34685 - Fundamentals of Orbital Mechanics

Learning outcomes

The student learns and knows how to independently apply subjects related to space activities. In particular, learns the basics of orbital mechanics (restricted two-body motion) and Launch Vechicle dynamics with particular reference to the ascent trajectories and the selection of launch sites. In addition, the student discusses the various types of Earth orbits, with their typical perturbations, and finally the various phases of an interplanetary mission are described.

Course contents

Reference Systems and fundamental laws

Keplerian Problem (or restricted two-body problem)

- Fundamental Equation of Astrodynamics

- Integrals of motion

- Parametric Equation of the trajectory

- Lagrangian Parameters

- Orbital energy

- Time problem on Keplerian Orbits – Kepler’s Equation

- Characteristics of conics

Some types of Orbits and Missions

- Geostationary orbits

- Sun-Synchronous Orbits

- Satellites’ Ground Track

- Multistationary Orbits

- Interplanetary Orbits

- Orbital Transfers

- Launch Sites

Orbital Perturbations

- Solution Methods

- Solution of the perturbed problem

- Main perturbation acting on Earth satellites

- Effect of J2 and main applications

- Intuitive analysis of J22 effect

- Effect of atmospheric drag and solar radiation pressure

Flight dynamics of launchers

- No external forces: Tsiolkovsky's equation

- Gravity losses: constant attitude and constant angle of attack

Readings/Bibliography

1) Lecturer's course notes (in Italian) "“FONDAMENTI DI MECCANICA ORBITALE”, P. Tortora, A. Palli, M. Zannoni

2) W.J. Larson, J.R. Wertz, Space Mission Analysis and Design, Kluver, 1992

Teaching methods

Lectures are held by the course teacher. In lecturing hours the subjects are presented by the course teacher, including the explicit proof of all mathematical formulas introduced and to the presentation of the methods to solve the problems given in the practicing hours. The proposed exercises require the use of pocket calculators for the solution of the mathematical end engineering problems given by the lecturer.

Assessment methods

The examination is written and usually constists of three questions on various subjects. In the course of the examination it will be assessed the ability of the student to resolve new problems or at least to set up the correct resolutive strategy. The assessment of such ability has a fundamental weight in the attribution of the final marks.

The student must deal all three questions, and must reach the full proficiency in at least two of them. Only one question may be not sufficient, with a minimum mark of 5/10.

The ability to solve particularly complex engineering and mathematical problems and the demonstration of a particular level of study depth are important factors for the possible awarding of honors.

Teaching tools

LCD projector and PC are used in addition to the standard blackboard.

Office hours

See the website of Marco Zannoni