Geopotential resonances on Vanguard orbits

Since their establishment in 1959 the orbits of Vanguard 3 (1959-7A) and the Vanguard 2 rocket (1959-2B) have been slowly contracting through at least five strong resonances of eleventh order. Tracking with Baker-Nunn cameras and the U.S. Navy space surveillance (radio interferometer) system over a 14-year period has revealed resonant fluctuations on them of up to 0.035 deg in inclination (peak to peak). Six geopotential terms (lumped coefficients) of eleventh order and three of twenty-second order have been measured by using orbit inclinations derived from this tracking record. The terms of eleventh order are significantly smaller than is predicted by Kaula's rule. (The lumped coefficients are sensitive to geopotential effects as high as thirty-seventh degree.) These observed terms are compatible with a recent 27-satellite geopotential solution (GEM 7) whose formal coefficent errors are increased by a factor of 3.3.