Abstract:
This work is dedicated to the study of the orbital motion of an artificial satellite moving
in the gravitational field of a viscoelastic planet, which in turn is moving in the gravitational
field of a massive attracting center and a satellite. The planet is modeled as a homogeneous
isotropic viscoelastic body, while the other celestial bodies are treated as material points. Under
the influence of the gravitational fields of the attracting center and the natural satellite, tidal
bulges arise in the viscoelastic body of the planet, which affect its gravitational potential and
serve as a disturbing factor for the orbital motion of artificial satellites in low-flying orbits.
The equations of motion for the artificial satellite are derived in terms of Delaunay canonical
variables. A procedure for averaging over the “fast” angular variables is carried out. In the
averaged equations, the “slow” Delaunay variables responsible for the evolution of the semimajor
axis and the eccentricity of the elliptical orbit remain unchanged. The entire effect of evolution is
concentrated in the change of inclination, longitude of the ascending node, and longitude of the
perigee from the ascending node. With respect to the specified orbital elements, an evolutionary
system of equations is derived. In the zero approximation for the dissipative terms, a closed
system of second-order differential equations is identified relative to the inclination and longitude
of the ascending node of the satellite’s orbit. Its stationary solutions are determined and their
stability is studied. The existence of stable stationary motions for polar satellites and satellites
close to equatorial ones is shown.
Keywords:satellite, orbital evolution, perturbations, orbital elements, tidal deformations
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