Introduction to Orbital Mechanics

Course Overview

This course bridges theory and practice in astrodynamics. You will learn how to model, simulate and analyze the motion of spacecraft and satellites in realistic environments, account for uncertainties, assess conjunction risks and apply these skills to mission design and operations. Through interactive lectures, hands-on computations and case studies, you will develop the analytical and programming skills required to tackle real challenges in spaceflight, navigation and space domain awareness.

You will learn to...

• Propagate orbits using analytical and numerical methods
• Model perturbations and assess their impact
• Analyze relative motion and rendezvous dynamics
• Propagate covariance and compute collision probability
• Work with real catalogs of space debris and background stars
• Apply astrodynamics to remote sensing mission analysis

Course highlights

• Advanced concepts explained with clarity
• Extensive hands-on exercises and projects
• Real-world datasets and professional toolkits
• Industry-relevant workflows and case studies

Course Vision

From equations to orbits, from models to missions

Develop the analytical rigor of a scientist, the practical mindset of an engineer, and the computational skills required to solve the astrodynamics challenges of the modern space age. Transform mathematical theory into operational capability through a program designed by a scientist, engineer, educator, and practitioner with experience spanning three decades in academia, industry, defence, and the international space community.

FROM EQUATIONS TO SPACE OPERATIONS

Modern space missions depend on professionals who can transform the mathematics of celestial mechanics into operational decisions. From orbit determination and mission design to conjunction assessment, collision avoidance, and Space Situational Awareness (SSA) / Space Domain Awareness (SDA), the demand for engineers and scientists trained in advanced astrodynamics has never been greater.

This professional training program bridges the gap between theory and practice by combining rigorous physical foundations with hands-on computational implementation using MATLAB/Octave, and Python. Participants learn not only the “why” behind orbital dynamics, but also the “how” used daily by flight dynamics engineers, mission analysts, SSA specialists, and spacecraft operators supporting real missions.

Designed for aerospace engineers, researchers, graduate students, and space professionals, the course progresses from classical orbital mechanics to contemporary topics including perturbation theory, numerical orbit propagation, orbit determination, relative motion, conjunction analysis, collision probability estimation, space debris modeling, and remote sensing mission applications.

Unlike traditional courses that stop at deriving equations, this program emphasizes implementation. Every major concept is reinforced through realistic case studies, numerical simulations, and scientific programming exercises. Participants build working computational tools while developing the physical intuition needed to understand and validate their results.

This program is created to complement—not replace—professional astrodynamics platforms such as Systems Tool Kit (STK). Participants will develop a deep understanding of the underlying orbital mechanics, perturbation models, estimation techniques, and numerical algorithms that power these tools, enabling them to use commercial software with greater confidence, rigor, and technical judgment.

BY THE END OF THE COURSE, YOU WILL BE ABLE TO:

• Model and propagate spacecraft trajectories using analytical and numerical methods.
• Analyze perturbations affecting operational spacecraft.
• Design orbital maneuvers and transfer trajectories.
• Perform conjunction assessment and collision risk analysis.
• Understand and model the orbital debris environment.
• Apply covariance analysis and uncertainty propagation techniques.
• Implement professional astrodynamics workflows in MATLAB/Octave, and Python.
• Transform equations into engineering decisions for real-world space missions.

WHO SHOULD ATTEND?

• Aerospace engineers and scientists
• Mission analysts and flight dynamics specialists
• Space Domain Awareness professionals
• Satellite operators
• Graduate students and researchers
• Professionals transitioning into the space sector

WHY THIS COURSE IS DIFFERENT

There is no shortage of astrodynamics textbooks. What is rare is a course that teaches participants how to transform theory into operational capability. Most courses focus on equations. Most online programs focus on software tools. This course teaches both.

Every major concept is derived from first principles, implemented in code, validated against realistic scenarios, and connected directly to the workflows used by mission analysts, spacecraft operators, and Space Domain Awareness teams. Participants do not simply learn orbital mechanics—they learn how modern astrodynamics is actually practiced.

WHAT MAKES THIS PROGRAM UNIQUE

Learn by Building

Every topic is accompanied by executable MATLAB, Octave, and Python examples. Participants implement orbit propagators, perturbation models, conjunction assessment algorithms, covariance propagation methods, and collision probability calculations rather than treating them as black boxes.

Real Operational Workflows

The curriculum reflects the analytical processes used throughout the space industry:

• Orbit propagation and mission analysis
• Space Situational Awareness (SSA/SDA)
• Conjunction assessment and Collision avoidance
• Space debris analysis
• Remote sensing mission design

From University Classroom to Industry Practice

Developed from advanced astrodynamics courses taught at Laval University and adapted for professional audiences, including presentation as a technical short course at the AMOS Conference, the premier international conference dedicated to Space Situational Awareness.

Understand Why, Not Just How

Participants learn the physical and mathematical foundations behind every model, algorithm, and numerical method. This enables them to design, evaluate, troubleshoot, and improve the computational tools used in operational environments.

Immediate Professional Relevance

The techniques covered are directly applicable to organizations involved in spacecraft operations, mission analysis, space surveillance, Earth observation, defense applications, and advanced aerospace research.

The result

Graduates leave with more than theoretical knowledge. They leave with a practical toolkit, working software implementations, and the confidence to really understand and tackle the astrodynamics challenges of modern space operations.

WHY LEARNING ASTRODYNAMICS FROM PROFESSIONAL SOFTWARE IS SO DIFFICULT

Professional astrodynamics software is extremely powerful, but it is designed primarily to solve operational problems—not to teach the physics behind them.

Complex calculations are often performed behind the interface, making it difficult to see how orbital mechanics, perturbation models, reference frames, numerical methods, and estimation techniques actually work together.

Without this foundation, it can be challenging to understand why a model was selected, recognize when an assumption is no longer valid, or determine whether a result is physically meaningful.

This program takes the opposite approach: understand the physics first, implement the methods yourself, and then use professional software with greater confidence, technical judgment, and understanding.

"A PICTURE IS WORTH A THOUSAND WORDS"

Orbital mechanics becomes much easier to understand when equations can be seen in action. Interactive simulations transform abstract mathematical concepts into trajectories, geometries, and motions that can be explored visually.

By changing orbital parameters and immediately observing their effects, you can develop an intuitive understanding of concepts that are often difficult to grasp from equations alone.

Throughout the program, visualization and simulation are used alongside theory to connect mathematical models with the physical behavior of real orbital systems.