(1) St. Petersburg University, St. Petersburg, Russia
(2) Dept. de Matematica Aplicada Fundamental,
Facultad de Sciencias, Valladolid, Spain
We consider the motion of a spherically-symmetric balloon satellite perturbed by Earth's oblateness and solar radiation pressure. For equatorial satellite orbits and neglecting the Earth obliquity and shadowing effects, the orbit-averaged equations for eccentricity and longitude of pericenter are integrable in quadratures (Krivov and Getino 1995, submitted to Astron. Astrophys.). Various phase portrait topologies and bifurcation effects are studied. The instability zone associated with the separatrix of a saddle equilibrium point in the phase space has been found and explored in depth. For semimajor axes about two Earth's radii, and for area-to-mass ratios in the order of several tens cm$^2$/g, the amplitude of eccentricity oscillations may change nearly twofold (from 0.25 to 0.42) under a small change of initial conditions or force parameters. As this takes place, the period of eccentricity variations also jumps almost twofold, from 13 to 30 years. Numerical integrations of non-averaged equations of motion with actual Earth obliquity of 23.5 degrees, with due account for shadowing, and with a more realistic force model support the existence of this phenomenon. However, spatiality of the problem destroys the saddle separatrix and generates complex stochastic dynamics. The quasirandom motions of space balloons are investigated in terms of two-symbol (0-1) sequences by methods of stochastic celestial mechanics.