# Recreating the eccentricity value of TLE

I cannot confirm the eccentricity value of a TLE using corresponding position and velocity vectors. Let me go through an example, ISS, to explain the situation.

Using this TLE for ISS,

1 25544U 98067A 17198.89938657 .00000988 00000-0 22167-4 0 9998

2 25544 51.6416 245.2318 0005849 47.2823 302.7554 15.54170925 66526

Tle data says eccentricity is 0.0005849. Propagating this tle for 0 minutes to get TEME vectors yield,

r=-3.468881045420031e+03, -5.752706429352231e+03, -9.339830044476138e+02

v= 3.693246416348322 , -3.17757480606644, 5.92375001851741

Using ordinary orbital mechanics formulations to obtain eccentricity from those vectors finds eccentricity as 0.0016. The error is 168% compared to TLE data.

Then, I tried converting to ECI since an inertial system is required to use usual orbital mechanics formulations. Converting TEME to ECI with a lot of assumptions about polar motion and nutation finds,

r = -3492.98975522683, -5739.01656212581, -928.333286976148

v = 3.69073985425235, -3.19228499069521, 5.91739984184932

eccentricity is again 0.0016.

What is the reason for this big difference in TLE and orbital calculations?

(eccentiricy is found as 0.0750 when calculated with ECEF vectors).

I also found this website (http://www.tle.info/data/ISS_DATA.TXT), it gives information about ISS orbit. First, it lists some orbital properties for ISS. It says eccentricity is 0.0005425, however, on the same page it also lists keplerian elements and says that eccentricity is 0.0018464. They have the same inconsistency that I'm trying to solve.

I'm aware TLE elements and coordinate transformations I used are not very precise but I don't think they would cause this much error.

• – Chris Aug 10 '17 at 15:14
• I'm not sure if eccentricity is an oscillating element. I'll check by comparing ecc. values of different TLEs. – VolkanOzcan Aug 10 '17 at 15:25
• Use SGP4 to propagate the trajectory over several orbits -- you'll see the instantaneous eccentricity oscillate. TLE values are average parameters meant to be used for the SGP4 orbit propagator only, which includes perturbations due to atmospheric drag and nonspherical gravitation. – Tristan Aug 10 '17 at 15:37
• I ran it for a day with one-minute intervals, the minimum was 0.0008 and maximum was 0.0021. I guess that explains my problem. I did not expect eccentricity vector to oscillate this much. – VolkanOzcan Aug 10 '17 at 15:58
• @uhoh I'll write soon. – VolkanOzcan Aug 11 '17 at 13:49

• Very nice answer! Personally I'd reinforce the point that not only in the propagator, but in reality Earth's gravity field at LEO distances is lumpy and not purely $1/r^2$, so while they may be close, orbits are simply not elliptical. This means that trying to use Keplerian elements is always going to be an approximation. – uhoh Aug 16 '17 at 4:56