(SC)RMI: A (S)emi-(C)lassical (R)elativistic (M)otion (I)integrator, to model the orbits of space probes around the Earth and other planets

Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current approach, with the increase of tracking precision (Ka-Band Doppler, interplanetary lasers) and clock stabilities (atomic fountains) is reaching its limits in terms of complexity, and is furthermore error prone. In the appropriate framework of General Relativity, we study a method to numerically integrate the native relativistic equations of motion for a weak gravitational field, also taking into account small non-gravitational forces. The latter are treated as perturbations, in the sense that we assume that both the local structure of space-time is not modified by these forces, and that the unperturbed satellite motion follows the geodesics of the local space-time. The use of a symplectic integrator to compute the unperturbed geodesic motion insures the constancy of the norm of the proper velocity quadrivector. We further show how this general relativistic framework relates to the classical one.Comment: 13 pages, 5 eps figures, 1 table, accepted in Acta Astronautica, presented at the International Astronautical Congress, Vancouver 2004, reference IAC-04-A.7.0

Analysis and mapping of lunar wrinkle ridges (LWRs) using automated LWRs detection process with LROC-WAC and LOLA data

Maps of lunar wrinkle ridges (LWRs) were created from 70°N to 70°S and 140°E to 140°W (extracted and highlighted the major LWRs area) using automated LWRs detection process with Lunar Reconnaissance Orbiter Camera wide range angle camera and Lunar Orbiter Laser Altimeter data. Automatic detection of LWRs is challenging because the ridges are of irregular shapes and many ridges have been eroded and/or degraded over time. It’s a preliminary study of automated ridge detection from DEM data. Statistics and measurements of the extracted LWRs, including orientation, extent, length, height, and elevation offset, were performed based on the mapping of lunar ridges. The identified ridges were classified based on their orientation, distribution, direction, and each class were further divided over basalts, and nearby highlands. According to the findings, 3,375 segments with a total length of 26,455.01 km were identified, and the average elevation offset, width, and height of all the wrinkle ridges were 40.39 m, 3.47 km, and 0.29 km respectively after weighting by length. The LWRs were divided into three morphologies and distributions: parallel ridges, isolated ridges, and concentric ridges. The vast majority of LWRs were found in basalts area, with an extension into neighboring highland. The relations between the morphological parameters were further quantitatively analyzed, and a similar linear correlation between the width and height was found in each class of lunar ridges, implying that small and large ridges were formed as a continuum and that the three classes of ridges were probably formed by some common processes. Finally, the relations between the lunar wrinkle ridges and other geomorphic phenomena were analyzed, indicating that purely volcanic origin or buried premare structures are difficult to reconcile with the investigation. In addition, the consistency between the occurrence of the lunar wrinkle ridges and the thickness of lunar maria indicates that the formation of lunar wrinkle ridges is closely related to the lunar maria; nevertheless, the statistical NW direction of individual classes of LWRs also proposes the presence of an appropriate stress field during the process of their formation

Beyond Mapping Functions and Gradients

Mapping functions and gradients in GNSS and VLBI applications were introduced in the sixties and seventies to model the microwave propagation delays in the troposphere, and they were proven to be the perfect tools for these applications. In this work, we revisit the physical and mathematical basis of these tools in the context of meteorology and climate applications and propose an alternative approach for the wet delay part. This alternative approach is based on perturbation theory, where the base case is an exponential decay of the wet refractivity with altitude. The perturbation is modeled as a set of orthogonal functions in space and time, with the ability to separate eddy-scale variations of the wet refractivity

High-resolution gravity and geoid models in Tahiti obtained from new airborne and land gravity observations: data fusion by spectral combination

International audienceFor the first time, we carry out an airborne gravity survey and we collect new land gravity data over the islands of Tahiti and Moorea in French Polynesia located in the South Pacific Ocean. The new land gravity data are registered with GPS-derived coordinates, network-adjusted and outlier-edited, resulting in a mean standard error of 17 μGal. A crossover analysis of the airborne gravity data indicates a mean gravity accuracy of 1.7 mGal. New marine gravity around the two islands is derived from Geosat/GM, ERS-1/GM, Jason-1/GM, and Cryosat-2 altimeter data. A new 1-s digital topography model is constructed and is used to compute the topographic gravitational effects. To use EGM08 over Tahiti and Moorea, the optimal degree of spherical harmonic expansion is 1500. The fusion of the gravity datasets is made by the band-limited least-squares collocation, which best integrates datasets of different accuracies and spatial resolutions. The new high-resolution gravity and geoid grids are constructed on a 9-s grid. Assessments of the grids by measurements of ground gravity and geometric geoidal height result in RMS differences of 0.9 mGal and 0.4 cm, respectively. The geoid model allows 1-cm orthometric height determination by GPS and Lidar and yields a consistent height datum for Tahiti and Moorea. The new Bouguer anomalies show gravity highs and lows in the centers and land-sea zones of the two islands, allowing further studies of the density structure and volcanism in the region

TIARES Project -Tomographic investigation by seafloor array experiment for the Society hotspot

http://www.godac.jamstec.go.jp/darwin/cruise/mirai/mr08-06_leg1/