The influence of tesseral harmonic $J_{22}$ term on the TLE orbit error of low polar orbit satellite

Abstract

By expanding the perturbation function of tesseral harmonic $J_{22}$ term of the earth’s non spherical gravitation, it is found that there is a term $\cos 2\Omega _{e}$ related to the rotation of the earth. The period of the term is half a day, and the coefficient includes the factor $\sin ^{2}i$ related to the orbital inclination angle. For the low polar orbit satellite with orbit inclination close to $90^{\circ }$ , $J_{22}$ term has a great impact on the orbit accuracy, which will reach the order of kilometers. Based on the measured orbit data (historical TLEs and GPS precise ephemeris) of the polar satellite GRACE-A/B, the influence of the tesseral harmonic $J_{22}$ term on TLE orbit error is further verified. It is found that the system bias caused by ignoring $J_{22}$ term exists in TLE orbit data for LEO, which shows a periodic change of 180 degrees with the geographic longitude in the in-track direction. In addition, the accuracy of TLE orbit in the northern hemisphere is significantly higher than that in the southern hemisphere, which is related to the distribution of SSN observation network. For GRACE-A satellite, the maximum system bias of TLE orbit can reach close to 1.5 km near the equator of the earth, and 8 km after a 7-day prediction period.