LAGEOS–type Satellites in Critical Supplementary Orbit Configuration and the Lense–Thirring Effect Detection

In this paper we analyze quantitatively the concept of LAGEOS–type satellites in critical supplementary orbit configuration (CSOC) which has proven capable of yielding various observables for many tests of General Relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense–Thirring effect. By using an entirely new pair of LAGEOS–type satellites in identical, supplementary orbits with, e.g., semimajor axes a = 12000 km, eccentricity e = 0.05 and inclinations iS1 = 63.4◦ and iS2 = 116.6◦, it would be possible to cancel out the impact of the mismodelling of the static part of the gravitational field of the Earth to a very high level of accuracy. The departures from the ideal supplementary orbital configuration due to the orbital injection errors would yield systematic gravitational errors of the order of few percent, according to the covariance matrix of the EGM96 gravity model up to degree l = 20. However, the forthcoming, new gravity models from the CHAMP and GRACE missions should greatly improve the situation. So, it should be possible to measure the gravitomagnetic shifts of the sum of their nodes ΣΩ̇LT with an accuracy level perhaps less than 1%, of the difference of their perigees ∆ω̇LT with an accuracy level of 5% and of ẊLT ≡ ΣΩ̇LT − ∆ω̇LT with an accuracy level of 2.8%. Such results, which are due to the non–gravitational perturbations mismodelling, have been obtained for an observational time span of about 6 years and could be further improved by fitting and removing from the analyzed time series the major time–varying perturbations which have known periodicities.