| Grant number: | 11/18819-0 |
| Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
| Start date: | November 01, 2011 |
| End date: | October 31, 2012 |
| Field of knowledge: | Physical Sciences and Mathematics - Astronomy - Positional Astronomy and Celestial Mechanics |
| Principal Investigator: | Nelson Callegari Júnior |
| Grantee: | Filipe Batista Ribeiro |
| Host Institution: | Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil |
Abstract The purpose of this undergraduate research project is to guide the student on topics of celestial mechanics and applications on the problem of rigid body rotation and resonance "spin-orbit". Emphasis will be given on the formulation of the problem and applications to some planets with physical parameters (e.g. radius and mass) consistent with the formation of a terrestrial type (e.g. rock) which belongs to multiple-planet systems. As an example, we study the planets CoRoT-7 b, Kepler-9 d, 55 Cnc e, Gliese 876 d, and the newly discovered Kepler-10 b, Kepler-11 b. The methodology is both analytic and numeric. The analytical part consists of: i) deduction of the equation of motion of the problem of rotation of a non-spherical body with symmetry, perturbed by a central point; ii) modeling the same problem through the inclusion of the third body in the star-planet system; iii) formulation of the concept of resonance "spin-orbit," in which the planet's orbital period is a multiple of its period of rotation. Topics on dynamic systems (e.g., equilibrium points, chaos, surfaces of section) will be initiated in this step. The numerical simulations are performed with numerical models developed in the analytical part. The main efforts will be focused on: I) numerical integration of differential equations, II) construction of surfaces of section (s.s.). In a first step, we consider the planet's orbit not disturbed by a third body in the star-planet system. In this case, the orbital eccentricity and semi-major axis of the planet is constant (consider the planar case). At this stage, the technique of s.s., widely used in dynamic systems will be applied to our problem. Then the elements of the planet will vary due to the action of a third body. Thus, in this work, we are developing a more realistic model of planetary rotation (and original one), than those written in the field of two bodies. The results in both cases are compared. Since the technique of s.s. is no longer applicable in the disturbing case, we quantitatively analyze the evolution of the characteristic angles of rotation (e.g. physical libration) studying individual orbits in dynamically important regions of phase space obtained in the case undisturbed.(AU) | |
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