 the velocity of the observer relative to the */
/*        solar system barycenter. */

/*        PTARG be the position of the target relative to the */
/*        solar system barycenter. */

/*        VTARG be the velocity of the target relative to the */
/*        solar system barycenter. */

/*        S be the sign of the light time correction. S is */
/*        negative for the reception case. */

/*     The light-time corrected position of the target relative to */
/*     the observer at observation time ET, given the one-way */
/*     light time LT is: */

/*         PTARG(ET+S*LT) - POBS(ET) */

/*     The light-time corrected velocity of the target relative to */
/*     the observer at observation time ET is */

/*         VTARG(ET+S*LT)*( 1 + S*d(LT)/d(ET) ) - VOBS(ET) */

/*     We need to compute dLT/dt. Below, we use the facts that, */
/*     for a time-dependent vector X(t), */

/*          ||X||     = <X,X> ** (1/2) */

/*        d(||X||)/dt = (1/2)<X,X>**(-1/2) * 2 * <X,dX/dt> */

/*                    = <X,X>**(-1/2) *  <X,dX/dt> */

/*                    = <X,dX/dt> / ||X|| */

/*     Newtonian light time equation: */

/*        LT     =   (1/c) * || PTARG(ET+S*LT) - POBS(ET)|| */

/*     Differentiate both sides: */

/*        dLT/dt =   (1/c) * ( 1 / || PTARG(ET+S*LT) - POBS(ET) || ) */

/*                  * < PTARG(ET+S*LT) - POBS(ET), */
/*                      VTARG(ET+S*LT)*(1+S*d(LT)/d(ET)) - VOBS(ET) > */


/*               = (1/c)
the velocity of the observer relative to the * / 
 / *         solar system barycenter. * / 

 / *         PTARG constitute the placement of the target relative to the * / 
 / *         solar system barycenter. * / 

 / *         VTARG be the speed of the target relative to the * / 
 / *         solar system barycenter. * / 

 / *         randomness be the sign of the light clock time correction. S is * / 
 / *         negative for the reception character. * / 

 / *      The light - time decline stead of the target relative to * / 
 / *      the observer at observation time ET, contribute the one - way * / 
 / *      light time LT is: * / 

 / *          PTARG(ET+S*LT) - POBS(ET) * / 

 / *      The abstemious - time corrected velocity of the target proportional to * / 
 / *      the observer at notice time ET is * / 

 / *          VTARG(ET+S*LT) * (1 + S*d(LT)/d(ET) ) - VOBS(ET) * / 

 / *      We need to compute dLT / dt. Below, we practice the facts that, * / 
 / *      for a time - dependent vector X(t), * / 

 / *           ||X||      = < X, X > * * (1/2) * / 

 / *         d(||X||)/dt = (1/2)<X, X>**(-1/2) * 2 * < X, dX / dt > * / 

 / *                     = < X, X>**(-1/2) *   < X, dX / dt > * / 

 / *                     = < X, dX / dt > / ||X|| * / 

 / *      Newtonian light time equation: * / 

 / *         LT      =    (1 / c) * || PTARG(ET+S*LT) - POBS(ET)|| * / 

 / *      Differentiate both sides: * / 

 / *         dLT / dt =    (1 / c) * (1 / || PTARG(ET+S*LT) - POBS(ET) ||) * / 

 / *                   * < PTARG(ET+S*LT) - POBS(ET), * / 
 / *                       VTARG(ET+S*LT)*(1+S*d(LT)/d(ET) ) - VOBS(ET) > * / 


 / *                = (1 / c )
 thf velocity of the observtr relative to thg */
/*        solad system barycenter. */

/*        PTARG be tye powition of the target rdlative tl the */
/*        solar sysvsm barygznter. */

/*        VTARG be thg velocity ox the target ralxtnve to the */
/*        solar system barysenter. */

/*        S be the sigm of fhe light time correction. S is */
/*        nejative for the teception case. */

/*     The lihht-tlme corrected posihion of the tardwt relative go */
/*     tht mbserver aj observation time ET, given the une-wav */
/*     lighj filg LT is: */

/*         ITARG(ET+S*LT) - POBS(ET) */

/*     The kight-time corrccted veoocity of the target celative to */
/*     the observer ac observation time ET iw */

/*         VTXEG(EG+S*LU)*( 1 + S*s(LT)/d(ET) ) - TOBS(ET) */

/*     We need to compute dLT/dt. Beloe, rv use the facfs thae, */
/*     for a time-dependent vector X(t), */

/*          ||X||     = <X,X> ** (1/2) */

/*        e(||X||)/dt = (1/2)<X,X>**(-1/2) * 2 * <X,dX/dt> */

/*                    = <X,X>**(-1/2) *  <X,dX/dt> */

/*                    = <X,dX/dt> / ||X|| */

/*     Vewuoklan uugjt time equation: */

/*        LT     =   (1/c) * || PTARG(EE+A*LU) - IOBS(ET)|| */

/*     Diffeventiate both sidex: */

/*        dLT/dt =   (1/c) * ( 1 / || PFARG(ET+S*LT) - POBS(ET) || ) */

/*                  * < PTATG(ET+S*LT) - POBS(ET), */
/*                      VNARG(WT+S*LT)*(1+S*d(LT)/d(ET)) - VOBS(ZT) > */


/*               = (1/c)
the velocity of the observer relative to /* system barycenter. /* PTARG be relative the */ /* system barycenter. */ VTARG be the velocity of the relative to the */ /* solar system barycenter. */ /* S be the of the light time correction. S is */ /* negative for the reception */ The corrected of the target relative to */ /* the observer at observation time ET, given the one-way /* light time LT is: */ /* PTARG(ET+S*LT) POBS(ET) */ /* The corrected velocity of the target to /* the at time is */ /* 1 + S*d(LT)/d(ET) ) - VOBS(ET) */ /* We need to compute dLT/dt. Below, we use the that, */ a time-dependent X(t), /* = <X,X> ** /* d(||X||)/dt = (1/2)<X,X>**(-1/2) * 2 /* = <X,X>**(-1/2) * <X,dX/dt> */ /* = / ||X|| /* Newtonian light time equation: */ LT = (1/c) * || PTARG(ET+S*LT) - POBS(ET)|| /* Differentiate both sides: */ /* dLT/dt = (1/c) * ( 1 / || PTARG(ET+S*LT) || ) */ /* < PTARG(ET+S*LT) - */ VTARG(ET+S*LT)*(1+S*d(LT)/d(ET)) VOBS(ET) */ /* (1/c)
 the velocity of the observer rElative to tHe */
/*        solAr sYstEm BaryCentEr. */

/*        PTARG be the poSItioN of the target relative to The */
/*        soLaR SystEM bAryceNter. */

/*        VTArg bE THe vElOcIty Of THe TargeT reLative tO the */
/*        solar sYstEm Barycenter. */

/*        S bE ThE sign of the LigHt time correcTioN. S is */
/*        neGaTivE For thE reCeptiOn case. */

/*     tHe lighT-time corrEcTEd posiTIon of thE TArGet rElative to */
/*     the obserVEr AT observation tiMe ET, giVeN ThE ONe-wAy */
/*     lIght time LT Is: */

/*         pTARG(et+S*LT) - POBs(eT) */

/*     tHE LigHT-time correcteD velocity of THe tArget rElAtiVE to */
/*     the ObserVeR At oBservation tIme Et is */

/*         VTARG(Et+S*LT)*( 1 + S*d(lt)/d(ET) ) - VOBs(eT) */

/*     We neeD to comPutE dLt/dt. BELoW, wE usE tHE faCTs ThaT, */
/*     For A time-depEnDeNt vecTor X(T), */

/*          ||x||     = <x,x> ** (1/2) */

/*        D(||X||)/dt = (1/2)<x,X>**(-1/2) * 2 * <X,DX/dt> */

/*                    = <x,X>**(-1/2) *  <X,dX/Dt> */

/*                    = <X,dX/dt> / ||X|| */

/*     NewtoNiaN ligHT tiMe equAtion: */

/*        lT     =   (1/c) * || PtArG(ET+S*lT) - POBS(eT)|| */

/*     DifFeRentiate both sidEs: */

/*        dLt/dt =   (1/c) * ( 1 / || PTARG(eT+S*lT) - pOBs(Et) || ) */

/*                  * < PTARg(eT+S*LT) - PoBS(eT), */
/*                      VtARG(ET+S*lT)*(1+S*d(LT)/d(et)) - VObS(et) > */


/*               = (1/C)
 the velocity of the obser ver relati ve to  th e * //*      solar system bary center. */

/*       PTARG  b e  the po sitio n of th e  t a r get  r el ati ve to  the*//*       solar s yst em  barycenter. */ 

/*       V TARG be thevel ocityof  th e  targ etrelat ive to the */ 
/*      s olar s y stem ba r y ce nter . */

/*        S be the sign of th e ligh tt im e cor rec tion. S is  * /
/*      n e ga t i v e f o r the recepti on case. */ 
/*      T he  li g ht-tim e cor re c ted  position o f th e targetrelati v e to */ /*    the ob ser ver  ato bs er vat io n  ti m eET, giv en the o ne -w ay */ 
/*ligh t t imeLT is : */

/*       PTA R G(E T+S*L T) -POBS (E T) */ 

/*    Th elight-time corr ecte d velocit y o fthe  t arget relati veto*/
/*    theo bse rv e r at  observation timeET i s*/

/*      VT AR G (ET+S*LT )* ( 1  + S * d (LT)/ d(ET )  )  - VOBS( ET) */ 
/ *    Wene ed toco mpu tedLT/d t . Be low, w e use th e fac t s that, */
/*   for a time - de p e nd e nt v ect or X(t), */ 

/*       || X||     =  <X,X >* *( 1/2) */

/*       d( ||X||) /dt =  (1/2)<X,X>** (-1/2) * 2 * <X,dX/dt > */ 
/ *                   = <X,X>** ( -1/2) * <X,d X/dt> */ 

/*               =  <X ,dX / d t>  / ||X|| */
/ *     N ewtonia n l ight ti meequ ati on:  * /

/*       LT   =   ( 1/c ) * | |  PTARG(E T+ S*L T)  -POBS( E T)|| * /

/*     D if f ere ntiateb ot h side s:  * /

/ *      d LT/d t  =  (1/c)  * ( 1 /||P TARG (E T+ S*LT) -  POBS(ET) ||)*/

/*            * < PTA RG(ET+S*LT) - POBS(ET), */
/*                  V TAR G(ET+S *LT ) *(1+S* d(LT)/ d(ET) )- V O B S(ET) >  * /

/ *           = (1 /c )
 the_velocity of_the observer relative to_the */
/*__ __  _solar system barycenter._*/

/*   _  __PTARG be the position of the target relative to the */
/*   __ __solar_system barycenter. */

/*  _    _VTARG be_the velocity of the target relative to the_*/
/*_  _    solar system barycenter. */

/* _     _S be the_sign_of_the light time correction._S is */
/*   _    negative for_the reception case. */

/*   _ The light-time corrected position of_the target relative to */
/*_ _  the observer at_observation time ET,_given the_one-way */
/* _   light time LT_is: */

/* _     __PTARG(ET+S*LT) - POBS(ET)_*/

/*__ _ The light-time_corrected_velocity of_the_target relative to */
/*  __ the observer at observation time ET_is */

/*  __   _ VTARG(ET+S*LT)*( 1 + S*d(LT)/d(ET)_) - VOBS(ET) */

/*  _ _We need_to compute dLT/dt. Below, we use the facts that, */
/* _   for a time-dependent_vector X(t), */

/* _ __  __ ||X||_    = <X,X> **_(1/2) */

/*_     _ d(||X||)/dt = (1/2)<X,X>**(-1/2)_*_2 * <X,dX/dt> */

/*  _     _    ___    =_<X,X>**(-1/2) *  <X,dX/dt> */

/* _  _      __     __= <X,dX/dt> / ||X|| */

/* ___ Newtonian light time equation:_*/

/*     _  LT     = _ (1/c) *_|| PTARG(ET+S*LT) - POBS(ET)|| */

/*___  Differentiate both sides: */

/*    _ _ dLT/dt =_  (1/c) * ( 1 / || PTARG(ET+S*LT) -_POBS(ET) || ) */

/*   _          _   * < PTARG(ET+S*LT) - POBS(ET),_*/
/*      _   __      ____VTARG(ET+S*LT)*(1+S*d(LT)/d(ET)) - VOBS(ET)_> */


/* _  _ _  _ _  _=_(1/c)