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Moderator's note
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The pdf seems to be ok. I've no problem viewing it with okular.
HvH.
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On Mar 12, 8:30am, "Jonathan Thornburg [remove -animal to reply]"
<
jth...@astro.indiana-zebra.edu> wrote:
> Chalky <
chalkys...@bleachboys.co.uk> wrote:
> > the only examples of GR being used for outer solar system
> > computations (that I have come across), are found in the papers on the
> > Pioneer anomalies.
>
> > Here, Anderson et al. specifically state that GR corrections have
> > additionally been used.
>
> > Having said that, this is precisely where anomalies have been
> > observed.
>
> > This leads me to wonder what GR corrections, precisely, they did use.
>
> According to page 3 of
>
> Folkner, Williams, and Boggs,
> "The Planetary and Lunar Ephemeris DE 421"
> IPN Progress Report 42-178 ? August 15, 2009
>
http://tmo.jpl.nasa.gov/progress_report/42-178/178C.pdf
Unfortunately, when I try to download this, I get a flash of a
redirection notice then, before I have time to read much more than the
title, the download aborts because Adobe Acrobat finds irresolvable
errors in the file.
Eric gisse's recommended pdf still downloads fine though.
> "For DE 421, the positions of the Moon and planets were integrated using
> an n-body parameterized post-Newtonian (PPN) metric [5,6,4]."
>
> The table later on that page includes both the inner *and the outer plane=
ts*.
> The cited references are
> [4] T. D. Moyer, Formulation for Observed and Computed Values of Deep Spa=
ce
> Network Data Types for Navigation, Monograph 2, Deep Space Commun=
ications
> and Navigation Series, Jet Propulsion Laboratory, Pasadena, Calif=
ornia,
> 2000.
> [5] C. M. Will and K. Nordtvedt, "Conservation Laws and Preferred Frames =
in
> Relativistic Gravity: I. Preferred-Frame Theories and an Extended=
PPN
> Formalism," Astrophysical Journal, vol. 177, pp. 757?774, 1972.
> [6] C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge
> University Press, 1981.
>
> There's also a footnote
> 5 F. B. Estabrook, "Derivation of Relativistic Lagrangian for n-body
> Equations Containing Relativity Parameters $\beta$ and $\gamma$,"
> JPL Interoffice Memorandum (internal document), Jet Propulsion
> Laboratory, Pasadena, California, 1971.
>
> So yes, DE421 does indeed include general relativistic effects.
> I believe this is standard in all modern lunar/planetary ephemerises.
>
> A nice discussion of how general relativistic (and indeed, more general
> relativistic-gravity) effects are (were) included in celestial mechanics
> calculations as of the mid-1980s can be found in
> @incollection
> {
> Hellings-in-GR10,
> author =3D "Ronald W Hellings",
> title =3D "Testing Relativity with Solar System Dynamics"=
,
> pages =3D "365--385",
> editor =3D "B Bertotti and F. de Felice and A. Pascolini"=
,
> booktitle =3D "General Relativity and Gravitation",
> booksubtitle =3D "Invited Papers and Discussion Reports o=
f the
> 10th International Confer=
ence on General Relativity
> and Gravitation, Padua (I=
taly), 3-8 July 1983",
> publisher =3D "Reidel",
> address =3D "Dordrecht (Holland)",
> year =3D 1984,
> isbn =3D "90-277-1819-9",
> snote =3D "++good review of experimental tests of GR
> using spacecraft tracking, planetary r=
adar, etc",
> }
>
> --
> -- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-z=
ebra.edu>
> Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indian=
a, USA
> "Washing one's hands of the conflict between the powerful and the
> powerless means to side with the powerful, not to be neutral."
> =
-- quote by Freire / poster by Oxfam
Point taken. However, even here they don't appear to use full blown GR
to compute the orbits. Instead they seem to use PPN formalism for the
lowest order corrections to Newtonian gravity.