This CSPICE spkcpo_c routine example outputs:

AZ/EL computed without frame kernel:

       Solar azimuth (deg):           316.67141786
       Solar elevation (deg):         -54.85253216

On my machine, I've computed the same position with the new azlcpo_c routine:

furnsh_c ( "de440.bsp" );
furnsh_c ( "pck00010.tpc" );
furnsh_c ( "naif0012.tls" );
furnsh_c ( "earth_000101_230601_230308.bpc" );

str2et_c ( "2003-Oct-13 06:00:00 UTC", &et );

obslat = 35.425901111 * rpd_c();
obslon = -116.889537582 * rpd_c();
obsalt = 1.00179621332;

bodvrd_c ( "EARTH", "RADII", 3, &n, radii );

re = radii[0];
rp = radii[2];
f  = ( re - rp ) / re;

georec_c ( obslon, obslat, obsalt, re, f, obspos );

           obspos, "EARTH", "ITRF93", azlsta, &lt );

printf ( "\n"
         " Solar azimuth (deg):   %20.8f\n"
         " Solar elevation (deg): %20.8f\n"
         azlsta[1] * dpr_c(), azlsta[2] * dpr_c() );

which outputs:

Solar azimuth (deg):           316.67141785
Solar elevation (deg):         -54.85253206

So far, so good.

Here's Horizons System's output (query URL):

Ephemeris / WWW_USER Fri Mar 10 08:31:14 2023 Pasadena, USA      / Horizons    
Target body name: Sun (10)                        {source: DE441}
Center body name: Earth (399)                     {source: DE441}
Center-site name: (user defined site below)
Start time      : A.D. 2003-Oct-13 06:00:00.0000 UT      
Stop  time      : A.D. 2003-Oct-13 06:00:01.0000 UT      
Step-size       : 1440 minutes
Target pole/equ : IAU_SUN                         {East-longitude positive}
Target radii    : 696000.0, 696000.0, 696000.0 km {Equator_a, b, pole_c}       
Center geodetic : 243.1104624, 35.4259011, 1.0018 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 243.1104624,5203.99728,3677.05257 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : ITRF93                          {East-longitude positive}
Center radii    : 6378.137, 6378.137, 6356.752 km {Equator_a, b, pole_c}       
Target primary  : Sun
Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE441}
Rel. light bend : Sun                             {source: DE441}
Rel. lght bnd GM: 1.3271E+11 km^3/s^2                                          
Atmos refraction: NO (AIRLESS)
RA format       : DEG
Time format     : BOTH
Calendar mode   : Mixed Julian/Gregorian
EOP file        : eop.230308.p230601                                           
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2023-MAR-08. PREDICTS-> 2023-MAY-31
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s 
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
Table cut-offs 3: RA/DEC angular rate (     0.0=NO )                           
 Date__(UT)__HR:MN Date_________JDUT     Azimuth__(a-app)__Elevation
 2003-Oct-13 06:00 2452925.750000000  m  316.671270018 -54.852559210

Discrepancies of 0.000147842 degrees in AZ, and 0.00002705 degrees in EL.

That seems like a significant difference. As a comparison, a 7~8 seconds difference in delta T (TT - UT) will result in similar discrepancies; equivalent to the Earth moving over 200 km around its orbit.

What am I missing?

  • 1
    $\begingroup$ It's been a while since I looked at SPICE. Am I reading it right that you are not using the built in Earth model? As there are warnings about its accuracy. But I agree, that is a much larger discrepancy than I'd expect. $\endgroup$ Mar 10, 2023 at 23:50
  • 1
    $\begingroup$ @GregMiller AFAIK, I'm using the ITRF93 high accuracy Earth rotation model (binary file). The model to avoid is IAU_EARTH, provided in text a file. $\endgroup$
    – phil5
    Mar 11, 2023 at 0:49
  • 1
    $\begingroup$ @phil5 ITRF93 is not exactly "high accuracy", and the JPL reimplementation of it in terms of Chebyshev polynomials is even less accurate. People who do sub-arcsecond astronomy use more recent models from the IAU. $\endgroup$ Mar 11, 2023 at 10:24
  • 1
    $\begingroup$ @DavidHammen I was just using the official wording by NAIF. I'm more interested in knowing the source of error, given that Horizons System and SPICE supposedly use the same EOP files and planetary ephemeris. $\endgroup$
    – phil5
    Mar 11, 2023 at 14:31
  • 1
    $\begingroup$ Regarding "a 7~8 seconds difference in delta T (TT - UT) will result in similar discrepancies; equivalent to the Earth moving over 200 km around its orbit": You are forgetting the Earth's one revolution per sidereal day rotation. Even a small time discrepancy in DUT1 can result in a significant az-el discrepancy. That said, I would not consider a half an arcsecond discrepancy between Horizons and CSPICE "significant". Lesson learned: Don't use CSPICE or Horizons for milliarcsecond astronomy. $\endgroup$ Mar 11, 2023 at 15:47

1 Answer 1


Discrepancies of 0.000147842 degrees in AZ, and 0.00002705 degrees in EL.

Those discrepancies are very small; they are essentially the same numbers. There is one difference: your CSPICE calculations were made using DE440 while Horizons used DE441. From The JPL Planetary and Lunar Ephemerides DE440 and DE441,

The ephemerides DE440 and DE441 are fit to the same data set, but DE441 assumes no damping between the lunar liquid core and the solid mantle, which avoids a divergence when integrated backward in time. Therefore, DE441 is less accurate than DE440 for the current century, but covers a much longer duration of years −13,200 to +17,191, compared to DE440 covering years 1550–2650.

Try using DE441 rather than DE440 in your CSPICE calculations to see if that reduces the discrepancy.

  • $\begingroup$ DE441 and DE440 yield the exact same results, down to at least 8 decimals (AZ/EL). $\endgroup$
    – phil5
    Mar 11, 2023 at 14:01
  • $\begingroup$ "Very small" is a relative term. The accuracy of both DE's are less than 1 meter. The errors mentioned above are about .5 arcsec and .1 arcsec. It should be possible to get several more decimals worth of accuracy. $\endgroup$ Mar 11, 2023 at 15:40
  • $\begingroup$ @GregMiller I wonder if a very slightly different epoch, something like a few tens of milliseconds could realign the two positions? Is there any chance they interpret the input time differently, perhaps assuming different timescales? Is obstim = "2003 OCT 13 06:00:00.000000 UTC"; what you used in both cases? $\endgroup$
    – uhoh
    Mar 11, 2023 at 23:08
  • $\begingroup$ @phil5 ditto... $\endgroup$
    – uhoh
    Mar 11, 2023 at 23:09

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