34685 - Fundamentals of Orbital Mechanics

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Industry, innovation and infrastructure

Academic Year 2021/2022

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

- Perturbed orbit and geostationary orbit

- Intuitive analysis of J22 effect

Flight dynamics of launchers


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

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 in each of them a marks of at least 5/10. In order to pass the exam, the student must be proficient in at least two out of the three questions placed by the lecturer in order.

Teaching tools

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

Office hours

See the website of Paolo Tortora