#### Event Details

**Título:**

*Some rigorous results on the 1:1 resonance of the spin-orbit problem*

**Impartida por:**Mauricio Misquero Castro (Universidad de Granada - Universidad de Tor Vergata (Roma))

**Resumen:**Consider the problem of an spinning oblate satellite (e.g. the Moon) with respect to its center of mass when it is moving in a Keplerian ellipse around a planet (e.g. the Earth). This is the spin-orbit problem and it is modeled by a pendulum-like equation. We study the resonance 1:1 (e.g. the dark side of the Moon) from an analytical point of view, with no requirements of smallness of the orbital eccentricity and taking into account dissipative forces. The problem depends on \(e\), the eccentricity of the orbit, and on \(\Lambda\), the oblateness of the spinning body. Our main concern is the capture into the 1:1 resonance for points of the \((e,\Lambda)\)-plane. First, we find a region of uniqueness of the 1:1 resonance, which is the continuation from the solution for \(e=0\). Then, a subregion of linear stability is estimated. We also study a separatrix close to the line \(e=e_*\approx 0.682\), beyond which the resonance is unstable. Finally, we study the dissipative case by estimating regions of asymptotic stability of the solution (capture into resonance) depending on the strength of the dissipation applied.

20 de diciembre de 2019, 12:30,

*Seminario 2ª planta*IEMath-GR