[Spice_discussion] how accurate is conics?

[Trent Waddington]

I'm trying to get a feel for how much ephemeris generated by the
HORIZONS system differs from the mathematical ideal.  I've been
looking at asteroids but, as a bit of a sanity check, I decided to
write some code to compare the output of conics with the precalculated
ephemeris of the Moon.  The kernels I'm using are:

\begindata

   KERNELS_TO_LOAD = ( 'naif0009.tls',
                       'pck00009.tpc',
                       'de421.bsp',
                       'earth_000101_101105_100814.bpc',
                     )

\begintext

and when stepping just 30 days I get a difference in position of
24891km using the following code.  Substituting another satellite
gives similar results.  Any hints on what I'm doing wrong here - or
even just whether my expectations are wrong - would be much
appreciated.


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

#define sun_mu 1.3271244001798698E+11
#define earth_mu 3.9860043289693922E+05

int main(int argc, char **argv)
{
    SpiceInt code = 301;
    SpiceDouble step = 30*24*60*60;

    furnsh_c("metakernel");

    // just an arbitrary start time
    SpiceDouble tdb;
    str2et_c("2000-JAN-01", &tdb);

    // grab current position of the Moon
    SpiceDouble gst[6];
    SpiceDouble light_time;
    spkez_c(code, tdb, "J2000", "NONE", 399, gst, &light_time);

    // convert to elements
    SpiceDouble elts[8];
    oscelt_c(gst, tdb, earth_mu, elts);

    // get the state after some step
    SpiceDouble st[6];
    conics_c(elts, tdb + step, st);

    // get the ephemeris at that step
    SpiceDouble ost[6];
    spkez_c(code, tdb + step, "J2000", "NONE", 399, ost, &light_time);

    // calculate the difference
    SpiceDouble diff[3];
    vsub_c(st, ost, diff);
    printf("change %f\n", vnorm_c(diff));

    return 0;
}