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Work related with IAU C52: RIFA

M.H. Soffel and W. Han

Les Journees 2014, St. Petersburg, September 22


Main work - ecliptic in a relativistic framework - fully documented relativistic VLBI model Related work - the post-linear metric (PPN-metric for light rays) - models for bodies with higher spin-multipole moments

Les Journees 2014, St. Petersburg, September 22


Ecliptic IAU 2006 Resolution B1: Recognizing 2. the need for a definition of the ecliptic for both astronomical and civil purposes ..... BUT · the ,ecliptic` basically has to be defined in the BCRS · the BCRS to GCRS transformation is a 4-dimensional space-time transformation · one cannot directly transform a BCRS-ecliptic as some BCRS Euclidean spatial coordinate (TCB = const.) plane into the GCRS · for special purposes an additional convention for some ,GCRS-ecliptic` might be adopted more information: talk by Nicole Capitaine on the subject
Les Journees 2014, St. Petersburg, September 22


Relativistic VLBI model Theoretical model should have an accuracy of at least 1 ps

It must be based upon Einstein`s theory of gravity

Les Journees 2014, St. Petersburg, September 22


Standard reference: IERS Technical Note No. 36 G. Petit, B.Luzum IERS Conventions 2010 Based upon CONSENSUS MODEL 1. 2. 3. 4. 5. Fanselow-Thomas-Treuhaft-Sovers Shapiro Hellings-Shadid-Saless Soffel-MЭller-Wu-Xu Zhu-Groten

Eubanks, T.M. (ed.) Proc. of the U. S. Naval Obs. Workshop on Relativistic Models for use in Space Geodesy, USNO, Washington, D. C.

Of importance: Klioner, S.A., 1991, in: Proc. AGU Chapman Conf. On Geodetic VLBI
W.E.Carter (ed.), NOAA Technical Report NOS 137 NGS 49

Les Journees 2014, St. Petersburg, September 22


The consensus model: - designed for very remote radio sources (quasars) only (no parallax, no proper motion) - designed for Earth-bound baselines only - 1 ps accuracy for the group delay - not a coherent model; needs detailed documentation Goals: To improve the consensus model: - accuracy 0.1 ps or less - much larger baselines (e.g., interplanetary) - valid also for near sources (e.g., on the Moon) - coherent and well documented
Les Journees 2014, St. Petersburg, September 22


Some kind of working group was established
Neil Ashby Marshall Eubanks Toshio Fukushima Sergei Klioner Michael Soffel Slava Turyshev Wenbiao Han (guest)

Les Journees 2014, St. Petersburg, September 22


We first concentrated on the following papers:

Damour, T., Soffel, M., Xu, C., 1991, Phys.Rev., D 43, 3273

Klioner, S.A., 1991, in: Proc. AGU Chapman Conf. On Geodetic VLBI
W.E.Carter (ed.), NOAA Technical Report NOS 137 NGS 49

Klioner, S.A., Kopeikin, S., 1992, Astron.J., 104, 897 Sekido, M., Fukushima, T., 2006, J.Geod., 80, 137

checked all calculations, tried to find simpler derivations and started with an exhaustive documentation
Les Journees 2014, St. Petersburg, September 22


Les Journees 2014, St. Petersburg, September 22


So far the following issues are treated in the Document on relativistic VLBI:

- definition of baselines, b:BCRS & B:GCRS - expressions for observable group delay (TT) and B - Relations with BCRS quantities (TCB, b) - expression for geometrical and gravitational delays

Les Journees 2014, St. Petersburg, September 22


BCRS metric

For a single body

Les Journees 2014, St. Petersburg, September 22


BCRS metric

1PN for light-rays

For a single body

Les Journees 2014, St. Petersburg, September 22


BCRS metric

1.5 PN for light-rays For a single body

Les Journees 2014, St. Petersburg, September 22


The gravitational time delay The PN-terms treated with the Time-Transfer-Function as obtained from

Les Journees 2014, St. Petersburg, September 22


The Shapiro time delay was derived for a body a) at rest

b) with a small, constant barycentric velocity
having all (constant) mass- and spin-multipole moments within a few lines for details see: arXiv: 1409.3743

Corrections for parallax and proper motion of the radio source have been discussed

Les Journees 2014, St. Petersburg, September 22


Related work

- the post-linear metric (PPN-metric for light rays) - models for bodies with higher spinmultipole moments

Les Journees 2014, St. Petersburg, September 22


Les Journees 2014, St. Petersburg, September 22


we started with the case of a spherically symmetric body; outside the body: Schwarzschild metric (sole parameter M) q_ij: during the calculation on faces expressions that depend upon the internal structure of the body (e.g., radius R) one has to show that all such ,bad expressions` - either cancel because of the local equations of motion - or can be removed by means of a (harmonic) gauge transformation -> one gets a new form of the Schwarzschild metric in harmonic coordinates (not the one in Weinberg, 1972)
Les Journees 2014, St. Petersburg, September 22


further work on the PPN-metric for light-rays: - we try to extend our calculations to a single body of arbitrary shape and composition (having all PN mass- and spin-moments) - we are trying to get the (post-linear) Erez-Rosen metric an exact solution of Einstein`s vacuum equations with two parameters m and q (mass and quadrupole moment) in harmonic coordinates

Les Journees 2014, St. Petersburg, September 22


Bodies with higher spin-multipole moments

: mass-energy current density
Les Journees 2014, St. Petersburg, September 22


E.g., for an oblate homogeneous spheroid (a > b) rotating about the symmetry axis with

More general body-models, e.g., with a liquid core or a differential rotation, have been studied Higher spin-multipole moments have been estimated for all solar-system bodies

Les Journees 2014, St. Petersburg, September 22


FIN

Les Journees 2014, St. Petersburg, September 22