CELESTIAL MECHANICS

Second cycle degree in ASTRONOMY

Campus: PADOVA

Language: English

Teaching period: Second Semester

Lecturer: STEFANO CASOTTO

Number of ECTS credits allocated: 6


Syllabus
Prerequisites: Students are expected to be familiar with Rational Mechanics and Mathematical Analysis, including the elementary theory of Ordinary Differential Equations.
A fair amount of curiosity about dynamical phenomena observed in the Solar and other planetary systems is useful, together with an interest in their precise modeling and computation and the design of exploration missions.
Examination methods: Homework, Final project report, Oral presentation of final report and discussion of the results and other topics covered during the lectures.
Course unit contents: 1. The equations of motion of gravitating systems
2. The Two-Body Problem and an initial value problem (IVP)
3. The Two-Body Problem and a boundary value problem (BVP)
4. Orbital maneuvers
5. Space and time reference systems
6. The computation of a Keplerian ephemeris
7. Preliminary orbit determination
8. Keplerian relative motion and its generalization
9. Regularization and Universal Formulation of the Two-Body Problem
10. The TBP as a boundary value problem (BVP) – Lambert targeting
11. The Problem of Three Bodies and its homographic solutions
12. The Circular Restricted Three-Body Problem – Jacobi’s integral, surfaces of zero velocity, Lagrangian points, Stability, Periodic orbits
13. The theory of Patched Conics and the design of gravity-assist interplanetary trajectories
14. Elements of perturbations and a the motion of an artificial Earth satellite