Orbit Injection Errors for the Proposed Lageos III Mission

An analysis is presented of the orbital injection errors for the Lageos III satellite mission. Several methods are introduced for the solution of the inverse problem in the theory of errors. The novelty of the present approach consists in the use of the full geopotential covariance matrix in the error propagation equations. The GEM-T1 covariance matrix is used. It is found that, by properly accounting for the correlation among the even zonal harmonic coefficients, the acceptable error bounds increase by an order of magnitude with respect to the case when only the variances are used. The most stringent constraint, even when using the full covariance, is on inclination, whose nominal value must be realized within approximately 0.1 deg for the recovery of the Lense-Thirring precession to be successful at the 3 percent level (accounting only for injection errors). The associated tolerance in the semimajor axis is about 30 km, while that in eccentricity is approximately 0.2. However, if the errors in semimajor axis and eccentricity can be kept to the routinely achievable levels of 10 km and 0.004, respectively, the tolerance in inclination can be relaxed to 0.2 deg.