The aims of this module are to enable students to understand the principles of spacecraft trajectory design, navigation and operations for planetary missions. Using mathematical methods and knowledge of the physical world, it is possible to design and/or estimate spacecraft trajectories, or to retrieve properties of planets and moons from measurements taken by planetary orbiters and space probes. Mastering those topics enable the student to design space missions (navigation and observation systems inclusive) that are used in the exciting area of space exploration.

Programming is an important part of the course, since the most interesting problems can only be solved numerically. For this reason, students are expected to have some programming experience, and will be asked to program in MATLAB. By the end of the course, students will have developed their own astrodynamics toolbox and acquired good numeracy and analytical skills.

On completion of this module, the students wi ll understand the numerical techniques used in Astrodynamics. By the end of the module, the students will have developed their own numerical tools for preliminary spacecraft trajectory design through MATLAB scripts. The students will learn to use the open source NASA's ephemeris toolbox called SPICE Toolkit (https://naif.jpl.nasa.gov/naif/toolkit.html) that is commonly used by the Space Industry and Space Agencies for orbit design and navigation.

Particular attention would be given to space agencies' "Clean Space initiative" regarding new space missions design impact across their entire life cycle (i.e. design of the end-of-life and disposal of a spacecraft).

(LO1) On successful completion of the module, the students will be able to OUTLINE the principles of space mission design including the environmental impact of space missions' life cycle.

(LO2) On successful completion of the module, the students will be able to DISCUSS the principles of mission navigation and operations in their own words.

(LO3) On successful completion of the module, the students will be able to CALCULATE the dynamics governing the motion of a spacecraft in the solar system.

(LO4) On successful completion of the module, the students will be able to DIFFERENTIATE between several numerical methods for trajectory design and optimisation.

(LO5) On successful completion of the module, the students will be able to DETERMINE the appropriate numerical method for solving an astrodynamics problem.

(LO6) On successful completion of the module, the students will be able to DESIGN an original group project dealing with the principle of space mission design.

(LO7) On successful completion of the module, the students will be able to UNDERSTAND the importance of space missions life cycle within the space agencies' Clean Space Initiative.

(S1) Problem solving skills by adapting concepts to new problems

(S2) Numeracy by practicing solving exercises in MATLAB

(S3) Reasoning logically by using a rational, systematic series of steps based on sound mathematical procedures and given statements to arrive at a conclusion.

(S4) Generalising by using the concepts learned and adapting them to new problems.

(S5) Team working through group project.

(S6) Presenting Skills through project progress meetings and final presentation. The students will learn to communicate effectively their own results.

(S7) IT Skills the students will learn to use external tools that requires installation and appropriate configuration.

We review basic orbital mechanics and several topics in applied mathematics relevant to astrodynamics, such as dynamical systems, numerical methods, Hamiltonian mechanics, optimal control theory, navigation techniques and mission operation principles. Advance astrodynamics topics are the core of the module to bring the students to pace with the state of the art in interplanetary trajectory design and optimization. Example of case study are Earth’s application missions as GEO and interplanetary missions as Moon transfer. The main topics include:

• Dynamical models (i.e. keplerian and non-keplerian ) and reference systems

• Orbit transfers (i.e. lambert)

• Space environment modelling and principles of perturbations i.e. gravity field, magnetic field, solar radiation pressure etc and how to preserve our space environment i.e. spacecraft's life cycle and end-of-life

• Principle of mission operations and nav igations

• Three body problem, Invariant manifold theory, Computation of Periodic orbits

• An overview of spacecraft subsystems and instruments

From timetable all online seminars allocated.
Lectures pre-session material (i.e. pre-recorded intro video + 1 reading) + online seminar 1.5 h per week
Practical Computing Sessions pre-session material (i.e. pre-recorded video on problem explanation + handout ) + online seminar 1.5h to answer questions and supporting resolution of course work 1.5 h per week
It is envisaged to have one guest online Seminar

A list of useful readings and supporting material will be provided. Reading list already available

Computing needs:

• Matlab
• NASA's SPICE Toolkit(*)

(*) opensource