the LAGEOS~I satellite orbit is considered. It is suggested
that two phenomena are responsible for the major part of these residuals:
(i) about $1.2$ \% mismodeling of the LAGEOS~I surface mean radiation
pressure coefficient, and (ii) the Yarkovsky-Schach thermal effect
with properly modeled evolution of the satellite spin axis. Minor
influence is also attributed to the asymmetric reflectivity of the
satellite surface and the asymmetric thermal emissivity of the Earth.
In all cases we give a suitable and compact formulation for the
long-term orbit analysis. It is argued that contrary to the case
of the LAGEOS~I along-track residuals adjustment, which does not
allow the determination of a particular combination of the
Yarkovsky-Schach effect parameters (being insensitive to it), the
combined analysis of the along-track residuals and the eccentricity
excitations allows for their decorrelation. The
resulting value of the Yarkovsky-Schach amplitude is estimated to be
approximately $175\;{\rm pm/s}^2$, about twice as large as
given in the preceding works.
It is also shown that the effect of the radiation
pressure of the Earth reflected sunlight (the albedo effect),
can be modeled with surprising precision by the redefinition of
the satellite surface reflectivity coefficient.
In view of the unexplained part of the eccentricity residuals, we
discuss the possible importance of several other non-gravitational
effects.
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