# SGP4 and TLE accuracy

From: Thomas Fly (thomasfly@j2ee-consultants.com)
Date: Wed Apr 23 2003 - 15:47:46 EDT

• Next message: Björn Gimle: "Obs Apr 23 #5918"

```I recently did some comparison calculations relating to the SGP4 model; for
easier viewing, this is also online at
http://j2ee-consultants.com/iss-transit/sgp4.htm

When observing a transit of the space station that's nearly overhead, the
"transit radius" is about 2 miles in diameter (the sun & moon have angular
want to be within a bullseye of 20% of the diameter of the sun or moon, you
therefore can deviate laterally from the transit path by only about +/- .2
miles, or 1000 feet -> 300 meters (proportionately more, if the transit
occurs at a low elevation angle).

Below, I ran some comparisons.  I found significant differences between the
ancient CelesTrak reference, and my own values, though my values (computed
by Java code) compare quite well with some tests done by Bill Gray (C++
code).

More worrisome are the differences I found between my computations, and
those given on the NASA web page, since they amount to much of the allowable
error (only errors that are lateral to the line of sight matter, of course).

Does anyone else have any calculations, for comparison?

TSINCE         X (km)         Y               Z
0.          2328.96594238  -5995.21600342  1719.97894287
2328.97070292  -5995.22083201  1719.9706582  WorldView;
EARTH_RADIUS = 6378.135, EARTH_FLATTENING = 1 : 298.26
2328.97070411  -5995.22083267  1719.97065591 Bill Gray
http://www.projectpluto.com/sat_code.zip (TEST2.OUT)

360.00000000  2456.00610352  -6071.94232177  1222.95977784
2456.1078549   -6071.93868494  1222.89555536
2456.10787315  -6071.93868109  1222.89554062

720.00000000  2567.39477539  -6112.49725342   713.97710419
2567.56292733  -6112.50381173   713.96185309
2567.56296196  -6112.50380107   713.96182567

1080.00000000  2663.03179932  -6115.37414551   195.73919105
2663.09012478  -6115.48276372   196.39911433
2663.09017487  -6115.48274400   196.39907429

1440.00000000  2742.85470581  -6079.13580322  -328.86091614
2742.55433733  -6079.66987202  -326.39144567
2742.55440172  -6079.66984111  -326.39149805

XDOT (km/s)  YDOT         ZDOT
2.91110113  -0.98164053  -7.09049922  CelesTrak
2.91207225  -0.98341531  -7.09081697  WorldView
2.91207225  -0.98341531  -7.09081697  Project Pluto

2.67852119  -0.44705850  -7.22800565
2.67938906  -0.4482884  -7.22879264
2.67938906  -0.44828838  -7.22879265

2.43952477   0.09884824  -7.31889641
2.44024486  0.09811113  -7.31995951
2.44024485   0.09811117  -7.31995951

2.19531813   0.65333930  -7.36169147
2.19612078  0.65241689  -7.36282421
2.19612076   0.65241695  -7.36282421

1.94707947   1.21346101  -7.35499924
1.94849699  1.21107414  -7.35619305
1.94849696   1.21107421  -7.35619305

Below, from
http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/
orbit/ISS/SVPOST.html

ISS  TRAJECTORY DATA

Lift off time (UTC)  :  N/A
Area (sq ft)  :  3325.0
Drag Coefficient (Cd) :   2.36
90 day mean solar flux (jansky)  :   172.4
12 month mean earth geomagnetic index  :   2.35

Maneuvers contained within the current ephemeris are as follows:

IMPULSIVE TIG (GMT)   M50 DVx(FPS)      LVLH DVx(FPS)      DVmag(FPS)
IMPULSIVE TIG (MET)   M50 DVy(FPS)      LVLH DVy(FPS)      Invar Sph
HA
DT                    M50 DVz(FPS)      LVLH DVz(FPS)      Invar Sph
HP
---------------------------------------------------------------------
---
There are no maneuvers.

Coasting Arc #1 (begining on orbit 1211)
---------------------------------------

Vector Time (GMT): 2003/111/04:16:12.228
Vector Time (MET): N/A
Weight (LBS)     : 396133.0

M50 Cartesian                         M50 Keplerian
-----------------------------------       --------------------------
------
X    =        4825000.71                 A    =         6776030.81
meter
Y    =       -4469367.23  meter          E    =           .0020221
Z    =        1585585.64                 I    =           51.40937
XDOT =       2329.384698                 Wp   =           56.30435
YDOT =       4560.772825  meter/sec      RA   =          306.09898
deg
ZDOT =       5725.744991                 TA   =          321.14417
MA   =          321.28937
Ha   =            216.422
n.mi
Hp   =            206.252

* My results (with differences from NASA's values):
*
*  Calendar is: 21 Apr 2003 / 4:16:12.228 UTC
*  julianDay = 2452750.67791931
*  year = 2003, dayOfYear = 111.17791931
*  timeElapsed since TLE epoch = -0.06098661 (fraction of day = -1.5 hours,
*
* Raw values (epoch of date)    J2000                                  M50
*
*  x =  4869714.11 meters         x =  4866972.63  diff. =  71.96      x =
4825071.69  diff. =  70.98
*  y = -4411611.02                y = -4415204.63          -11.99      y
= -4469379.80          -12.57
*  z =  1610483.26                z =  1608921.70         -211.30      z =
1585374.09         -211.55

M50 Cartesian                         J2K Cartesian
-----------------------------------       --------------------------
------
X    =       15830054.83                 X    =         4866900.67
Y    =      -14663278.32  feet           Y    =        -4415192.64
meter
Z    =        5202052.64                 Z    =         1609133.00
XDOT =       7642.338249                 XDOT =        2250.405630
YDOT =      14963.165437  feet/sec       YDOT =        4586.372359
meter/sec
ZDOT =      18785.252594                 ZDOT =        5736.872024

The mean element set is posted at the UTC for which position is just
north of the
next ascending node relative to the above vector time

TWO LINE MEAN ELEMENT SET

ISS
1 25544U 98067A   03111.23890592  .00041100  00000-0  34010-3 0
9003
2 25544  51.6314 306.3227 0006560  42.4273 317.7388 15.58334166
12129

Here, I computed the values for the start of the TLE epoch, day of year
111.23890592:

x =  4035830.69
y = -5432723.81
z =      210.36

As indicated by the NASA note, the space station is slightly north (210
meters) of the earth's equatorial plane at that time.

6378.135 km -
6378.1363   - http://www.ngs.noaa.gov/GRD/GPS/DOC/files/ac_noaa.html (9
Feb 2003)

EARTH_FLATTENING
1 : 298.26    -

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```

This archive was generated by hypermail 2b29 : Wed Apr 23 2003 - 15:58:51 EDT