Michael H. Soffel

Relativity in Astrometry, Celestial Mechanics and Geodesy

“Astrometry is the part of Astronomy that is devoted to the measurement of the positions, motions, distances, dimensions, and geometry of celestial bodies. Until the advent of Astrophysics a century ago, Astronomy consisted only of what is now called Astrometry and its theoretical counterpart — Celestial Mechanics. Practically all that was known about the Universe at the turn of the present century was obtained uniquely by astrometric techniques.

Considerations concerning the non-rigid Earth nutation theory.

This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earths density and theological properties) for the calculation of the Earths transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earths transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earths nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5.Each level is discussed at the state of the art of the developments.

Relativistic effects in the motion of artificial satellites: The oblateness of the central body II

The motion of artificial satellites in the gravitational field of an oblate body is discussed in the post — Newtonian framework using the technique of canonical Lie transformations. Two Lie transformations are used to derive explicit results for the longperiodic and secular perturbations for satellite orbits in the Einstein case.

Relativistic celestial mechanics with PPN parameters

Starting from the global parametrized post-Newtonian ~PPN! reference system with two PPN parameters g and b we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to h54b2g23 reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in general relativity. We also show that the tidal gravitational field as seen in the local PPN reference system can be expanded into powers of local coordinates similar to the tidal expansion in general relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle ~an Earth satellite! in that system. The translational and rotational equations of motion for center of mass and spin of each of N extended massive bodies possessing arbitrary multipole structure are derived. All equations of motion are presented also in the form of multipole expansions. Several interesting features of the equations are discussed. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived. For the first time, these equations are derived in a self-consistent manner which does not require any additional assumptions about the behavior of bodies such as secular stationarity.

Consistent relativistic VLBI theory with picosecond accuracy

A new theory for the group delay in VLBI is presented. It is based upon a consitent formulation of reference systems in the (first) post-Newtonian framework which has recently been introduced by Damour T. et al. (1990, Les Journees 1990). This formulation leads to improved relations between barycentric and geocentric quantities. The final result for the group delay has an accuracy of better than 1 ps thereby improving results which have been published earlier

On the use of STF-tensors in celestial mechanics

The purpose of this article is to emphasize the usefulness of STF-tensors in celestial mechanics. Using STF-mass multipole moments and Cartesian coordinates the derivations of equations of motion, the interaction- and tidal-potentials for an isolated system ofN arbitrarily shaped and composed, purely gravitationally interacting bodies are particularly simple. Using simple relations between STF-tensors and spherical harmonics it is shown how all Cartesian formulas can be converted easily into the usual spherical representations. Some computational aspects of STF-tensors and spherical harmonics are discussed. A list of useful formulas for STF-tensors is provided.

Space-time reference systems

List of Symbols.- Preface.- 1 Introduction.- 2 Time.- 3 Space-Time.- 4 Barycentric Dynamical Reference System.- 5 Classical Astronomical Coordinates.- 6 Astrometry.- 7 Celestial Reference System.- 8 Terrestrial Reference System.- 9 From the GCRS to the ITRS.- 10 Astronomical Software - Yearbooks.- 11 Astronomical constants.- References.- List of acronyms.- Appendix A: Solutions to Exercises.- Appendix B: Description of the AstroRef Package.- Index 304.

Relativity in fundamental astronomy

An overview is given over the broad field of Relativity in Fundamental Astronomy. The present status is recalled and deficiencies are pointed out that might lead to future work within IAU Commission 52.

The two-body problem in the (truncated) PPN — Theory

The solution of the two-body problem in the (truncated) PPN theory is presented. It is given in two different analytical forms (the Wagoner-Will and Brumberg representation) and by the method of osculting elements.

A Kennedy-Thorndike experiment using LLR data

Abstract We have analyzed data from Lunar Laser Ranging to determine the combination / vbζ 1 − ζ 0 −1/ vb of Robertson-Mansouri-Sexl parameters of special relativity. In such a Kennedy-Thorndike experiments we obtained a realistic upper limit for this combination of 1.5 × 10 −4 only a factor of two or so worse than that obtained with modern laser techniques in the laboratory.