# Difference between the TLE and the model at the epoch of the TLE file

See original GitHub issueWhen I propagate the orbit using the twoline2rv and propagate functions to the epoch day, I don’t obtain the same orbital parameters that appear on the TLE file. Am I doing something wrong or is it a limitation of the model itself?

I made the following example using the current TLE of the ISS:

```
from numpy import pi, sqrt
from sgp4.earth_gravity import wgs72, wgs84
from sgp4.ext import rv2coe
from sgp4.io import twoline2rv
line1 = "1 25544U 98067A 21041.71818700 .00002037 00000-0 45184-4 0 9998"
line2 = "2 25544 51.6445 248.2549 0002750 357.9058 122.1739 15.48954337268990"
rad2deg = 180/pi
G = 6.67408*10**(-20) # Gravitational constant
M = 5.9722*10**24 # Earth's mass
mu = G*M # Standard gravitational parameter
#====================== TLE orbital parameters and epoch =====================#
TLE_i = 51.6445 # Inclination
TLE_RAAN = 248.2549 # Right Ascention of the Ascending Node
TLE_e = 0.0002750 # Eccentricity
TLE_w = 357.9058 # Argument of the Perigee
TLE_MA = 122.1739 # Mean Anomaly
TLE_MM = 15.48954337 # Mean Motion (revolutions per day)
year = 2021
month = 2
epoch_day = 41.71818700
day = epoch_day - 31
hour = (day - int(day))*24
minute = (hour - int(hour))*60
second = (minute - int(minute))*60
#================================= SGP4 model ===============================#
sat_model = twoline2rv(line1, line2, wgs84)#wgs72)
pos, vel = sat_model.propagate(year, month, int(day),
int(hour), int(minute), second)
p, a, e, i, RAAN, w, theta, MA, argl, tlon, lonp = rv2coe(pos, vel, mu)
#================== Difference between the TLE and the model =================#
i_diff = abs(TLE_i - i*rad2deg)
RAAN_diff = abs(TLE_RAAN - RAAN*rad2deg)
e_diff = abs(TLE_e - e)
w_diff = abs(TLE_w - w*rad2deg)
MA_diff = abs(TLE_MA - MA*rad2deg)
a = a
n = sqrt(mu/(a**3))
period = 2*pi/n
MM = 86400/period
MM_diff = abs(TLE_MM - MM)
def print_differences():
print("Incl. (TLE): {}°, incl. (model): {}°, diff.: {}°".format(TLE_i, i*rad2deg, i_diff))
print("RAAN (TLE): {}°, RAAN (model): {}°, diff.: {}°".format(TLE_RAAN, RAAN*rad2deg, RAAN_diff))
print("Eccentricity (TLE): {}, Eccentricity (model): {}, diff.: {}".format(TLE_e, e, e_diff))
print("w (TLE): {}°, w (model): {}°, diff.: {}°".format(TLE_w, w*rad2deg, w_diff))
print("MA (TLE): {}°, MA (model): {}°, diff.: {}°".format(TLE_MA, MA*rad2deg, MA_diff))
print("Mean motion (TLE): {}, mean motion (model): {}, diff.: {}".format(TLE_MM, MM, MM_diff))
print_differences()
```

### Issue Analytics

- State:
- Created 3 years ago
- Comments:7 (4 by maintainers)

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## Top GitHub Comments

Brandon’s intuition is correct. rv2coe returns the osculating elements, not the SGP4 elements. They’re different. He’s also correct about the generation of TLEs from state vectors. It’s not a simple process. You need to take many state vectors over time and “fit”: an estimated TLE that when propagated, minimizes the error between the resultant state vectors and the source state vectors.

On Thu, Feb 11, 2021 at 8:30 AM Brandon Rhodes notifications@github.com wrote:

– Very Respectfully,

Dan CaJacob

Thank you both @brandon-rhodes and @dcajacob for your answers. I haven’t replied because I have been doing research on this topic. I found this document from JPL that I’m studying right now: https://trs.jpl.nasa.gov/bitstream/handle/2014/44785/10-0441_A1b.pdf?sequence=1&isAllowed=y

If I implement a solution in python I will post it here. Thanks again and take care.