  The stability of the motion of the planet satellites is considered in the
model of the general three-body problem (Sun-planet-satellite). "Sundman
surfaces" are constructed, by means of which the concept "Sundman stability" is
formulated. The comparison of the Sundman stability with the results of
Golubev's c2h method and with the Hill's classical stability in the restricted
three-body problem is performed. The constructed Sundman stability regions in
the plane of the parameters "energy - moment of momentum" coincide with the
analogous regions obtained by Golubev's method, with the value (c2h)cr. The
construction of the Sundman surfaces in the three-dimensional space of the
specially selected coordinates xyR is carried out by means of the exact Sundman
inequality in the general three-body problem. The determination of the singular
points of surfaces, the regions of the possible motion and Sundman stability
analysis are implemented. It is shown that the singular points of the Sundman
surfaces in the coordinate space xyR lie in different planes. Sundman stability
of all known natural satellites of planets is investigated. It is shown that a
number of the natural satellites, that are stable according to Hill and also
some satellites that are stable according to Golubev's method are unstable in
the sense of Sundman stability.
