Abstract
The dynamics of small bodies around the Earth has gained a renewed interest, since the awareness of the problems that space debris can cause in the nearby future. A relevant role in space debris is played by lunisolar secular resonances, which might contribute to an increase of the orbital elements, typically of the eccentricity. We concentrate our attention on the lunisolar secular resonance described by the relation $2\dot{\omega}+\dot{\Omega}=0$, where $\omega$ and $\Omega$ denote the argument of perigee and the longitude of the ascending node of the space debris. We introduce three different models with increasing complexity. We show that the growth in eccentricity, as observed in space debris located in the MEO region at the inclination about equal to $56^\circ$, can be explained as a natural effect of the secular resonance $2\dot{\omega}+\dot{\Omega}=0$, while the chaotic variations of the orbital parameters are the result of interaction and overlapping of nearby resonances.
Highlights
Thousands of man-made objects, abandoned during space missions or remnants of operative satellites, orbit around the Earth at different altitudes
We provide the definition of FLI in Supplementary Materials. Their values provide a numerical indication of the stable and chaotic behavior of the dynamical system as the initial conditions or some internal parameters are varied
Background described by model b, and which does not change significantly in a vicinity of several km from the nominal distance of a = 29, 546 km, one should superimpose the exact resonances shown in different colors in the right bottom panel of Figure 1
Summary
Thousands of man-made objects, abandoned during space missions or remnants of operative satellites, orbit around the Earth at different altitudes. The simplest model is described by a one degree-of-freedom autonomous Hamiltonian, which is obtained by averaging over the fast angles and by neglecting the rates of variation of the lunar longitude of the ascending node. This model provides the essential features, like the location of stable equilibria with large as well as with small libration amplitude. The last model includes the variation of the lunar longitude of the ascending node and shows that large chaotic regions can appear, contributing to an irregular variation of the orbital elements
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