tdb2tdt.pro

basic median filter simulation

;+
; NAME:
;   TDB2TDT
;
; AUTHOR:
;   Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
;   [e-mail]
;   UPDATED VERSIONs can be found on my WEB PAGE: 
;      http://cow.physics.wisc.edu/~craigm/idl/idl.html
;
; PURPOSE:
;   Relativistic clock corrections due to Earth motion in solar system 
;
; MAJOR TOPICS:
;   Planetary Orbits
;
; CALLING SEQUENCE:
;   corr = TDB2TDT(JD, TBASE=, DERIV=deriv)
;
; DESCRIPTION:
;
;   The function TDB2TDT computes relativistic corrections that must
;   be applied when performing high precision absolute timing in the
;   solar system.
;
;   According to general relativity, moving clocks, and clocks at
;   different gravitational potentials, will run at different rates
;   with respect to each other.  A clock placed on the earth will run
;   at a time-variable rate because of the non-constant influence of
;   the sun and other planets.  Thus, for the most demanding
;   astrophysical timing applications -- high precision pulsar timing
;   -- times in the accelerating earth observer's frame must be
;   corrected to an inertial frame, such as the solar system
;   barycenter (SSB).  This correction is also convenient because the
;   coordinate time at the SSB is the ephemeris time of the JPL
;   Planetary Ephemeris.
;
;   In general, the difference in the rate of Ti, the time kept by an
;   arbitrary clock, and the rate of T, the ephemeris time, is given
;   by the expression (Standish 1998):
;
;      dTi/dT = 1 - (Ui + vi^2/2) / c^2
;
;   where Ui is the potential of clock i, and vi is the velocity of
;   clock i.  However, when integrated, this expression depends on the
;   position of an individual clock.  A more convenient approximate
;   expression is:
;
;     T = Ti + (robs(Ti) . vearth(T))/c^2 + dtgeo(Ti) + TDB2TDT(Ti)
;
;   where robs is the vector from the geocenter to the observer;
;   vearth is the vector velocity of the earth; and dtgeo is a
;   correction to convert from the observer's clock to geocentric TT
;   time.  TDB2TDT is the value computed by this function, the
;   correction to convert from the geocenter to the solar system
;   barycenter.
;
;   As the above equation shows, while this function provides an
;   important component of the correction, the user must also be
;   responsible for (a) correcting their times to the geocenter (ie,
;   by maintaining atomic clock corrections); (b) estimating the
;   observatory position vector; and and (c) estimating earth's
;   velocity vector (using JPLEPHINTERP).
;
;   Users may note a circularity to the above equation, since
;   vearth(T) is expressed in terms of the SSB coordinate time.  This
;   appears to be a chicken and egg problem since in order to get the
;   earth's velocity, the ephemeris time is needed to begin with.
;   However, to the precision of the above equation, < 25 ns, it is
;   acceptable to replace vearth(T) with vearth(TT).
;
;   The method of computation of TDB2TDT in this function is based on
;   the analytical formulation by Fairhead, Bretagnon & Lestrade, 1988
;   (so-called FBL model) and Fairhead & Bretagnon 1990, in terms of
;   sinusoids of various amplitudes.  TDB2TDT has a dominant periodic
;   component of period 1 year and amplitude 1.7 ms.  The set of 791
;   coefficients used here were drawn from the Princeton pulsar timing
;   program TEMPO version 11.005 (Taylor & Weisberg 1989).
;
;   Because the TDB2TDT quantity is rather expensive to compute but
;   slowly varying, users may wish to also retrieve the time
;   derivative using the DERIV keyword, if they have many times to
;   convert over a short baseline.
;
; Verification
;
;   This implementation has been compared against a set of FBL test
;   data found in the 1996 IERS Conventions, Chapter 11, provided by
;   T. Fukushima.  It has been verified that this routine reproduces
;   the Fukushima numbers to the accuracy of the table, within
;   10^{-14} seconds.
;
;   Fukushima (1995) has found that the 791-term Fairhead & Bretagnon
;   analytical approximation use here has a maximum error of 23
;   nanoseconds in the time range 1980-2000, compared to a numerical
;   integration.  In comparison the truncated 127-term approximation
;   has an error of ~130 nanoseconds.
;
;
; PARAMETERS: 
;
;   JD - Geocentric time TT, scalar or vector, expressed in Julian
;        days.  The actual time used is (JD + TBASE).  For maximum
;        precision, TBASE should be used to express a fixed epoch in
;        whole day numbers, and JD should express fractional offset
;        days from that epoch.
;
;
; KEYWORD PARAMETERS:
;
;   TBASE - scalar Julian day of a fixed epoch, which provides the
;           origin for times passed in JD.
;          Default: 0
;
;   DERIV - upon return, contains the derivative of TDB2TDT in units
;           of seconds per day.  As many derivatives are returned as
;           values passed in JD.
;
;
; RETURNS:
;   The correction offset(s) in units of seconds, to be applied as
;   noted above.
;
;
; EXAMPLE:
;
;   Find the correction at ephemeris time 2451544.5 (JD):
;     IDL> print, tdb2tdt(2451544.5d)
;       -0.00011376314
;   or 0.11 ms.
;
;
; REFERENCES:
;
;   Princeton TEMPO Program
;      http://pulsar.princeton.edu/tempo/
;
;   FBL Test Data Set
;      ftp://maia.usno.navy.mil/conventions/chapter11/fbl.results
;
;   Fairhead, L. & Bretagnon, P. 1990, A&A, 229, 240
;     (basis of this routine)
;
;   Fairhead, L. Bretagnon, P. & Lestrade, J.-F. 1988, in *The Earth's
;     Rotation and Reference Frames for Geodesy and Geodynamics*,
;     ed. A. K. Babcock and G. A. Wilkins, (Dordrecht: Kluwer), p. 419
;     (original "FBL" paper)
;
;   Fukushima, T. 1995, A&A, 294, 895  (error analysis)
;
;   Irwin, A. W. & Fukushima, T. 1999, A&A, 348, 642  (error analysis)
;
;   Standish, E. M. 1998, A&A, 336, 381 (description of time scales)
;
;   Taylor, J. H. & Weisberg, J. M. 1989, ApJ, 345, 434 (pulsar timing)
;
;
; SEE ALSO
;   JPLEPHREAD, JPLEPHINTERP, JPLEPHTEST
;   
; MODIFICATION HISTORY:
;   Original logic from Fairhead & Bretagnon, 1990
;   Drawn from TEMPO v. 11.005, copied 20 Jun 2001
;   Documented and vectorized, 30 Jun 2001
;   
;
;  $Id: tdb2tdt.pro,v 1.4 2001/07/01 07:37:40 craigm Exp $
;
;-
; Copyright (C) 2001, Craig Markwardt
; This software is provided as is without any warranty whatsoever.
; Permission to use, copy and distribute unmodified copies for
; non-commercial purposes, and to modify and use for personal or
; internal use, is granted.  All other rights are reserved.
;-


function tdb2tdt_calc, jd, deriv=deriv, tbase=tbase

  common tdb2tdt_common, const0, freq0, phase0, texp
  if n_elements(const0) EQ 0 then begin
fbldata = [ $
1656.674564d,   6283.075849991d, 6.240054195d, $
  22.417471d,   5753.384884897d, 4.296977442d, $
  13.839792d,  12566.151699983d, 6.196904410d, $
   4.770086d,    529.690965095d, 0.444401603d, $
   4.676740d,   6069.776754553d, 4.021195093d, $
   2.256707d,    213.299095438d, 5.543113262d, $
   1.694205d,     -3.523118349d, 5.025132748d, $
   1.554905d,  77713.771467920d, 5.198467090d, $
   1.276839d,   7860.419392439d, 5.988822341d, $
   1.193379d,   5223.693919802d, 3.649823730d, $
   1.115322d,   3930.209696220d, 1.422745069d, $
   0.794185d,  11506.769769794d, 2.322313077d, $
   0.447061d,     26.298319800d, 3.615796498d, $
   0.435206d,   -398.149003408d, 4.349338347d, $
   0.600309d,   1577.343542448d, 2.678271909d, $
   0.496817d,   6208.294251424d, 5.696701824d, $
   0.486306d,   5884.926846583d, 0.520007179d, $
   0.432392d,     74.781598567d, 2.435898309d, $
   0.468597d,   6244.942814354d, 5.866398759d, $
   0.375510d,   5507.553238667d, 4.103476804d, $
   0.243085d,   -775.522611324d, 3.651837925d, $
   0.173435d,  18849.227549974d, 6.153743485d, $
   0.230685d,   5856.477659115d, 4.773852582d, $
   0.203747d,  12036.460734888d, 4.333987818d, $
   0.143935d,   -796.298006816d, 5.957517795d  ]
fbldata = [ fbldata, $
   0.159080d,  10977.078804699d, 1.890075226d, $
   0.119979d,     38.133035638d, 4.551585768d, $
   0.118971d,   5486.777843175d, 1.914547226d, $
   0.116120d,   1059.381930189d, 0.873504123d, $
   0.137927d,  11790.629088659d, 1.135934669d, $
   0.098358d,   2544.314419883d, 0.092793886d, $
   0.101868d,  -5573.142801634d, 5.984503847d, $
   0.080164d,    206.185548437d, 2.095377709d, $
   0.079645d,   4694.002954708d, 2.949233637d, $
   0.062617d,     20.775395492d, 2.654394814d, $
   0.075019d,   2942.463423292d, 4.980931759d, $
   0.064397d,   5746.271337896d, 1.280308748d, $
   0.063814d,   5760.498431898d, 4.167901731d, $
   0.048042d,   2146.165416475d, 1.495846011d, $
   0.048373d,    155.420399434d, 2.251573730d, $
   0.058844d,    426.598190876d, 4.839650148d, $
   0.046551d,     -0.980321068d, 0.921573539d, $
   0.054139d,  17260.154654690d, 3.411091093d, $
   0.042411d,   6275.962302991d, 2.869567043d, $
   0.040184d,     -7.113547001d, 3.565975565d, $
   0.036564d,   5088.628839767d, 3.324679049d, $
   0.040759d,  12352.852604545d, 3.981496998d, $
   0.036507d,    801.820931124d, 6.248866009d, $
   0.036955d,   3154.687084896d, 5.071801441d, $
   0.042732d,    632.783739313d, 5.720622217d  ]
fbldata = [ fbldata, $
   0.042560d, 161000.685737473d, 1.270837679d, $
   0.040480d,  15720.838784878d, 2.546610123d, $
   0.028244d,  -6286.598968340d, 5.069663519d, $
   0.033477d,   6062.663207553d, 4.144987272d, $
   0.034867d,    522.577418094d, 5.210064075d, $
   0.032438d,   6076.890301554d, 0.749317412d, $
   0.030215d,   7084.896781115d, 3.389610345d, $
   0.029247d, -71430.695617928d, 4.183178762d, $
   0.033529d,   9437.762934887d, 2.404714239d, $
   0.032423d,   8827.390269875d, 5.541473556d, $
   0.027567d,   6279.552731642d, 5.040846034d, $
   0.029862d,  12139.553509107d, 1.770181024d, $
   0.022509d,  10447.387839604d, 1.460726241d, $
   0.020937d,   8429.241266467d, 0.652303414d, $
   0.020322d,    419.484643875d, 3.735430632d, $
   0.024816d,  -1194.447010225d, 1.087136918d, $
   0.025196d,   1748.016413067d, 2.901883301d, $
   0.021691d,  14143.495242431d, 5.952658009d, $
   0.017673d,   6812.766815086d, 3.186129845d, $
   0.022567d,   6133.512652857d, 3.307984806d, $
   0.016155d,  10213.285546211d, 1.331103168d, $
   0.014751d,   1349.867409659d, 4.308933301d, $
   0.015949d,   -220.412642439d, 4.005298270d, $
   0.015974d,  -2352.866153772d, 6.145309371d, $
   0.014223d,  17789.845619785d, 2.104551349d  ]
fbldata = [ fbldata, $
   0.017806d,     73.297125859d, 3.475975097d, $
   0.013671d,   -536.804512095d, 5.971672571d, $
   0.011942d,   8031.092263058d, 2.053414715d, $
   0.014318d,  16730.463689596d, 3.016058075d, $
   0.012462d,    103.092774219d, 1.737438797d, $
   0.010962d,      3.590428652d, 2.196567739d, $
   0.015078d,  19651.048481098d, 3.969480770d, $
   0.010396d,    951.718406251d, 5.717799605d, $