Spacecraft Orbital Mechanics

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Understand the physical and mathematical principles of relative orbital motion, and apply the Clohessy-Witshire equations to relative motion problems such as docking maneuvers and formation flying.
• Understand how rotational motion theory is used to derive torque-free motion of rotationally symmetric bodies and apply the resulting equations to satellite attitude dynamics and coning maneuvers.
• Design interplanetary preliminary trajectories by applying the method of patched conics while applying planetary phasing considerations. Refine these trajectories by rephrasing the problem as a numerical trajectory optimization in high-fidelity dynamics using the NASA GMAT software package.
• Understand the mathematical formulation of 3D rotational motion including direction cosines, Euler angles, and quaternion representations and Euler's equation in inertial and rotating frames.
• Understand the basic principles of preliminary orbit determination by applying Gauss' method, Gibbs' method, and Lambert's problem.
• Design complex 3D space trajectories around Earth and the solar system using impulsive maneuvers (planar and inclined). Apply extended Hohmann and Hohmann-like transfers, single-impulse maneuvers, phasing maneuvers, plane change maneuvers in Keplerian dynamics and in the presence of perturbations (including drag, radiation pressure, third body perturbations, gravitational field) to problems of space mission design.
• Recognize the physical and mathematical principles behind the three body problem. Apply the dynamics of the circular restricted three body problem, such as Lagrange points and libration orbits, to space mission designs at the forefront of the field.

Orbital Manoeuvres

* Coplanar Manoeuvres

* Non-Coplanar Transfers

Orbital Perturbations

* Non-Uniform Gravity Field

* Third-Body Perturbation

* Atmospheric Drag

* Solar Radiation Pressure

Orbital Propagation Techniques

* Analytical

* Semi-analytical

* Numerical

Observations and Orbit Determination

* Observation Techniques

* Reference Frames and Time

* Preliminary Orbit Determination

Relative Orbital Motion

* Relative Orbital Motion

* Linearisation & State Transition Matrix

Interplanetary Trajectories

* Lambert’s Problem

* Patched Conics

* Gravity-assisted fly-by trajectories

N-Body Problems

* N-Body Problem

* Circular Restricted Three-Body Problem

* Natural Dynamics around Libration Points

Attitude Dynamics and Representation:

* Reference frames

* Euler’s equation

* Direction Cosine Matrix

* Euler Angles

* Quaternions

* Torque-free Motion

* Orbital Perturbations

Teaching and learning methods

Teaching methods will include 36h of in-person lectures and tutorials as well as 11h of accompanying videos. Panopto recordings of the lectures along with the slide deck will be made available on Blackboard wherever possible.

Teaching is complemented by 4 supervised 2h in-person computer lab sessions.

Resources & Reading list

General Resources

Matlab/Python and GMAT. Scientific computing environment and GMAT mission analysis tool (open source) will be used in the computer labs.

Assessment strategy

* Summative coursework: report on numerical space mission design using GMAT or Python

* Summative final exam with equation booklet provided and one page of personal notes allowed

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External