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Exploring Lagrange Points & Rectilinear orbits...Let's start with the Moon Retrograde Square Orbit Why explore this intriguing region of space in KSP with Principia & RSS? The upcoming ESA/NASA/JAXA Lunar Gateway DSL station & SLS Artemis III+ missions & the 'mind puzzle' of navigating the 'shape' of forces in this region of space. One simple way to start exploring the 'shape' of force potentials around the Moon gravity well in the Earth-Moon system is the DRO 'Lunar Retrograde Square': an orbit from near L2 towards L5, back near L1 then towards L4, & falling back towards L2... Update: Principia added an EML reference frame -- with the option to show equipotential lines for the sum of forces associated with gravity & rotation in the plane defined by the orbital of the Moon around Earth... These equipotential lines are shown for a single plane & for the 'current time' & do shift slightly with the Moon's distance from Earth i.e. the location of the equipotential lines will be slightly different when a craft actually reaches a given point on the Principia projected fuchsia or dashed paths... the shift is quite noticeable over time along the direction of an imaginary line say from L4 to L5. a visual explanation of equipotential in a video by Scott Manley The EML frame offers an insightful way to visualize the dynamics shaping the Lunar Retrograde Square Orbit... For example, for the 'square' orbit plotted in the MCI frame... see how a lower AP creates a more rounded 'corner' (e.g. see the AP on the L4 side of the orbit in the screenshots below); where as, traveling further towards L4 or L5 creates a sharper 'corner' (e.g. see the AP on the L5 side of the orbit in the screenshots below)... well, that is at least until you get close to a transfer to L4 or L5 where you will see a loop 'ear' corner instead. Note: To help interpret the craft path, I have added to the screenshots in yellow text approximate L point information...this is _not_ shown in game. The above animation shows the 'Square' orbit over 7 years in MCI (Moon Centered Inertial) frame (fyi...with the small vessel in this save the 'square' path persisted for about 18 years with no station keeping). Clarification: the Earth is traveling along the blue-ish arc counter-clockwise. Summary of Earth-Moon system Challenges: Challenge #1 (Beginner): "Get a feel for the dynamics that shape the 'Retro Square' orbit: Make a 'Moon Pentagon' orbit" Challenge #2 (Intermediate): 'Transfer to an Artemis III & Gateway Station type of Moon NRHO [pdf] (see animation & NASA graphic below)" Challenge #3 (Intermediate): 'Transfers along the 'Lunar Retro Square' to halo orbits around L2, L1, L4, L5' Challenge #4 (Advanced): "Moon L1 halo to Moon L2 halo transfer similar to the 2010 ARTEMIS-P1 mission (see NASA drawing below)" Challenge #5 (Advanced): "Create a 'Lunar Gateway (images post by NASA of the planned station) ' type station (module link sequence video NASA) (or a magic potatoroid mining station [Matt Lowne] ) in a long term 'Lunar Retro Square Orbit' (since a Moon NRHO might require more frequent station keeping) for ease of docked ship transfers to Moon NRHO, L2, L1, L4, L5" Challenge #6: Create an even better n-body related challenge & share it! Challenge #1: "Get a feel for the dynamics that shape the 'Retro Square' orbit: Make a 'Moon Pentagon' orbit" In the provided save, with a single less than 10s burn, turn the Retrograde "Moon Square" orbit into a "Moon Pentagon" orbit: Inspired by the @maccollo "Principia Mun Retrograde Square Orbit" during the afternoon of an 'at home from school not so well day', my son & I decided to see if a related "Square Retrograde Moon" orbit could be created in Principia RSS. Indeed, we found something similar that we could also manipulate purposefully with a single small burn at a specific time: In this 1st case, turn the "Moon Square" orbit into a "Moon Pentagon" orbit as shown in the images with a single less than 10s burn like we did (yes, that's a hint, & improvements welcome). We share this as an introduction of a thread to explore, discuss & share refined versions of this orbit as well as new saves of other intriguing orbits with the 'flight plan' of burns to reach them... Discovery either by blind fortune dragging Principia maneuver burn sliders or intricate use of KSPTOT 1.6.9 welcome! KSP version: 1.12.x Required Mods: Principia, RSS Optional Mods: RealScaleBoosters, SMURRF, KOS To load: download the "Moon Square Orbit" save create a KSP 1.12.x GameData with Principia, RSS load KSP & create a new save game, find the folder with the name you gave to that newly created save game on your hard drive & copy into that folder the "MoonSquare.sfs" Load the MoonSquare save as normal from the usual in game menu (e.g. from the Space Center screen) Find the craft in the Tracking Station & select it to fly. if you are unfamiliar with Principia here is a link to a post with some visuals & suggestions. Metrics: Orbit Uniformity & Stability (both improved revisions as well as your own original orbits welcome) Quality & Ease of the flight plan (the easier/simpler to execute the better) in the save you share discovery of a simple regular maintenance maneuver(s) would be a nice plus most importantly -- the fun factor: how much fun we all have exploring what you improve/create! Objectives: 1) Fun (with Principia RSS ;-) 2) hands on play with fascinating orbits, one barely new existed, with saves someone else took the effort to make 3) improve a save: create & share Principia 'flight plans' of maintenance burn(s) that make a given orbit more uniform & stable 4) make a new save (with a simplified mod list): and share your own flight plan for some type of cool orbit... Flight Plan to make the "Moon Square": requires RealScaleBoosters added to GameData in addition to Principia & RSS Related to Challenge #1: The recent SLS Artemis 1 mission made use of a Lunar distant retrograde orbit (DRO) [source link for animation below] (not square though ;-) The Principia EML frame is similar to the left 'Earth-Moon Pulsating Rotating Frame': Challenge #2 (Intermediate): Transfer to a SLS Artemis III & Gateway Station Moon NRHO: NASA explains why a NRHO vs DRO or low lunar orbit for Gateway station: https://www.planetary.org/space-images/near-rectilinear-halo-orbits Challenge #3 (Intermediate): 'Transfers along the 'Lunar Retro Square' to halo orbits around L2, L1, L4, L5' Challenge #4 (Advanced): "Moon L1 halo to Moon L2 halo transfer similar to the 2010 ARTEMIS-P1 mission" 2010 "ARTEMIS-P1 - The First Earth-Moon Libration Orbiter": Additional videos: NASA Scientific Visualization Studio 2010 ARTEMIS at Lagrange: "In this version, the satellite trails are are constructed in a lunar-centric inertial coordinate system so the trails reveal the motion of the satellites relative to the Lagrange points in INERTIAL space (fixed with the distant stars)" Some examples of additional orbits to explore: Near Rectilinear Halo Orbit (NRHO) "KSPTOT LVD: (Tools -> Halo Orbit Constructor menu)" Arrowstar's post with details about this new tool (link) Lissajous orbit WMAP at Sun–Earth L2,[7] Earth-Moon L points Visual Data Mission ideas: place a station, gravitational wave 'telescope' (link), or comsat(s) at the stable Earth-Moon L4 & L5 Note: L3 is an unstable L point = requires small periodic maintenance burns. Images: source source source

So with the awesome announcement of the sequel of our favorite game a question has to be asked... Will N-body physics à-là Principia be implemented? What do you think.

http://www.drewexmachina.com/2014/10/02/the-fate-of-comet-halley/ Well based on this article the precise orbit of Halley cannot be predicted beyond a revolution and a half, therefore its future orbit cannot be predicted. The introduce a variable known as the Lyapunov exponent which sets a maximum limit on predictability.