# SGP4 gravity model accuracy

From a simulation, I obtain the instantaneous radius vector of the SFERA 2 satellite. If I compare that radius vector with the one obtained from the SGP4 propagator, I get very big differences. The following graph shows what I mean:

How the radius vector is calculated

SGP4: starting from the TLE 17247.56557513, I propagate that TLE for 1 orbit centered on the TLE epoch to find the perigee and the apogee and I do the same for the next 539 TLEs (the SGP4 plot shows 540 points obtained from 540 TLEs).

The other 3 plots are obtained from a numerical propagator based on the DOPRI853 integrator. The initial TLE is the same used for the SGP4 plot (17247.56557513). The blue plot is obtained when I use the GRACE Gravity Model Version 3 Combined truncated to the order and degree 25, for the orange plot I use a spherical Earth and for the green plot I add the J2 perturbation.

Is it possible that the blue plot shows the true shape of the radius vector, while the SGP4 plot show just an approximate shape? In other words, is it possible that the SPG4 propagator is so wrong?

• SGP4 model show 1~3km error with each day. I think grace is better takes much more harmonics into consideration – Prakhar Apr 29 '18 at 15:48
• Not sure I'm understanding your method right, but if you're plugging in orbital elements straight from the TLE into your numerical integrator, don't do that – Chris Apr 29 '18 at 16:04
• @Chris I convert the TLE elements to the osculating initial state with the SGP4, then I convert the TEME osculating state to J2000 osculating state. – Cristiano Apr 29 '18 at 16:59
• @Prakhar. But if we take the blue plot as the most accurate, the SGP4 error is incredibly big (up to 40 km!) – Cristiano Apr 29 '18 at 17:03
• @Cristiano well, that's the way to do it. Carry on – Chris Apr 29 '18 at 19:27