lemoine, Mark H. Torrence, Erwan Mazarico


The orbit determination of LRO is particularly important because the mission is designed to select landing sites for future robotic and human landings. For these purposes the program needs an accurate geodetic model of the Moon that provides the best knowledge of the positions of features on the surface, including the far side, and the gravity field to enable spacecraft to return to, or visit, a particular location. LRO is expected to provide this information. The baseline tracking system for LRO is S-band with Doppler accuracy of ~1 mm/s for approx. 20 hours per day but this will not be accurate enough for the LRO requirements which are estimated to be ±50m or better in along track position . One-way laser ranging at 10 cm precision has been added to the spacecraft to assist in orbit determination, and in conjunction with the laser altimeter (LOLA) at 10 cm accuracy is expected to provide the position of LRO and, by inference, the position of surface features to the desired accuracy. Important aspects of LRO orbit determination are gravity model improvement, improvement of spacecraft timing and pointing knowledge, and laser altimetry and laser tracking of LRO are expected to be critical components.

New accurate atmospheric correction of SLR observations

Dudy D. Wijaya and Fritz K. Brunner

Engineering Geodesy and Measurement Systems, Graz University of Technology, Austria

The atmospheric propagation effects have been widely known as one of the most limiting factors that usually degrade the precision of SLR (Satellite Laser Ranging) and GNSS (Global Navigation Satellite System) measurements. In order to reduce these effects, one can use, for example, the Mendes and Pavlis formula with FCULa mapping function for SLR measurements and the Saastamoinen model with Niell mapping function for GNSS measurements. As there is obviously only one atmosphere, it seems to be of advantage to develop a general atmospheric correction formula for both SLR and GNSS measurements.
We have developed a unified theory of atmospheric corrections based on the geometric optics principle, and the perturbation technique to solve the propagation problem. This development can be applied to derive an atmospheric correction formula not only for single frequency SLR and GNSS measurements, but also for linear combinations of SLR and GNSS measurements that is useful to eliminate some of the atmospheric effects.
We have further developed a new atmospheric correction formula for the two-colour SLR measurements, and for co-located SLR and GNSS measurements to a GNSS satellite equipped with a laser reflector array. The proposed formula eliminates the total atmospheric density effect and takes into account the water vapor density and the arc-to-chord correction. Numerical simulations show that this new formula produces the atmospheric range correction with an accuracy better than 1 mm at any elevation angle.
Unlike other correction formulae, this new formula does not require any hydrostatic mapping function nor a hydrostatic horizontal gradient mapping function as the total atmospheric density effect can be eliminated. Concerning the required information about the water vapour distribution along the propagation path, it can be calculated using GPS or Water Vapour Radiometer data. The accuracy demand on this data is moderate, thus we propose to use a co-located GPS receiver. The arc-to-chord correction requires an atmospheric model which will be discussed in detail. However, the required measurement precision for the difference of the two-colour SLR measurements and the co-located SLR and GNSS measurements, i.e. better than 30 μm, exceeds the capability of the current state-of-the art SLR and GNSS systems.

Lunar Core and Mantle. What Does LLR See?

James G. Williams

Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA, USA

The lunar interior is hidden, but Lunar Laser Ranging (LLR) senses interior properties through physical librations and tides. The mean density of the Moon is like rock and the mean moment of inertia is only 1.6% less than a uniform body would have. Neither is compatible with a large dense core like the Earth?s, though a small dense core is permitted. The solid-body tides are proportional to Love numbers which depend on interior structure and the radial dependence of elastic parameters and density. A small core, either solid or fluid, increases the Love numbers by a few percent, but uncertainty of deep elastic parameters also affects Love number computations. LLR sees three effects through the physical librations that indicate a fluid core. The strongest effect is from energy dissipation arising at the fluid-core/solid-mantle boundary (CMB). Since there is also dissipation from tides in the solid mantle, we separate tide and CMB dissipation by determining phase shifts in multiple periodic libration terms. The second indicator of a fluid core comes from the oblateness of the CMB which causes a torque as the fluid moves along the oblate surface. The third effect comes from the moment of inertia of the fluid core which affects the amplitude of a physical libration term. The fluid moment is difficult to detect, but it is now weakly seen and its determination should improve from future LLR data. LLR does not separate fluid core density and size, but if the fluid core has the density of iron then a radius of roughly 330-400 km is suggested. Lower density materials would have larger radii; Fe-FeS mixtures are attractive because they have lower freezing points. The dissipation analysis which gives CMB dissipation also gives tidal Q vs frequency. At one month Q is ~30, while Q is ~35 at one year. These low values may come from the lower mantle which is suspected to be a partial melt. How can the core and mantle parameter determinations be improved? Expanded modeling may improve fits and add parameters. Long LLR data spans are important, so future accurate ranges to the four retroreflector arrays are requested. Expanding the number and spread of lunar retroreflector sites, by finding the lost Lunokhod 1 rover or placing new retroreflectors on the Moon, would also benefit the extraction of scientific information from LLR data.

Volatile Exchange on Mars

Maria T. Zuber


The movement of CO2 from the atmosphere of Mars to the polar caps on a seasonal basis and the subsequent sublimation of the material back into the atmosphere is the long-term dominating atmospheric processes on Mars. This process is observable in the orbits of Mars spacecraft determined from tracking data and the quantity of material can be estimated from changes in the gravity field. These observations of the motion of volatiles is not necessarily restricted to the exchange of CO2 between the atmosphere and polar caps but, like Earth, to any movement of mass on or in the planet, including the possible flow of ground water, and the escape of volatiles from the regolith. The measurement of these motions is largely dependent on the quality of the orbit determination and hence the tracking data. Laser tracking of spacecraft around other planets is potentially the most accurate source of data for observing and monitoring these changes.