arXiv subjects

Christophe Le Poncin-Lafitte

Publications and source records attributed to Christophe Le Poncin-Lafitte.

42 records · Page 3Linked to original sources

arXiv2008

Tidal dynamics of extended bodies in planetary systems and multiple stars

With the discovery during the past decade of a large number of extrasolar planets orbiting their parent stars at a distance lower than 0.1 astronomical unit (and the launch and the preparation of dedicated space missions such as CoRoT and KEPLER), with the position of inner natural satellites around giant planets in our Solar System and with the existence of very closed but separated binary stars, tidal interaction has to be carefully studied. In particular, a question arises about the validity of usual approximations used in the modelling of this interaction. The purpose of this paper is to examine the step beyond the ponctual approximation for the tidal perturber. To achieve this aim, the gravitational interaction between two extended bodies and more precisely the interaction between mass multipole moments of their gravitational fields and the associated tidal phenomena are studied. Use of Cartesian Symmetric Trace Free (STF) tensors, of their relation with spherical harmonics and of the Kaula's transform enables to derive analytically the tidal and mutual interaction potentials as well as the associated disturbing functions in extended bodies systems. The tidal and mutual interaction potentials of two extended bodies are derived. Next, the external gravitational potential of such tidally disturbed extended body is obtained, using the Love's number theory, as well as the associated disturbing function. Finally, the dynamical evolution equations for such systems are given in their more general form without any linearization. The dynamical equations for the gravitational and tidal interactions between extended bodies and associated dynamics are derived in a form where they could be directly implemented to perform coherent numerical simulations of planetary systems or multiple stars tidal evolution.

astro-ph↗

arXiv2008

General post-Minkowskian expansion of time transfer functions

Modeling most of the tests of general relativity requires to know the function relating light travel time to the coordinate time of reception and to the spatial coordinates of the emitter and the receiver. We call such a function the reception time transfer function. Of course, an emission time transfer function may as well be considered. We present here a recursive procedure enabling to expand each time transfer function into a perturbative series of ascending powers of the Newtonian gravitational constant $G$ (general post-Minkowskian expansion). Our method is self-sufficient, in the sense that neither the integration of null geodesic equations nor the determination of Synge's world function are necessary. To illustrate the method, the time transfer function of a three-parameter family of static, spherically symmetric metrics is derived within the post-linear approximation.

gr-qc↗

arXiv2007

Influence of mass multipole moments on the deflection of a light ray by an isolated axisymmetric body

Future space astrometry missions are planned to measure positions and/or parallaxes of celestial objects with an accuracy of the order of the microarcsecond. At such a level of accuracy, it will be indispensable to take into account the influence of the mass multipole structure of the giant planets on the bending of light rays. Within the parametrized post-Newtonian formalism, we present an algorithmic procedure enabling to determine explicitly this influence on a light ray connecting two points located at a finite distance. Then we specialize our formulae in the cases where 1) the light source is located at space infinity, 2) both the light source and the observer are located at space infinity. We examine in detail the cases where the unperturbed ray is in the equatorial plane or in a meridian plane.

astro-ph↗

arXiv2007

A universal tool for determining the time delay and the frequency shift of light: Synge's world function

In almost all of the studies devoted to the time delay and the frequency shift of light, the calculations are based on the integration of the null geodesic equations. However, the above-mentioned effects can be calculated without integrating the geodesic equations if one is able to determine the bifunction $Ω(x_A, x_B)$ giving half the squared geodesic distance between two points $x_A$ and $x_B$ (this bifunction may be called Synge's world function). In this lecture, $Ω(x_A, x_B)$ is determined up to the order $1/c^3$ within the framework of the PPN formalism. The case of a stationary gravitational field generated by an isolated, slowly rotating axisymmetric body is studied in detail. The calculation of the time delay and the frequency shift is carried out up to the order $1/c^4$. Explicit formulae are obtained for the contributions of the mass, of the quadrupole moment and of the internal angular momentum when the only post-Newtonian parameters different from zero are $β$ and $γ$. It is shown that the frequency shift induced by the mass quadrupole moment of the Earth at the order $1/c^3$ will amount to $10^{-16}$ in spatial experiments like the ESA's Atomic Clock Ensemble in Space mission. Other contributions are briefly discussed.

gr-qc↗

arXiv2006

Angular distances in metric theories

The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at a finite distance from the observer. The aberration and the gravitational deflection of light are treated in a unified way. Assuming the gravitational field to be weak, an explicit expansion of the angular separation within the post-post-Minkowskian approximation is carried out. The angular separation within the post-Newtonian approximation truncated at the order $1/c^3$ is straightforwardly derived.

gr-qc↗

arXiv2004

World function and time transfer: general post-Minkowskian expansions

In suitably chosen domains of space-time, the world function may be a powerful tool for modelling the deflection of light and the time/frequency transfer. In this paper we work out a recursive procedure for expanding the world function into a perturbative series of ascending powers of the Newtonian gravitational constant G. We show rigorously that each perturbation term is given by a line integral taken along the unperturbed geodesic between two points. Once the world function is known, it becomes possible to determine the time transfer functions giving the propagation time of a photon between its emission and its reception. We establish that the direction of a light ray as measured in the 3-space relative to a given observer can be derived from these time transfer functions, even if the metric is not stationary. We show how to deduce these functions up to any given order in G from the perturbative expansion of the world function. To illustrate the method, we carry out the calculation of the world function and of the time transfer function outside a static, spherically symmetric body up to the order G^2, the metric containing three arbitrary parameters.

gr-qc↗