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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 nearbyfuture. A relevant role in space debris is played by lunisolar secularresonances, which might contribute to an increase of the orbital elements,typically of the eccentricity. We concentrate our attention on the lunisolarsecular resonance described by the relation $2\dot{\omega}+\dot{\Omega}=0$,where $\omega$ and $\Omega$ denote the argument of perigee and the longitude ofthe ascending node of the space debris. We introduce three different modelswith increasing complexity. We show that the growth in eccentricity, asobserved in space debris located in the MEO region at the inclination aboutequal to $56^\circ$, can be explained as a natural effect of the secularresonance $2\dot{\omega}+\dot{\Omega}=0$, while the chaotic variations of theorbital parameters are the result of interaction and overlapping of nearbyresonances.

A study of the lunisolar secular resonance $2\dot{\omega}+\dot{\Omega}=0$