15th order resonance terms using the decaying orbit of TETR-3

The orbit of TETR-3 (1971-83B), inclination: 33°, passed through resonance with 15th order geopotential terms in February 1972. The resonance caused the orbit inclination to increase by 0.015°. Analysis of 48 sets of mean Kepler elements for this satellite in 1971–1972 (across the resonance) has established the following strong constraint for high degree, 15th order gravitational terms (normalized):

$\text{10}{}^9\text{(}\text{C, S}\text{)}{}_{15}\text{= (28.3 ± 3.0, 7.4 ± 3.0) =}\text{0.001(}\text{C, S}\text{)}{}_{\mathrm{15,15}}\text{?0.015(}\text{C, S}\text{)}{}_{\mathrm{17,15}}\text{+0.073(}\text{C, S}\text{)}{}_{\mathrm{19,15}}\text{?0.219(}\text{C, S}\text{)}{}_{\mathrm{21,15}}\text{+0.477(}\text{C, S}\text{)}{}_{\mathrm{23,15}}\text{?0.781(}\text{C, S}\text{)}{}_{\mathrm{25,15}}\text{+1.000(}\text{C, S}\text{)}{}_{\mathrm{27,15}}\text{?0.0963(}\text{C, S}\text{)}{}_{\mathrm{29,15}}\text{+0.622(}\text{C, S}\text{)}{}_{\mathrm{31,15}}\text{?0.119(}\text{C, S}\text{)}{}_{\mathrm{33,15}}\text{?0.290(}\text{C, S}\text{)}{}_{\mathrm{35,15}}\text{+0.403(}\text{C, S}\text{)}{}_{\mathrm{37,15}}\text{?0.223(}\text{C, S}\text{)}{}_{\mathrm{39,15}}\text{?0.058(}\text{C, S}\text{)}{}_{\mathrm{41,15}}\text{+…}$

This result combined with previous results on high inclination 15th order and other resonant orbits suggests that the coefficients of the gravity field beyond the 15th degree are smaller than Kaula's rule ($\text{10}{}^{\mathrm{?5}}\text{l}{}^2$).