The influence of tesseral harmonic J22 term on the TLE orbit error of low polar orbit satellite

By expanding the perturbation function of tesseral harmonic J₂₂ term of the earth's non spherical gravitation, it is found that there is a term cos2 Ω_e related to the rotation of the earth. The period of the term is half a day, and the coefficient includes the factor sin²i related to the orbital inclination angle. For the low polar orbit satellite with orbit inclination close to 90^∘, J₂₂ 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 J₂₂ term on TLE orbit error is further verified. It is found that the system bias caused by ignoring J₂₂ 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.