Lagrange points

[KvickFlygarn87]

I don't get it! What are they, or rather, what do they do?

[K^2]

In simplest terms, for a 2-body system, Lagrange points are points where you can put a 3rd body so that it stays there.

In more precise terms, Lagrange points are extrema of the effective gravitational potential of the two-body system.

For example, if we consider the Earth-Sun system, there are five Lagrange points. The L1 is between Earth and Sun, L2 is always behind the Earth, L3 is always on the opposite side of the Sun from the Earth and L4 and L5 are leading and lagging, respectively, in Earth's orbit. Most of these points aren't stable, but they have stable orbits around them. (Halo orbits, Lissajous orbits, etc.) If you want a satellite that stays in the same position relative to both Earth and the Sun, these are the points you'd put your satellite. So L1 is useful for solar observatories, and L2 is good if you want a place where sunlight does not interfere with you watching the sky. Other three points aren't particularly useful, but they do tend to capture asteroids. Not so much in the Earth-Sun system, but very much so in Sun-Jupiter L4 and L5. That's where the Trojan asteroids are located.

Edited January 4, 2014 by K^2

[Kerbin Dallas Multipass]

If you put stuff at those points it appears to "stay" there. Meaning the distance to both bodies (in the picture Earth and Sun) always remains the same.

In this case "stay" is relative to Earth - the stuff will rotate around the sun once a year just like Earth does.

[FenrirWolf]

http://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Lagrange_points2.svg/330px-Lagrange_points2.svg.png

If you put stuff at those points it appears to "stay" there. Meaning the distance to both bodies (in the picture Earth and Sun) always remains the same.

In this case "stay" is relative to Earth - the stuff will rotate around the sun once a year just like Earth does.

Good explanation.

Also, you have the best username. Just sayin'

[Kerbin Dallas Multipass]

@FenrirWolf thanks

[Kryten]

If you put stuff at those points it appears to "stay" there. Meaning the distance to both bodies (in the picture Earth and Sun) always remains the same.

But bear in mind this is only if you are able to keep something exactly at the point, which isn't possible in practice. Orbiting around the points is possible, but only orbits around L4 and L5 are stable in the long-term.

[Palladium Corp]

Scott Manley wrote a simulation of "Trojan" asteroids which lurk in Jupiter's L4 and L5 points. They more or less stay there. Also in the video of the simulation, is a simulation of the "Hilda" asteroids, which oscillate between points L3, L4 and L5 in a 3:2 resonance with Jupiter. The link here:

In my opinion, this is a pretty good representation of what Lagrange Points are (or at least, the L3, L4 and L5 points).

[MC.STEEL]

So thats what its all about!

ive heard about the trojans but only now i get what this phenomenon is called

[BlackBicycle]

Just to point out: with the current implementation of gravity model in KSP, LPs are not possible. I personally started a row about it a year or more ago, they said LPs are out of the question with the current model. They also said a complicated model involving LPs is beyond their capabilities. They blamed it on the current state of computing speeds. I myself am of the different opinion, having played an Earth-Moon system with (albeit a single) LP between them not so long ago - in the middle of the 80s. On a programmable calc, too.

[Ralathon]

Just to point out: with the current implementation of gravity model in KSP, LPs are not possible. I personally started a row about it a year or more ago, they said LPs are out of the question with the current model. They also said a complicated model involving LPs is beyond their capabilities. They blamed it on the current state of computing speeds. I myself am of the different opinion, having played an Earth-Moon system with (albeit a single) LP between them not so long ago - in the middle of the 80s. On a programmable calc, too.

Making KSP run on multibody physics shouldn't be too hard or computationally intensive. The problem is that it wouldn't be very fun to play. Gravity would constantly toss your stations out of whack, so if you need to time warp to Jool you'd need to do station keeping on all your orbits every few seconds. I don't know about you, but I don't consider station keeping a very fun activity.

What would we actually get in return for that? Lagrange points and slightly more accurate slingshot maneuvers. Personally I don't think that's worth it. L1 to 3 are unstable in the first place, so keeping a station there would be hell. L4 and L5 are pretty stable, but so is a 60 degree leading/trailing synchronous orbit with the current model. The view from a Lagrange point isn't that special either. So it just seems like a useless gimmick that causes a lot of trouble.

[K^2]

I myself am of the different opinion, having played an Earth-Moon system with (albeit a single) LP between them not so long ago - in the middle of the 80s. On a programmable calc, too.

Was it capable of simulating 200+ objects at time warp factor of 1,000,000 with sufficient precision to give good predictions for all of the orbits well ahead? What you are talking about isn't even in the same category of problems.

Try and write a simulation that manages to keep track of an asteroid or a comet in the Solar system. Then come back and talk about how easy it is to implement something like this.

[Nibb31]

Making KSP run on multibody physics shouldn't be too hard or computationally intensive. The problem is that it wouldn't be very fun to play. Gravity would constantly toss your stations out of whack, so if you need to time warp to Jool you'd need to do station keeping on all your orbits every few seconds. I don't know about you, but I don't consider station keeping a very fun activity.

What would we actually get in return for that? Lagrange points and slightly more accurate slingshot maneuvers. Personally I don't think that's worth it. L1 to 3 are unstable in the first place, so keeping a station there would be hell. L4 and L5 are pretty stable, but so is a 60 degree leading/trailing synchronous orbit with the current model. The view from a Lagrange point isn't that special either. So it just seems like a useless gimmick that causes a lot of trouble.

The issue isnt' running an n-body simulation in real-time. It's being able to rapidly predict the orbital parameters of each body at any moment in the future.

When you warp in KSP, everything is put on rails. The physics are no longer computed, but it's easy to compute the position of each body when the time warp is stopped, because the orbital parameters are effectively the same as when the time warp was started. With n-body physics, orbital parameters change all the time as each body is affected by each other body.

[BlackBicycle]

Was it capable of ... Try and write a simulation that ... Then come back and talk about how easy it is to implement something...

Oh my..... very well, here I go.

My dear fella, I was not implying that I can make this all happen. I was merely remembering the good old days when a assembly program shorter than 128 commands (yes, single commands like "this mem reg plus this mem reg, which are both in the stack atm" or "set this memory register to store this particular value") could actually fly you from Moon to Earth (or the other way around), while taking into consideration the LP, at least the one between the two bodies.

I don't even want to elaborate. Those in the know will understand.

[K^2]

I don't even want to elaborate. Those in the know will understand.

I've written in Assembly and machine code across a range of platforms. I also know how to write code for integrating trajectories. I have written code that's perfectly capable of computing an Earth-Moon transfer. And yeah, I can do that in Assembly. Oh, and just so that you know, it's not 128 commands, because immediate operands are written into the code space, so you actually get considerably fewer than 128.

This is a completely different class of problem. And like I said, if you have no experience with this sort of thing, don't pretend like you know what you are talking about.

[andrewas]

Just to point out: with the current implementation of gravity model in KSP, LPs are not possible. I personally started a row about it a year or more ago, they said LPs are out of the question with the current model. They also said a complicated model involving LPs is beyond their capabilities. They blamed it on the current state of computing speeds. I myself am of the different opinion, having played an Earth-Moon system with (albeit a single) LP between them not so long ago - in the middle of the 80s. On a programmable calc, too.

As I understand it, the user interface is the hard part. Specifically, calculating the result of a maneuver. With KSPs current system, it can be done quickly enough to show the result in real time as the player tweaks a maneuver node. I doubt the same would be possible with n-body physics.

[BlackBicycle]

I've written in Assembly and machine code across a range of platforms....

...if you have no experience with this sort of thing, don't pretend like you know what you are talking about.

For some reason, those two phrases don't seem like they are coming from the same person. All coders that I have the honor to be friends with do not reek of elitism.

[AeroEngy]

Here is good video explaining Lagrange points and some of their uses.

[K^2]

For some reason, those two phrases don't seem like they are coming from the same person. All coders that I have the honor to be friends with do not reek of elitism.

Next thing you'd be telling me that you are surprised that some electrical engineers act elitist, because none of the electricians you're friends with are.

You might not like to hear it, but you just keep exposing your ignorance of the subject. A coder is a mechanic. There is nothing wrong with being a mechanic, of course, but if that's all you are, there is nothing to be elitist about. These are dime a dozen. We are talking here about integrating equations of motion with a non-conservative potential, doing that about million times faster than real time, and with sufficient precision to extract meaningful orbital elements from it. This is not something you can ask a typical coder to do and expect anything but total garbage out. Granted, almost any person who knows how to solve such a problem is going to be able to put it into code, and so can technically be called a coder, but comparing these people with general population of coders is just laughable.

[BlackBicycle]

Next thing you'd be telling me ... but comparing these people with general population of coders is just laughable.

Proving my point, are we : ?

[K^2]

You've never had one! The discussion is about Lagrange points, and all you've been contributing are some fantasies based on code that you don't understand anything about. The topic of n-body simulation in KSP has been discussed before, and a number of well-qualified people have weighted on why it would be very challenging to add it in a way that preserves quality of the gameplay. If you wish to derail a topic, at least do so on a subject in which you actually understand something, or take it to a place other than the Science Labs sub-forum. People have standards here.