The 3-body problem: an overview
• Libration points correspond to potential equilibrium in space: 5 solutions exist
• True for any 3 body system
• Trajectories are highly nonlinear
- No general analytic solutions without assumptions
• Dynamical stability is important characteristic
- Measured using eigenvalues of STM
- More stable – lower stationkeeping cost
- Less stable – more transfer options
• Transfers between
- Look for connecting unstable/stable manifolds
State Transition and Monodromy matrices
How are multibody trajectories different from near-Earth orbits?
Near Earth
• Earth gravity dominates
• Classical two-body orbit solutions take the form of conic sections (circles, ellipses, hyperbolas)
• Design typically takes place in an inertial frame
• Real orbits differ slightly from ideal orbits
• Descriptive orbital elements
Multibody
• Earth and other central body gravity are equally important (more or less)
• No general solutions exist. Behaviors vary greatly depending on locale
• Extremely sensitive to ICs -> need constraints
• In many cases, real orbits require frequent maintenance to retain identifying characteristics of ideal orbits
Ansys features for Multibody trajectory design
Some cislunar orbits using CR3BP
Mission to Libration Points: typical workflow
• Scenario set up:
- Set up geometric elements:
• Libration Points
• Custom axes:
• Earth Centred (Origin at Earth centre, X towards L4, Z normal to ecliptic plane)
• L4 centred (Origin at L4, ..)
- Set up transfer (TLI)
• Target parameters (outgoing asymptote, RA Dec)
• Lunar swingby (B plane targeting)
- Set up corrections (TCMs)
• Target arrival conditions (plane crossing, Rmag, XYZ condition etc.) - Set up capture and maintenance burns (long term propagation)
L1/L2 Transfer trajectory
L4/L5: Transfer with Departure Asymptote
Transfer with Lunar Swingby
Could also perform B plane targeting of moon with BdotT and BdotR found through targeting L4 arrival conditions
The B plane
Stationkeeping
Real case references
https://astrogatorsguild.com/why-we-used-phasing-loops-on-ladee/
https://www.csmonitor.com/Science/2013/1008/Moon-mission-LADEE-arrives-after-an-amazingly-precise-looping-flight
https://www.nasa.gov/content/goddard/nasas-lro-snaps-a-picture-of-nasas-ladee-spacecraft/
LRO Chandrayaan-2 collision avoidance planned with STK
https://www.wionews.com/india-news/explained-how-indias-lunar-orbiter-chandrayaan-2-avoided-collision-with-nasas-lro-429955
Debris in cislunar space – Chang’e 5 third stage
The 3-body problem: an overview
• Libration points correspond to potential equilibrium in space: 5 solutions exist
• True for any 3 body system
• Trajectories are highly nonlinear
- No general analytic solutions without assumptions
• Dynamical stability is important characteristic
- Measured using eigenvalues of STM
- More stable – lower stationkeeping cost
- Less stable – more transfer options
• Transfers between
- Look for connecting unstable/stable manifolds
State Transition and Monodromy matrices
How are multibody trajectories different from near-Earth orbits?
Near Earth
• Earth gravity dominates
• Classical two-body orbit solutions take the form of conic sections (circles, ellipses, hyperbolas)
• Design typically takes place in an inertial frame
• Real orbits differ slightly from ideal orbits
• Descriptive orbital elements
Multibody
• Earth and other central body gravity are equally important (more or less)
• No general solutions exist. Behaviors vary greatly depending on locale
• Extremely sensitive to ICs -> need constraints
• In many cases, real orbits require frequent maintenance to retain identifying characteristics of ideal orbits
Ansys features for Multibody trajectory design
Some cislunar orbits using CR3BP
Mission to Libration Points: typical workflow
• Scenario set up:
- Set up geometric elements:
• Libration Points
• Custom axes:
• Earth Centred (Origin at Earth centre, X towards L4, Z normal to ecliptic plane)
• L4 centred (Origin at L4, ..)
- Set up transfer (TLI)
• Target parameters (outgoing asymptote, RA Dec)
• Lunar swingby (B plane targeting)
- Set up corrections (TCMs)
• Target arrival conditions (plane crossing, Rmag, XYZ condition etc.) - Set up capture and maintenance burns (long term propagation)
L1/L2 Transfer trajectory
L4/L5: Transfer with Departure Asymptote
Transfer with Lunar Swingby
The B plane
Stationkeeping
Real case references
https://astrogatorsguild.com/why-we-used-phasing-loops-on-ladee/
https://www.nasa.gov/content/goddard/nasas-lro-snaps-a-picture-of-nasas-ladee-spacecraft/
LRO Chandrayaan-2 collision avoidance planned with STK
https://www.wionews.com/india-news/explained-how-indias-lunar-orbiter-chandrayaan-2-avoided-collision-with-nasas-lro-429955
Debris in cislunar space – Chang’e 5 third stage