Why Spacecraft Are Using These Crazy Routes To The Moon - Weak Stability and Ballistic Capture.

For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity.
They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft.
Some of the orbit visualizations use Universe Sandbox
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[@MrArzorth]

I’m an orbital mechanics engineer at ESA and I wouldn’t have explained it better 👏🏼👏🏼

[@blaksu]

hi, do you know Prof Mark McCaughrean?

[@Bramon83]

No offense but probably worse for the layman

[@realcygnus]

Awesome

[@anteshell]

I'm an orbital mechanics engineer at KSC and I have no idea how to reach orbit. I just add more boosters.

[@carlosalbinanaburdiel8791]

Hi! I am a Spanish Aerospace Engineering graduate and 1st year student of Space Engineering MSc at Politecnico di Milano. I am falling in love with mission design and orbital mechanics and hopefully I can do an internship for N-body orbit simulations this summer at the University. Is there anyway I could contact you? I have some questions regarding how to get to positions such as yours, working at ESA. THANKS

[@duxangus]

This is mathematically and physically beautiful and I cannot imagine the happiness the original scientists felt when putting all of this together

[@conradandrew825]

As a straight man, I don't think penises are beautiful, but hey, you do you! 😆

[@WoWSondo]

@@conradandrew825 U not seen them tip to tip then =/

[@Tinil0]

It always strikes me how complex yet simple orbital mechanics are. Like, it's absolutely complex but we can VERY easily describe the movements of the heavens with surprising accuracy far into the past or future with "simple" equations.

[@spacelapsus8835]

Belbruno almost lost his job at JPL researching this topic in the early days LOL. There's a TEDtalk he did on it quite a while back.

[@simonmultiverse6349]

Never mind KERBAL space program... what about *HERBAL* space program? Take enough herbal stuff and you'll *REALLY* feel as if you're flying. It might technically be ever so slightly illegal, and you can't buy it at a chemist, but it's unforgettable.

[@konstantinkh]

Thinking of the Lagrange points as low effective potential "portals" between Hill spheres is an amazing insight. Thanks for sharing it. I've seen (and derived) the effective potential contour maps many, many times in my life, but never thought of the implications in quite this way. It certainly makes the captures, whether planned or accidental, so much more intuitive.

[@seunghobaik4447]

Danuri is Korea’s first lunar satellite! It wasn’t originally planned to do these harder, efficient orbit maneuvers but they kept adding new equipments and sensors to the satellite to a point where they had no options but to take the harder approach. Crazy considering that this is our first spacecraft to the moon. Anyways, huge thanks to Scott for covering space launches and projects from Korea in your videos!

[@UD503J]

It is a really innovative solution to get an efficient orbital trajectory. Hopefully it will inspire others to get low-cost scientific payloads to the Moon.

[@dsdy1205]

> kept adding new eqpts and sensors to the satellite scope creep is a hell of a drug

[@pkkkpkpkpkkk]

And here is another Korean subscriber same as me lol

[@sxj42]

Thanks for additional information!

[@sirjohniv]

Hitchhikers Guide to Lunar Orbit

[@andrewharrison8436]

Don't Panic

[@pucmahone3893]

Gravitate to the watering hole, Drink 3 intergalactic gargle blasters and wait for the gold brick wrapped in lemon to smash your head. Then everything seems so normal!

[@stuart207]

🖖

[@dmacpher]

Do YOU know where your TLI burn towel is?

[@petevenuti7355]

@@andrewharrison8436 if you got your thumb out, not enough time to panic.

[@Ranged66]

Awesome stuff, n-body physics interactions are fascinating. Have you heard of the Interplanetary Transport Network? It's the concept that all these chaotic interactions create 'pathways' between the Lagrange points of pretty much every body in the solar system. From the Moon to Jupiter, without a single drop of fuel. You'll just need a LOT of patience. (for everything to line up, and for all the natural gravity assists...)

[@absalomdraconis]

I think there technically is a little fuel requirement, to get the initial kick from Lagrange to the path you actually want instead of staying at the Lagrange point. And I guess a bit to compensate for inaccuracies, but eh, details.

[@jasonreed7522]

I think the need for patience is a problem with it, unfortunately humans get old and die, and hardware goes obsolete so its not like we can wait 50years for something to navigate it way out to Neptune riding this network just to save on fuel. (Although it may be useful within a planetary system like Jupiter or Saturn where the travel distance is much smaller so the timeframe is reduced to something much more tollerable)

[@CharlotteBennett492]

The "interplanetary highway" concept is awesome, I'm pretty lucky to have gotten the opportunity to learn underneath faculty who has contributed immensely to it. So with that I have to plug his youtube channel - kzbin.info/door/9ZvnHwvAR4XkjKzKxhYDDg

[@Winallmoney]

He's mentioned it before. Nothing in depth that I'm aware of, just as a concept.

[@elmobrandao9849]

Maybe someday, this way, one will be able to finally lend Venus a moonlet

[@bprud6443]

I really need to try one of these with the Principia mod one of these days. Amazing stuff and the 3D diagram of gravity around the lagrange points really makes everything click into place.

[@clayel1]

principia has a 3d diagram of gravity?

[@Archgeek0]

@@clayel1 I don't think it does, but I feel like it definitely should! (In a limited capacity, so as not to melt players' machines)

[@user-si5fm8ql3c]

@@Archgeek0 Thats actually a planned feature, funnily enough, simplifying the gravity diagram is where they are stuck right now from what i can gather. Not because the PC cant render it, but because the player cant get use out of a diagram too complicated

[@bprud6443]

@@clayel1 Oh no, sorry, I meant the diagrams in the video make it click into place for me.

[@kylenolan3138]

I've struggled to visualize how bodies are captured into orbits without delta-V. Now it's crystal clear. Thank you.

[@Kyzyl_Tuva]

Great stuff Scott. I love your deep-dives in orbital mechanics.

[@spacedbro]

My favorite line "Did any of you find this overly complicated? Don't worry it's much more complex in real life" 😂

[@williampeek7943]

I remember reading about Bellbruno's work a little over a decade ago. I hunted him down online and emailed him to ask if it was possible to recreate this kind of orbit on the space flight simulator called Orbiter. He actually wrote me back with all kinds of diagrams and explanations. I still haven't been able to totally recreate it on Orbiter but your video helps out a lot. Thanks.

[@fratop]

Did my PhD on ballistic capture, worked with Ed Belbruno at Princeton University, and I'm currently an active researcher on this topic. Yet, I'm always fascinated by this concept as the first days I started studying it.

[@izharulhaq2436]

Your email address please

[@bermchasin]

and still find the lunar transfer chart very phallic

[@Liuxw666]

then what's the difference between weak stability boundary and invariant manifold? and I'm always confused about the real advantage of these methods, after all we need to do a lot of numerical calculations to get these. could you help me figure this out？

[@fratop]

@@Liuxw666 It can be shown that weak stability boundaries and invariant manifold are two different tools to study the same phenomenon, which is ballistic capture trajectories. Invariant manifolds have maybe the advantage of being useful to perform trajectory design and analysis for Lagrange point missions too. Yes, they require a lot of calculations, but in the and all space trajectories require that, even the simpler ones!

[@Liuxw666]

@@fratop thank you so much! I just wonder if there is any method like lambert transfer which you don't need too much calculation in CRTBP problem

[@davidfell5496]

Awesome video. Love the casual solving of a 4-body problem by 2 x 3-bidy problems!

[@jackryan6446]

I thought that was really interesting too. Sort of like breaking a normal physics problem into multiple vectors, then adding them up, except in 3D and with exponential relationships LOL

[@AbsoluteHuman]

That's not a 4 or even 3 body problem tho? The mass of the spacecraft is negligible and the Sun - Mun interactions are not the focus of it. It's 1 body (which is the spacecraft) and a field of different forces.

[@I.amthatrealJuan]

I never thought of using Universe Sandbox to reverse engineer orbits like that. Now I have something new to play with. Thanks, Scott. I also am quite surprised that these techniques were developed only very recently.

[@cognitivefailure]

I'd be really interested to hear much mass (as a percentage of the spacecraft's mass) these maneuvers save the craft's designers. Seems like it has to be substantial for the time and effort they spend to perform it successfully! The calculation and risk assessment that must go into it is mind-boggling.

[@lancelotlake7609]

I don't believe these low delta-v trajectories should EVER be considered for manned space flight. Exposing astronauts to the stresses of Earth-Lunar transit for an additional 3 days, round trip, is unconscionable. It's not like they're taking extra payload.. they're not even taking a lander, FFS!

[@sil8127]

You’d be interested in the delta V difference

[@johndododoe1411]

@@sil8127 I'm guessing he wants the mass cost of that delta-v for those real spacecraft with their real technical limitations.

[@dsdy1205]

@@johndododoe1411 well that depends a lot on other factors, like the dry mass, the thruster specific impulse, etc. It's easier to use the delta-v savings as a yardstick, then go from there. For instance, spacecraft propellant mass is directly proportional to dry mass. So a 1 ton dry mass craft might save a thousand times more propellant mass than a 1 kilogram dry mass spacecraft given the same delta-v savings

[@termitreter6545]

This one is pretty easy to make a vague guess. Scott said the apogee rise to the moon is 2800 d/v, plus 50 for the high orbit. And then you save most of the insertion burn. According to google, thats 600-700 d/v for an isertion burn you mostly save. Which doesnt sound like much, but considering rocket size (and cost) rises exponentially compared to range, its probably worth it. I dont think the risk and calculation is a big deal tho. Someone figured out the math, made the tools and software. From then onwards you get easy, accurate numbers in comparably little time. Just a guy trying numbers in a compture, then doubly check the course. If your spacecraft can do an accurate lunar insertion, then it can probably do this maneuver already, its just a longer mission.

[@user-vp1sc7tt4m]

Kudos to your acknowledgment of Ed Bellbruno and his contribution to object deployment in the space environment.

[@MonKeed5E]

This is a great example on how to do terrific outreach, kudos to Scott. I am a PhD Candidate at Politecnico di Milano, Italy, and at the Deep-space Astrodynamics Research and Technology (DART) group we are currently researching on how to engineer the ballistic capture mechanism for autonomous interplanetary CubeSats with limited onboard resources. We have released in open access on Zenodo a dataset of initial conditions granting temporary capture at Mars in case you are interested!

[@MartinMizner]

It's kinda crazy that only 50 meters of dV is enough to go past Moon to the edge of Earth's sphere of influence.

[@killsode4760]

That's gravity wells for ya

[@Br3ttM]

It's only enough if you do it close to the earth, when you're going fastest. Escaping a gravity well costs energy, but your fuel budget is change in velocity, with how rockets work. Since energy is proportional to the square of velocity, changing velocity when you're going fast is a much bigger difference than when you are going slowly (it's called the Oberth effect).

[@beenaplumber8379]

@@Br3ttM Square of velocity relative to what? The place of origin? The object being orbited? It seems to me the energy required to change speed by x m/s would be the same for any object in an inertial frame, which a satellite is. I'm probably wrong, but what am I missing? (I'm sure it's something simple.)

[@xxvmvxx]

@@beenaplumber8379 total kinetic energy is 1/2 * m * v^2. So adding some delta-v will add more kinetic energy into the orbit if you do it at a already high velocity. Check out wikipedia on the mentioned Oberth effect for more details if you want to. The section called "Description_in_terms_of_work" is p much what I said but it has a lot more details, numerical examples and clarity. I guess the reference frames would be that the energy needed to change velocity of the spaceship (thrust -> force -> accelleration) is relative to c, but the energy of the orbit we are considering is the potential+kinetic relative to the body that's being orbited (in the simplest terms). I'm thinking out loud in this part though so I'd love to be corrected.

[@Flourish38]

Seeing that capture tube extend all the way out from the moon was so cool!! It really helped tie the concept together in my head as well. ❤

[@truBador2]

Great stuff. I heave a sigh of relief over straightforward mechanical explanations. This is a perfect public level of science. Well done!

[@filip5519]

This is so high level, big respect Mr. Manley!

[@AndyStarr0]

I took a class this last semester that focused entirely on finding periodic and quasi-periodic orbits and orbital transfers in the circular restricted 3 body problem, as well as extending these results to find solutions in ephemeris models. Fascinating stuff and really cool to see it used in real life!!

[@joshuahammond1862]

I know someone who worked on the Lunar Flashlight mission, learning more about it is so cool :O

[@rpaulcelso]

As I watched the video, I wondered if you would get around to giving Ed Belbruno the credit he deserves. I was the Lunar GAS system engineer, Kerry Nock was the project leader, so I saw genius at work. Ed explained the math to me in the hall at JPL. I am still in awe.

[@edbelbruno1]

Fabulous video and explanation! Loved it! Thank you Edward Belbruno

[@mortiphago]

Who would've thunk that rocket science was this complex

[@trevorbradley3737]

In a computational physics undergrad course over 25 years ago, we had an assignment to fire a spaceship from Earth, have it orbit around the moon, and return safely to the earth. If I recall correctly we implemented the Runge-Kutta method which took the 3 body problem and had variable time steps to give the most accurate simulation. I took the assignment way too far, and graphed out the entire space. Given a starting angle (x-axis) and initial velocity (y-axis) what happened to the spacecraft? Impacted the moon? Lost in deep space? Skipped off the earth and ejected? The graph was not simple. I recall one set of initial parameters had a free return trajectory that ridiculously skirted the moon's surface by about 1.5mm, then returned safely to earth. All of this to say that your video has me really curious. All kinds of "bank shots" off those Lagrange points (L1 and L2, both sun and moon) could lead to some fascinating paths with minimal fuel. Would love to see more on this topic. (even if just a recommendation for other videos)

[@MoonWeasel23]

I think if you did a video on coordinate transformations, you'd have enough material to just teach a university orbital mechanics course. Certainly better than the one I got...

[@mini_bunney]

honestly yes, I've certainly learned more about orbital mechanics from Scott than from the one or two lectures about it that we had in our space technology courses...

[@benhouse5515]

That is absolutely wild. Blew my mind. The illustrations really do it justice. Thanks for documenting this!

[@DimensionO]

Thanks for the lowdown, Scott! Hello from Vandenberg Space Force Base!

[@multivariateperspective5137]

I got to see Scott. I always look forward to watching your videos. Awesome stuff. Thanks for all your time and energy. Excellent job.

[@The_Mister]

I’m amazed that anyone figured this stuff out.

[@andrewharrison8436]

At a high level this makes sense. At a detail level of actual calculations it's a nightmare of instabilities and corrections and changing coordinates between earth, moon and sun. Glad someone else is doing the number crunching.

[@Sacto1654]

Modern computers can do the hard work of navigating for such a complicated flight.

[@Cattactular]

Wow, Scott, I’ve always had a trouble getting my head around body influences, until you explained langrange points like a topological map and it blew my mind, thank you so much.

[@jlynch1024]

That is amazing. Thank you Ed Belbruno for discovering these orbits. Genius!

[@MikeWiggins1235711]

THIS is why all the JPL scientists have to be locked up every night! 🤭

[@aemrt5745]

Orbital Mechanics has become much more complex (and cooler) than what I studied in the 1980s!

[@tijm6140]

Bravo, Scott! One of your best explanations.

[@robokuni]

Nice video, but you got a few things wrong. 0:19 Hakuto-R is a landing demonstration programme. The lander is simply called Series 1. The rover is Rashid and is a payload here. 12:00 Hiten is MUSES-A yes, but the smaller satellite is Hagoromo. It's not actually known if Hagoromo made it into orbit because the antennae failed and they were unable to verify its orbit :(. MUSES-B is a radio telescope satellite, not a part of the Hiten mission.

[@peterhall6656]

To really understand this stuff you need to have some background iin KAM theory (Kolmogorov- Arnold-Moser ) in the context of dynamical systems. Helmut Hofer has done some good Princeton IAS videos on the technical issues in the context of explaining what Ed Belbruno did with the Hiten probe and the concept of ballistic capture. Ed was one of Jurgen Moser's students. Dynamical system stuff is pretty deep - according to Helmut when Ed came up with his idea of saving Hiten many of his colleagues said he was nuts but his ideas worked.

[@mskellyrlv]

Excellent video! I wondered about the Artemis mission timeline from the moment I first saw it published - since I remember hearing about Sputnik, and remember watching Vanguard 1 fall back and explode on the pad, am an Apollo junkie, and have been in the space game ever since. My very favorite book of any genre is Richard Battin's "An Introduction to the Methods and Mathematics of Astrodynamics", and despite its deep mathematical insights, it contains nothing of this sophistication. Thank you so much for this one, Mr. Manley!

[@irvalfirestar6265]

having a more efficient trajectory also means less weight contributed for fuel, which means less weight overall, means less payload to orbit, means cheaper launches etcetc, ultimately cascading into more people able to launch smaller, cheaper payloads to the lunar orbit

[@robertoler3795]

well done. tracking these satellites has required an upscaling of my orbital dynamics and this is a great discussion/explanation hope the flying is going well. RGO

[@DragosIlas]

The way I think about it is basically a bi-elliptic transfer from LEO to the moon's orbit, but using the Sun's gravity to perform the velocity change at apogee.

[@Lew114]

I've been curious about this for my entire life. I never thought it was something I could understand. Thank you so much Scott! You are an amazing teacher.

[@Nexfero]

Using L1 & L2, LaGrange Points for a Ballistic slowdown into lunar orbit is a neat idea. 🚀🌙

[@TheJustinJ]

Better idea: Build a lunar roadhouse vacation space-station orbiting earth between the moon at the L1 point, then change the rules for the pool area.

[@seedmole]

Taking advantage of the highly-complex locations where a minute bit of thrust can produce massive differences in trajectory. Simply brilliant.

[@jfobear1953]

This video contains some of the best illustrations and explanations of Lagrange points and orbital mechanics that I’ve ever encountered. Thanks!

[@jpdemer5]

Every time I read or hear somebody proposing that a planet "captured" a passing body and made it a moon, I think of the delicate - and extremely unlikely - orbital mechanics required to make that possible. You'd need some sort of decelerating collision, at just the right time and place, to act as an "insertion burn". (Anybody think that tidal forces could enable the process, given enough time?)

[@index7787]

Interesting thought on tidal forces.

[@rays2506]

Back in the early 1990s while the Strategic Defense Initiative Organization (SDIO) was still in existence, we had designed a lunar orbiter that had a small 2MeV linear accelerator aboard. The spacecraft would be targeted for a 60 km altitude. The proton beam would hit the lunar surface and produce neutrons with energy distribution characteristic of the atoms on the surface. The launch vehicle was the Delta 2. We had Ed Belbruno consult with us on using his weak stability boundary/ballistic capture trajectories since the payload was too heavy for the Delta 2 to fly an Apollo-like trajectory. Alas, there was no interest from either NASA or the Ballistic Missile Defense Organization (BMDO), which was working on its Clementine lunar orbiter, which carried six science instruments for mapping the lunar surface in 1994. Clementine was launched on a Titan II.

[@PsychoMuffinSDM]

Wow... just as I feel I am starting to make my way up the second mountain, Scott Manley firmly puts me back onto the first mountain of the Dunning-Kruger peaks. Thank you for teaching us these awesome things!

[@PTuffduty]

I listened to everything that you said. all very interesting. I am writing to commend you for your interest and understanding of all things space and for helping us mere mortals grasp the details.

[@PaulTopping1]

Love this one. Almost makes me want to play around with this stuff. I do have a question which might also be an idea for one of your videos. With all the variables involved, I imagine that various trajectory adjustments (aka burns) have to be calculated just before they are done in order to deal with actual velocity rather than those calculated before launch. This must especially be the case with these critical paths near Lagrange points. How sensitive are they? How precise do the pointing and burn times have to be? I imagine some missions fail because they get this wrong and fall outside the envelope in which adjustments can be made.

[@joshholder359]

Haven’t worked as an astrodynamicist specifically, but have worked in spacecraft GN&C design. In general, orbital trajectories are VERY sensitive, and trajectories designed using this method even more so. Even a difference of 5ms of burn (so a second or two of firing) can cause huge differences when propagated for a long time. Nowadays, though, we’re pretty good at navigating these missions, even with the almost unimaginable precision required. The key is that adjustments are constantly made throughout the journey, not just before burns. Hopefully, you never arrive at a burn at a velocity far different than what you expected, because you corrected it at 1 m/s off rather than waiting until 50 m/s off.

[@johnkeck]

Very understandable explanation, thank you, Scott!

[@unvergebeneid]

Somehow the video title gave me "The 10 Best Lunar Transfer Orbits and Number 8 Might Surprise You" vibes 😄

[@i-love-space390]

You are a terrific astrophysicist. I hope your employer appreciates you as much as your KZbin fans.

[@Ph33NIXx]

As a guy dappling into KSP - these long entry arcs blew my mind.. Imidatly when i saw the animation of it tourning back and then being catched by the moon i was like "damn thats so smart!" Can you do this in Kerbal?

[@sadham2668]

If you had a mod that had Lagrange points but not in stock

[@nathanbishop6850]

So good! Thanks for explaining this beyond-Kerbal idea with such detail and diagrams. Drinking wine at conferences paid off, surely this justifies a bit more?

[@ProfessorRoss]

Hi Scott, I love your videos. Very interesting stuff. Pretty sure I made those figures starting at 8:45. I'd love to collaborate regarding visualizing the trajectories in Earth-Moon space if you're interested, especially the idea of stable orbits surrounded by chaotic orbits which are a kind of "chaotic sea" through which spacecraft can navigate to go essentially anywhere in the Sun-Earth-Moon system. We have a group that's starting to use AR/VR to help space engineers visualize these complicated paths.

[@peterford5408]

The odds aren't great that Scott will see your message here. But there are probably other avenues that are pretty much guaranteed to work, like maybe the "Discord server" that he frequents?

[@matthenekk]

It’s honestly amazing that at 26 I basically grew up in a world where n-body simulations are trivial. I know about this stuff, but every time I hear about more of the specifics of how this stuff actually works the more it’s incredible anybody not only solved 3+ body problems by hand, but that we figured out how to make computers solve them for us. The more you learn about engineering the more you realize how insanely unbelievably useful computers have been for science. It’s not all about social media lol. The speed of computation allows brute force methods like this. You would spend a million lifetimes solving 10,000 4 body problems by hand, but nasa supercomputers can back date probably a million possibilities in a reasonable amount of time and we have these orbits that basically just would be incomprehensible without computers. We have the knowledge to understand the process without computers, we just don’t have the power to calculate that fast as humans.

[@luckyirvin]

the amount of computation required for these lovely dances still blows my mind and the amount of wacky imagination required to conceive these orbits blows my mind out past pluto

[@aurelienyonrac]

That is realy well explained. Thank you kind Sir

[@JohnJohansen2]

I don't remember any explanation this intuitive, ever!👍👍👍

[@stevenswapp4768]

This stuff is so cool! It's become perhaps my favorite area of space/science. Thank you Scott, we are all lucky you know this so well. Fly safe!

[@sloanemactire8780]

I heard Scott say "this orbit is perfectly balanced..." and now I'm just imagining a certain KZbinr at NASA talking about how the orbit is perfectly balanced with no exploits... Joking aside, really interesting and as always, your breaking down complex orbital mechanics into layman's guide is appreciated!

[@Flor-ian]

Great video! Love this kind of content. Very informative and not too computation-intensive!

[@matthewellisor5835]

0:30 What a very sturdy-looking orbit. I don't think a grade 7 pupil could (/would) have done better (/differently.)

[@red_rassmueller1716]

I was wondering how far I would have to scroll to find the first comment about it

[@dylanwho]

Very sturdy indeed...

[@Henrik.Yngvesson]

Good to know I wasn't the only one 🤣

[@jnawk83]

Real Civil Engineer would be very proud.

[@korona277]

Rock hard orbit

[@alexs36zero]

I saw many Apollo lunar landing profiles like the one at 0:43 drawn on walls in many cities. Never knew taggers are such space fans.

[@bermchasin]

KSP fans everywhere!

[@Damien.D]

Once clearly explained like this, surfing on gravitational forces seems pretty intuitive. I hope KSP2 will have some kind of n-body simulation. That would be so much fun to improvise a last resort trajectory around a L point to prevent Jeb being slingshoted towards the sun. Er. I mean.... that would be so much intellectual satisfaction to carefully plan in advance complex missions using such gravitational tricks. Of course.

[@backwashjoe7864]

LOL!

[@miltonmiller]

This was one of the most interesting videos about space exploration i've seen!

[@marcofaustinelli7010]

Beautiful stuff clearly explained, as usual. I remember viewing your material about distant retrograde orbits some time ago. Are there two distinct cases for DROs and for what you present in this video? Does it make sense to compare them? What are the pros and cons of each one?

[@ioresult]

That's a nice idea to implement in KSP2. Not exactly Principia, but n-body gravity with planets and moons on rails. Only the spacecrafts would be dynamically affected by lagrange points.

[@DJWILDCARD46]

Scott, excellent work! Very informative for me personally!! Some i's dotted, some t's crossed, so thank you!! 👌 🚀 Fly safe!! 🙏

[@kainpwnsu]

How timely! I started learning in ernest about Lagrange, yesterday. This is a fantastic example! Fly safe. :)

[@glenwoodriverresidentsgrou136]

Wow, well done. You answered my question! Great video.

[@garyengelman7867]

SUPER, frist time I’ve had a explanation that made sense. Nice job.

[@walter2990]

These types of discussions are WAY outside my pay grade, but I can still appreciate the thought & the amount of computations that it requires. Stay curious!

[@LiamDennehy]

I could never understand how a planet can capture a body and turn it into a moon - if they're arriving they are necessarily in a hyperbolic trajectory (forwards and backward being the same) and should simply fly off. Finally I can see how a capture can happen, especially with the saddle visualisations. Thanks! I still don't know how two galaxies can merge, again hyperbolic trajectories, but maybe that's a future video? :P

[@simongeard4824]

It's not quite that simple though, because as Scott pointed out, it's reversible - if you can be captured this way without spending energy, you can also be ejected again the same way... which is why these craft are still using a regular injection burn to stabilise their orbit.

[@tanakaobi]

This was brilliantly explained! TYSM!

[@astra1653]

You really are so good at distilling down complex concepts and serving them up in easily digested bites of information. In other words, you dumb it down real good so that even dodos like me can follow the plot. Kudos! No, seriously, this was a really good video. Make more!

[@8bitwiz_]

I was disappointed that Scott didn't point out how the "primary" body changed back to Earth for a moment during the final capture. This math is crazy, but with a wonderful result. I'm sure there's a bit of chaos function in the math for those orbits, so tracing it backwards like that probably is the best way to solve it.

[@l.mcmanus3983]

I noticed! It was fascinating to see the orbit change and then flip and all that.

[@EddieA907]

Nothing like a fantastic orbital trajectory vid. Awesome, thank u sir!

[@sunnyjim1355]

Cool, I can't wait to try out 3-Body orbital mechanics in KSP2.

[@sciencecompliance235]

As I understand it, they're only going to have 3-body physics for a pair of binary planets in an extra-Kerbolar system, so you're going to have to wait a while for interstellar travel to come out.

[@velcroman98]

This was awesome! I don't think I could do the math, but you explained it perfectly.

[@General_Confusion]

This video explains why I'm not a rocket scientist, I would have just made sure to blast off at night.

[@kcouche]

What you're saying is that these careful orbital maneuvers are more elegant than brute force, and elegance is always better in flight...

[@GiovanniV69]

Universe Sandbox is really amazing! Great video!

[@mibo747]

Amazing explanation

[@Digital-Dan]

Reminds me of many all-nighters playing Spacewar in the late 60's.

[@markolson4660]

Great explanation of a complicated subject!

[@WillArtie]

Love this type of vid from Scott!!! xxx

[@mikes2381]

Would've been nice to hear about this in any of my orbits or GNC classes. Lol. Though maybe I got through before this was much known. Welp. That's why I follow people like you Scott.

[@Karen_Baldwin.Composer.Pianist]

Happy Xmas Cousin Scott🎄☃️🎅

[@eshafto]

Brilliant explanation. Thanks so much.

[@TheAlchemisification]

The refinement of orbital mechanics has come along way since Apollo making deep space missions much more accessible to countries and spacecraft that otherwise would be able to participate. We really are in the Renaissance of space travel!

[@WebHead948]

Scott Manley is a treasure.

[@druspork7737]

Fabulous work, really clear. 😊

[@ericmelton4186]

My new favorite Scott Manley video. The other favorite video is. WTH is orbital mechanics

[@gerardoconnor4278]

Very good explanatory video. Thank you.

[@antonioveritas]

This shows how well designed and well organised the universe is, like a giant mechanical clock, only more complicated!

[@themollerz]

Amazeballs video mate. I learned a new level in my education on orbital mechanics. So cool.

[@jamestickle3070]

I’d be worried about making some critical mistake figuring out these weird orbits. I mean, even with the Apollo orbits like 0:37, it looks easy to cock things up.

[@Shortstuffjo]

I get it!

[@dajuggernaut124]

IIRC there was a special team of 15 people at the Johnson Space Center who were called the Pen15 Team lead by a guy called Richard Weenis. They were in charge of calculating short & long orbits (Sh-Long Orbits) for the Apollo missions. They all did the same calculations to make sure no one person dong-gone cocked the mission up.