Index Page eqncpv_c

A B C D E F G H I J K L M N O P Q R S T U V W X

Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       void eqncpv_c ( SpiceDouble        et,
                       SpiceDouble        epoch,
                       ConstSpiceDouble   eqel[9],
                       SpiceDouble        rapol,
                       SpiceDouble        decpol,
                       SpiceDouble        state[6] )

#### Abstract

       Compute the state (position and velocity of an object whose
       trajectory is described via equinoctial elements relative to some
       fixed plane (usually the equatorial plane of some planet).

#### Required_Reading

       None.

#### Keywords

       EPHEMERIS

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       et         I   Epoch in seconds past J2000 to find state
       epoch      I   Epoch of elements in seconds past J2000
       eqel       I   Array of equinoctial elements
       rapol      I   Right Ascension of the pole of the reference plane
       decpol     I   Declination of the pole of the reference plane
       state      O   State of the object described by eqel.

#### Detailed_Input

       et         is the epoch (ephemeris time) at which the state
                  of the target body is to be computed. et is measured
                  in seconds past the J2000 epoch.

       epoch      is the epoch of the equinoctial elements in seconds
                  past the J2000 epoch.

       eqel       is an array of 9 double precision numbers that
                  are the equinoctial elements for some orbit expressed
                  relative to the equatorial frame of the central body.
                  (The z-axis of the equatorial frame is the direction
                  of the pole of the central body relative to some
                  inertial frame.  The x-axis is given by the cross
                  product of the Z-axis of the inertial frame
                  with the direction of the pole of the central body.
                  The Y-axis completes a right handed frame.
                  (If the z-axis of the equatorial frame is aligned
                  with the z-axis of the inertial frame, then the
                  x-axis of the equatorial frame will be located at
                  90 degrees + rapol in the inertial frame.)

                  The specific arrangement of the elements is spelled
                  out below.  The following terms are used in the
                  discussion of elements of eqel

                      inc  --- inclination of the orbit
                      argp --- argument of periapse
                      node --- longitude of the ascending node
                      e    --- eccentricity of the orbit

                  eqel[0] is the semi-major axis (a) of the orbit in km.

                  eqel[1] is the value of 'h' at the specified epoch.
                          ( e*sin(argp+node) ).

                  eqel[2] is the value of 'k' at the specified epoch
                          ( e*cos(argp+node) ).

                  eqel[3] is the mean longitude (mean0+argp+node) at
                          the epoch of the elements measured in radians.

                  eqel[4] is the value of 'p' (tan(inc/2)*sin(node))at
                          the specified epoch.

                  eqel[5] is the value of 'q' (tan(inc/2)*cos(node))at
                          the specified epoch.

                  eqel[6] is the rate of the longitude of periapse
                          (dargp/dt + dnode/dt ) at the epoch of
                          the elements. This rate is assumed to hold
                          for all time. The rate is measured in
                          radians per second.

                  eqel[7] is the derivative of the mean longitude
                          ( dm/dt + dargp/dt + dnode/dt ). This
                          rate is assumed to be constant and is
                          measured in radians/second.

                  eqel[8] is the rate of the longitude of the ascending
                          node ( dnode/dt). This rate is measured
                          in radians per second.

       rapol      Right Ascension of the pole of the reference plane
                  with respect to some inertial frame (measured in
                  radians).

       decpol     Declination of the pole of the reference plane
                  with respect to some inertial frame (measured in
                  radians).

#### Detailed_Output

       state      State of the object described by eqel relative to the
                  inertial frame used to define rapol and decpol. Units
                  are in km and km/sec.

#### Parameters

       None.

#### Exceptions

       None.

#### Files

       None.

#### Particulars

       This routine evaluates the input equinoctial elements for
       the specified epoch and return the corresponding state.

       This routine was adapted from a routine provided by
       Bob Jacobson at JPL.

#### Examples

       Any numerical results shown for this example may differ between
       platforms as the results depend on the SPICE kernels used as input
       and the machine specific arithmetic implementation.

          Compute a state vector from a set of equinoctial elements.

          #include "SpiceUsr.h"
          #include <stdio.h>
          #include <math.h>

          int main()
             {

             /.

             Suppose you have classical elements and rates of
             change of the ascending node and argument of periapse
             for some satellite of the earth.

             By transforming the classical elements this routine
             compute the state of the object at an arbitrary epoch.
             The code below illustrates how to do this.

             The table below illustrates the meanings of the various
             variables used in the discussion below.

                  Variable     Meaning
                  --------     ----------------------------------
                  a            Semi-major axis in km.
                  ecc          Eccentricity of orbit.
                  inc          Inclination of orbit.
                  node         Longitude of the ascending node at epoch.
                  omega        Argument of periapse at epoch.
                  m            Mean anomaly at epoch.
                  dmdt         Mean anomaly rate in radians/second.
                  dnode        Rate of change of longitude of ascending node
                               in radians/second.
                  domega       Rate of change of argument of periapse in
                               radians/second.
                  epoch        is the epoch of the elements in seconds past
                               the J2000 epoch.

                  eqel[0] = a
                  eqel[1] = ecc * sin( omega + node )
                  eqel[2] = ecc * cos( omega + node )

                  eqel[3] = m + omega + node

                  eqel[4] = tan(inc/2.0) * sin(node)
                  eqel[5] = tan(inc/2.0) * cos(node)

                  eqel[6] = domega
                  eqel[7] = domega + dmdt + dnode
                  eqel[8] = dnode

             In this case, the rates of node and argument of
             periapse are zero and the pole of the central
             frame is aligned with the pole of an inertial frame.

             ./

             SpiceInt               i;

             SpiceDouble            a;
             SpiceDouble            argp;
             SpiceDouble            decpol;
             SpiceDouble            ecc;
             SpiceDouble            eqel   [9];
             SpiceDouble            et;
             SpiceDouble            gm;
             SpiceDouble            inc;
             SpiceDouble            m0;
             SpiceDouble            n;
             SpiceDouble            node;
             SpiceDouble            p;
             SpiceDouble            rapol;
             SpiceDouble            t0;
             SpiceDouble            theta;
             SpiceDouble            state  [6];

             p    =      1.0e4;
             gm   = 398600.436;
             ecc  =      0.1;
             a    = p/( 1. - ecc );
             n    = sqrt ( gm / a ) / a;
             argp = 30. * rpd_c();
             node = 15. * rpd_c();
             inc  = 10. * rpd_c();
             m0   = 45. * rpd_c();
             t0   = -100000000.;

             eqel[0] = a;
             eqel[1] = ecc*sin(argp+node);
             eqel[2] = ecc*cos(argp+node);
             eqel[3] = m0 + argp + node;
             eqel[4] = tan(inc/2.)*sin(node);
             eqel[5] = tan(inc/2.)*cos(node);
             eqel[6] = 0.;
             eqel[7] = n;
             eqel[8] = 0.;

             rapol    = -halfpi_c();
             decpol   =  halfpi_c();

             et = t0 - 10000.0;

             for ( i = 0; i < 10; i++)
                {
                et = et + 250.;

                eqncpv_c ( et, t0, eqel, rapol, decpol, state );
                printf ("\nPos = %16.6f %16.6f %16.6f \n",
                                 state[0], state[1], state[2] );
                printf (  "Vel = %16.6f %16.6f %16.6f \n",
                                 state[3], state[4], state[5] );
                }

             return 0;
             }

       The program outputs:

          Pos =    -10732.167433      3902.505791      1154.451615
          Vel =        -2.540767        -5.152269        -0.761576

          Pos =    -11278.382863      2586.179875       955.184099
          Vel =        -1.827156        -5.362916        -0.830020

          Pos =    -11645.295454      1228.612448       740.709574
          Vel =        -1.108096        -5.482811        -0.883256

          Pos =    -11832.799901      -147.990984       514.805250
          Vel =        -0.393421        -5.515905        -0.921508

          Pos =    -11843.089312     -1522.469846       281.175257
          Vel =         0.308288        -5.466565        -0.945128

          Pos =    -11680.364607     -2874.784755        43.424394
          Vel =         0.989520        -5.339364        -0.954552

          Pos =    -11350.589872     -4186.049765      -194.958526
          Vel =         1.643649        -5.138938        -0.950269

          Pos =    -10861.293274     -5438.536175      -430.610411
          Vel =         2.264759        -4.869899        -0.932792

          Pos =    -10221.410986     -6615.660644      -660.298988
          Vel =         2.847476        -4.536794        -0.902651

          Pos =     -9441.170335     -7701.967890      -880.925189
          Vel =         3.386822        -4.144103        -0.860382

#### Restrictions

       The equinoctial elements used by this routine are taken
       from  "Tangent" formulation of equinoctial elements

          p = Tan(inclination/2) * Sin(R.A. of ascending node)
          q = Tan(inclination/2) * Cos(R.A. of ascending node)

       Other formulations use Sine instead of Tangent.  We shall
       call these the "Sine" formulations.

          p = Sin(inclination/2) * Sin(R.A. of ascending node)
          q = Sin(inclination/2) * Cos(R.A. of ascending node)

       If you have equinoctial elements from this alternative
       formulation you should replace p and q  by the
       expressions below.

         P = P / sqrt( 1.0 - P*P - Q*Q )
         Q = Q / sqrt( 1.0 - P*P - Q*Q )

       This will convert the Sine formulation to the Tangent formulation.

#### Literature_References

       JPL Engineering Memorandum 314-513 "Optical Navigation Program
       Mathematical Models" by William M. Owen, Jr. and Robin M Vaughan
       August 9, 1991.

#### Author_and_Institution

       W.L. Taber      (JPL)
       R.A. Jacobson   (JPL)
       B.V. Semenov    (JPL)

#### Version

       -CSPICE Version 1.0.0, 20-MAR-2012  (EDW)

#### Index_Entries

       Compute a state from equinoctial elements

#### Link to routine eqncpv_c source file eqncpv_c.c

    Wed Apr  5 17:54:34 2017