MEEG467/667 Spaceflight Mission Planning

Course Description

This course presents the fundamental principles of orbital mechanics and space flight dynamics with emphasis on applications. Includes analysis of the 2-body and restricted 3-body problems and orbital transfer using impulsive forces. Also includes designing Earth-orbiting satellites, Earth-Moon and interplanetary probe trajectories for given specifications.

Syllabus

  1. Introduction.
1.1 A historical review of orbital mechanics.
1.2 A brief description of the solar system. 
1.3. A historical review of lunar and interplanetary flights.

  1. Circular orbital motions.

  2. The two-body gravitational problem.

3.1. Geometric characterization of orbits as conic sections (ellipse, parabola, hyperbola).
3.2. Kepler’laws. 
3.3. Elliptic vs hyperbolic orbits. Relationship between the eccentricity and energy of the orbit. The escape velocity.
  1. Orbital position vs time for 2-body orbital motions:
4.1. Kepler's equation in terms of the eccentric anomaly for elliptic orbits. Generalization to hyperbolic and parabolic orbits.
4.2. Lambert’s Theorem: determination of the elliptic orbital elements of elliptic orbits of spacecrafts from time measurements.
4.3. Time series expansion solutions of the position and velocity vectors.
  1. 3D orbital elements.
5.1. The six classical orbital elements.
5.2 Determination in terms of the position and velocity vectors.
  1. Basic orbital maneuvers.
6.1. Orbit transfer and Lambert problem: determination of the transfer (elliptic or hyperbolic) orbit that connects specified endpoints in a specified transfer time.
6.2. Impulsive orbital maneuvers. What is impulsive thrust? 
6.3 Two-impulse transfer between circular orbits as a solution to interplanetary transfer.
6.4 Interplanetary Hohmann transfer orbits as minimum-fuel solutions.
6.5. Geosynchronous and geostationary orbits. Molniya orbits.
6.6. Application: The Earth to Jupiter Hohmann transfer orbit.
6.7. Multiple Hohmann transfers. Faster elliptic transfers. Hohmann transfer from circular to elliptic orbits. Inclined Hohmann transfer. Inclined bi-elliptic transfer.
  1. Interceptions and rendez-vous.
7.1 Feasibility conditions for interception.
7.2 Application: conditions for Earth to Mars Hohmann transfer.
  1. Interplanetary flights.
8.1. Classification of missions.
8.2. Gravity assist: advantages and downsides.
8.3. Example: Mars Reconnaissance Orbiter (direct transfer) vs Cassini–Huygens Mission (insertion into Saturn after gravity assist with Earth, Venus and Jupiter).
8.4. Concept of sphere of influence of a planet.
8.5. Method of patched conic.
  1. Application 1: Earth to Venus mission.
  2. Application 2: Earth to Mars mission.
  3. Application 3: Cassini–Huygens Mission.
8.6. Geometric demonstration of the increase of the magnitude of the spacecraft’s heliocentric velocity after the gravity-assist.
   Case 1: Trailing-edge gravity assist. 
   Case 2: Leading-edge gravity assist.
  1. Heliocentric transfers using accurate ephemeris:
9.1. Infeasible heliocentric transfer to Mars.
9.2. An iterative algorithm for solving Lambert problem.
9.3. Heliocentric Transfers: Pork-Chop Plots.
  1. Orbital rendezvous.
10.1 Accurate prediction of the relative motion.
10.2 2d linear orbit maneuvers toward rendezvous: Clohessy–Wiltshire equations.
10.3 Linearization of orbital relative motion equations: generalization to nonplanar, non circular orbits (3D orbital rendezvous).
  1. Orbital Perturbations.
11.1 Gauss  planetary equations for the osculating elements.

  Application 1: tangential thrust.
  Application 2: atmospheric drag.
  Application 3: Earth Oblateness.
  
11.2. Orbital perturbation: Averaged Equations.
11.3 Orbital perturbation: lunar Gravity.
11.4 Orbital perturbation: solar Gravity.
  1. Lunar Flights.
12.1. Two-body lunar trajectories.
12.2 Hohmann lunar orbits.
12.3 Patched-conic 2D lunar flights.
12.4. Noncoplanar lunar trajectories.
12.5 Lunar ephemeris.
12.6 Patched-conic 3D lunar flights.
12.7 Lunar trajectories by numerical integration.
  1. The 3-body Problem.
13.1 Historical notes.
13.2 Jacobi’s formulation of the 3-body problem.
13.3 Application: the Lunar Case.
13.4 Lagrange triangular solutions.
13.5 The restricted 3-body problem:
  Periodic Orbits: The Copenhagen problem.
  Hill’s surface.
  Stability of the libration points.
  Lyapunov orbits.
  Application of Lagrange points to space exploration.

Textbook

  1. Optional: Orbital Mechanics, 2nd edition, by Prussing & Conway.

  2. Optional: Orbital Mechanics for Engineering Students, 4th edition, by Curtis

Additional Tools & Resources

Spaceflight simulation video games

  1. Universe Sandbox

  2. Kerbal Space Program 2

Astronomy apps

SkySafari 7: displays stars, star clusters, galaxies, Solar System’s major planets and moons, and asteroids, comets, and satellites.

Github Repository

Astrodynamics with Python https://github.com/alfonsogonzalez/AWP

Expected Work

Final paper (see the 2025 version).

Mission Design to Jupiter

Interest in the exploration of Jupiter and its moons remain as strong today as it was in the early days of space travel with the arrival of Pioneer 10 into the Jovian system in 1973. Jupiter has been the most visited of the Solar System’s outer planets as all missions to the outer Solar System have used Jupiter flybys. New probes are currently en route to Jupiter. Sending a spacecraft to Jupiter is challenging, mostly due to large fuel requirements and the effects of the planet’s harsh radiation environment.