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Secular and seasonal variations of the coefficient $J_2$ of the geopotentialare studied from the analysis of laser measurements of distances to thegeodetic satellites LAGEOS~1 (1988--2003) and LAGEOS~2 (1992--2003). It isconfirmed that beside the well-known annual variations with the amplitude$\approx 2.5 \times 10^{-10}$ there also exist very significant semi-annualvariations of a comparable amplitude. Phases of these two modes are such thatthe total effect may be described as a sharp postive splash of $J_2$ in Augustand considerably smaller variations in the rest part of year.

Large Variations of the coefficient $J_2$ of geopotential, and the  dynamical Love number $k_2^d$ from the analysis of laser ranging to LAGEOS~1  and LAGEOS~2