Sophie Pireaux

Solar quadrupole moment and purely relativistic gravitation contributions to Mercury's perihelion Advance

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.).The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einsteins theory of gravitation characterized by β=γ=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters γ,β and the observational bounds for the perihelion advance of Mercury, Δωobs. A second point will address the values given, up to now, to the solar quadrupole moment by several authors. Then, we will briefly comment why we use a recent theoretical determination of the solar quadrupole moment, J2=(2.0 ± 0.4) 10-7, which takes into account both surfacic and internal differential rotation, in order to compute the solar contribution to Mercurys perihelion advance. Further on, combining bounds on γ and J2 contributions, and taking into account the observational data range for Δωobs,we will be able to give a range of values for β. Alternatively, taking into account the observed value of Δωobs, one can deduce a dynamical estimation of J2 in the setting of G.R. This point is important as it provides a solar model independent estimation that can be confronted with other determinations of J2 based upon solar theory and solar observations (oscillation data, oblateness...). Finally, a glimpse at future satellite experiments will help us to understand how stronger constraints upon the parameter space (γω J2) as well as a separation of the two contributions (from the quadrupole moment, J2, or purely relativistic, 2α2+2αγ–β) might be expected in the future.

LISACode: A scientific simulator of LISA

A new LISA simulator (LISACode) is presented. Its ambition is to achieve a new degree of sophistication allowing to map, as closely as possible, the impact of the different subsystems on the measurements. LISACode is not a detailed simulator at the engineering level but rather a tool whose purpose is to bridge the gap between the basic principles of LISA and a future, sophisticated end-to-end simulator. This is achieved by introducing, in a realistic manner, most of the ingredients that will influence LISAs sensitivity as well as the application of TDI combinations. Many user-defined parameters allow the code to study different configurations of LISA thus helping to finalize the definition of the detector. Another important use of LISACode is in generating time-series for data analysis developments.

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

Abstract 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.

Solar quadrupole moment from planetary ephemerides: present state of the art

We discuss the present state of the art of the solar quadrupole moment from planetary ephemerides.

Time scales in LISA

The LISA mission is a space interferometer aiming at the detection of gravitational waves in the [10−4, 10−1] Hz frequency band. In order to reach the gravitational wave detection level, a time delay interferometry (TDI) method must be applied to get rid of (most of) the laser frequency noise and optical bench noise. This TDI analysis is carried out in terms of the coordinate time corresponding to the Barycentric Coordinate Reference System (BCRS), TCB, whereas the data at each of the three LISA stations are recorded in terms of each station proper time. We provide here the required proper time versus BCRS time transformation. We show that the difference in rate of station proper time versus TCB is of the order of 5 × 10−8. The difference between station proper times and TCB exhibits an oscillatory trend with a maximum amplitude of about 10−3 s.

LISACode: Simulating Lisa

A new LISA simulation code is presented. It is highly structured and programmed in C++. The simulator has the purpose to bridge the gap between the basic principles of LISA and a sophisticated end‐to‐end engineering level simulator. LISA sensitivity curves are presented for various configurations of the detector. This software package, which runs on most computer platforms, can be downloaded from the Lisa‐France web site.

Relativistic approach of the LISA mission

The three LISA spacecraft aim at the interferometric detection of gravitational waves in the [10−4, 10−1] Hz band. They are to be launched in 2014, 5 million kilometers appart, in a triangular configuration, orbiting around the Sun. This work in progress deals with the development of a simulator for the LISA mission (LISACode). It requires a description of orbitography and optical links in a native relativistic framework. The corresponding time delays, crucial for the TDI (Time Delay Interferometry), are provided including Sagnac and relativistic Doppler effects. The frequency shift of photons is also given. We further discuss planetary effets on photon flight time.