Earth Deformations from Lageos Orbit

Abstract

In recent years it has become of relevant geophysical interest to detect a possible time variation of the low-degree coefficients of the Earth’s gravity field: in particular the observed drift of the geomagnetic pole could be connected with a secular variation of the phase angle λ₂₂ of the J₂₂ term of the gravitational field of order 10^-5 – 10^-4 yr^-1 (1). We investigate the possibility of detecting such a phenomenon via analysis of the tracking data from LAGEOS, the passive geodynamics satellite tracked by laser ranging from the ground.

The perturbations caused by J₂₂ on the orbit of LAGEOS can be computed by the usual perturbative approach of Lagrange’s equations, and the results are: i) no long-periodic perturbation is produced: ii) the main terms have a period of 12 sidereal hours, with an amplitude of 160 m in the along-track direction, 26 m in the radial direction and ~ 50 m (≃ 1 arcsec) in the out-of-plane direction, all the other terms being one order of magnitude smaller (2).

Therefore a relative accuracy of 10^-4 in the measure of J₂₂ requires a centimetric or subcentimetric accuracy of the tracking data: this seems difficult to be achieved mainly because of the degraded predictability of the orbit due to a non-modellable drag-like force of the order of 3.10^-10 cm s^-2 (3), whose effect reaches ~ 1 cm after ~ 1 day (in the along-track direction) or ~ 1 week (in the radial direction). The out-of-plane perturbation can be measured with even a worse precision due to the poor knowledge of the polar motion and Universal Time. Finally, we remark that at a higher precision one has to take into account also the small variations of the gravitational field produced by oceanic tides which cause a similar 12^h signature in the orbit of LAGEOS: the total amount of these perturbations is 3.10^-5 of the J₂₂ effect.