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I've been playing the Kerbal Space Program (KSP) game lately; it's funny how when you actively use orbital mechanics, thinking about them is easier. This fourt

by claar 12y ago

I've been playing the Kerbal Space Program (KSP) game lately; it's funny how when you actively use orbital mechanics, thinking about them is easier. This fourth dimension observation is cool and likely very useful mathematically, but it's also kinda obvious (at least after playing KSP) that if you subtract the time/gravity element from an orbit, it becomes circular. It's equivalent to saying that if you subtract out the gravity effects of the planet you're orbiting, your orbital speed is constant, which just makes sense intuitively. Calling this observation a fourth dimension is useful, but perhaps unnecessarily complicated for the simple concept.

fixermark 12y ago
I was a little sad to learn that because KSP's orbital model uses conic sections, it's not physically accurate enough to model things like Lagrange points. Then I remembered that it's still accurate enough to be awesome and stopped worrying about it. :)
- Coincoin 12y ago
  As a matter of fact, I think that its simplicity is what makes KSP so fun to play. If it was real n-body orbital mechanics with real drag the game would quickly become much too complicated and tedious for casual play (and too slow).
  - TeMPOraL 12y ago
    Yup. One of the Fun things that are less known that comes from n-body orbital mechanics is the instability of orbits. You can't just leave your satellite out there and fast-forward two years because you have an Eve mission going - your satellite needs to make correction burns as other bodies perturb its orbit. http://en.wikipedia.org/wiki/Orbital_station-keeping http://en.wikipedia.org/wiki/Orbital_station-keeping But anyway, I still hope that Principia mod (the n-body simulation addon mentioned elsewhere in this thread) will get released. This will really bring KSP into Dwarf Fortress level of enjoyment. Also, you'd get to make some really weird-ass stuff: http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamma1Var.gif http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamm... http://tuvalu.santafe.edu/~moore/crisscross123.loop.gif http://tuvalu.santafe.edu/~moore/crisscross123.loop.gif
  - gohrt 12y ago
    For broader accessibility: a system like Civ's, where the system can play itself / do computations for you, but lets you dial up the amount of player-control.
    - TeMPOraL 12y ago
      You have MechJeb mod for that.
- valarauca1 12y ago
  Actually Newtonian Conic Sections is how we (humans) calculated orbital, and interplanetary trajectories up until the 1980's. There weren't powerful enough computers to model full Eisenstein N-Bodies Systems until actually very recently (also its complete over kill for inner-solar system travel). Relativity is really complex math, and even modern computer clusters struggle to model very complex systems. Yes we sent astronauts to the moon using KSP math.
  - TeMPOraL 12y ago
    Thankfully, we only used KSP math, and not KSP engineering.
  - titanomachy 12y ago
    Aren't Lagrange points present in Newton's model? Why would they be missing from the game?
    - Rumford 12y ago
      They're missing from KSP not merely because it uses Newtonian physics, but because it only uses two-body gravitational physics at any given time. The planets and moons are on rails and you are in only one gravity well at a time. Lagrange points exist in the intersections between two gravity wells.
  - theothermkn 12y ago
    > Yes we sent astronauts to the moon using KSP math. I'm almost positive that we did not. While patched conics would have been used very early on for rough mission analysis and design, we had a very good understanding of perturbation theory at the time. Wikipedia tells me that the restricted 3-body problem was also essentially solved in 1917. I've seen very detailed plots of the free return trajectories that the Apollo missions followed, too. Using patched conics for the earth moon system would have resulted in an error on the scale of lunar escape velocity upon entering the sphere of influence of the Moon.
    - valarauca1 12y ago
- Lutin 12y ago
  Well if you're still interested in following the ongoing work to change that check out Principia :) http://forum.kerbalspaceprogram.com/threads/68502-WIP-Principia-N-Body-Gravitation-and-Better-Integrators-for-Kerbal-Space-Program http://forum.kerbalspaceprogram.com/threads/68502-WIP-Princi... https://github.com/mockingbirdnest/Principia https://github.com/mockingbirdnest/Principia
  - titanomachy 12y ago
    I thought for a second you were facetiously referring to Philosophiae Naturalis Principia Mathematica... "hey, check out this cool new work on orbital mechanics" :P
Florin_Andrei 12y ago
Well, it's a different parameter space, that's all. We tend to operate in the usual 6-dimensional parameter space for everything we do (3 position vectors, 3 speed vectors), but there are equivalent parameter spaces that do the job just as well. In some cases, the alternate spaces are more useful - polar coordinates are the most common example. The paper quoted in the article found a parameter space where very interesting transformations and symmetries take place.
- gohrt 12y ago
  This is exacly right, and it's a shame that article pushes the "woo, magic" perspective, instead of using the opportunity to highlight the little-known fact (among the lay public and students) of theoretical phyisics: it's a about model-building, "dimensions" aren't real except in the sense that a certain mathematical model (with N dimensions) is (a) consistent with experiment, and (b) has a lot of symmetry and simplicity relative to its explanatory/predictive power.
  - Florin_Andrei 12y ago
    TBH, when you stumble upon a really useful parameter space, it does seem like magic. Also, these days I'm reading Max Tegmark's "Our Mathematical Universe" and, being immersed in that argumentation, the whole "real vs unreal" dichotomy seems a bit transparent. Anyway, having formerly played a bit with computational physics, I'm primarily after what's useful.
    - sonoffett 12y ago
      General semantics helped me be aware of how easy it is to confuse the map for the territory, as well as adopt models based on their usefulness. As a great philosopher once said, reality is what you can get away with.
TeMPOraL 12y ago
With barely 200 hours of flight under my belt, I think I haven't played the game enough, because I haven't reached that intuition yet to see this article's insight as obvious. What this means, of course, is that I need to go back playing more KSP :). Seriously, it's amazing how this game can let you understand space travel and make you want to know the math behind it.
- fixermark 12y ago
  Here's the shortest, sweetest "a-ha" I've yet learned in KSP. So you're piloting ship A and you want to rendezvous with ship B in a stable orbit. Let's assume that A and B are on identical, basically circular orbits, and A is behind B, so your distances from each other aren't really changing much. The maneuver you're looking for is.... Point retrograde (i.e. "away from the direction that will take you to where B is now") and burn. In the short run, you increase your distance from B (of course), but you also dropped your orbital altitude and therefore the area of the arc swept between your ship and your center of orbit over time... and by Kepler's second law, you are now orbiting faster (more full revolutions per unit of time). So you'll swing under B and eventually come up "in front" of it; time your burns right, and you come up epsilon distance in front of B; rendezvous successful. It's totally counter-intuitive to accelerate away from something to approach it, except you're basically on a sphere. :-p
  - hobs 12y ago
    Agreed, and I had played over 200 hours of KSP before I really got a handle on rendezvous, and had many failed attempts before intuitively getting it, and it becoming easy. After that point no maneuver was daunting in KSP, just something that was a matter of time and making sure I quick save occasionally.
troubled5 12y ago
How can you subtract gravity from an orbit and end up with a circle? If you have no gravity the particle will simply move in a straight line, and that's not a motion I would call an orbit.
- claar 12y ago
  You're absolutely right, of course. I was talking about the "time-gravity" component they subtract in the article to circularize the orbit, not all of gravity. During an orbit, gravity is of course stronger when you're near the planet, and weaker when you're away from the planet. So they equalize the gravity by subtracting the relative time/gravity differential and calling it a separate dimension. This leaves a constant gravity force and velocity, making certain calculations and transformations more natural in this model.

by claar 12y ago

fixermark 12y ago

I was a little sad to learn that because KSP's orbital model uses conic sections, it's not physically accurate enough to model things like Lagrange points. Then I remembered that it's still accurate enough to be awesome and stopped worrying about it. :)

Coincoin 12y ago
As a matter of fact, I think that its simplicity is what makes KSP so fun to play. If it was real n-body orbital mechanics with real drag the game would quickly become much too complicated and tedious for casual play (and too slow).
- TeMPOraL 12y ago
  Yup. One of the Fun things that are less known that comes from n-body orbital mechanics is the instability of orbits. You can't just leave your satellite out there and fast-forward two years because you have an Eve mission going - your satellite needs to make correction burns as other bodies perturb its orbit. http://en.wikipedia.org/wiki/Orbital_station-keeping http://en.wikipedia.org/wiki/Orbital_station-keeping But anyway, I still hope that Principia mod (the n-body simulation addon mentioned elsewhere in this thread) will get released. This will really bring KSP into Dwarf Fortress level of enjoyment. Also, you'd get to make some really weird-ass stuff: http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamma1Var.gif http://images.scholarpedia.org/w/images/f/f6/NbodyChoreoGamm... http://tuvalu.santafe.edu/~moore/crisscross123.loop.gif http://tuvalu.santafe.edu/~moore/crisscross123.loop.gif
- gohrt 12y ago
  For broader accessibility: a system like Civ's, where the system can play itself / do computations for you, but lets you dial up the amount of player-control.
  - TeMPOraL 12y ago
    You have MechJeb mod for that.
valarauca1 12y ago
Actually Newtonian Conic Sections is how we (humans) calculated orbital, and interplanetary trajectories up until the 1980's. There weren't powerful enough computers to model full Eisenstein N-Bodies Systems until actually very recently (also its complete over kill for inner-solar system travel). Relativity is really complex math, and even modern computer clusters struggle to model very complex systems. Yes we sent astronauts to the moon using KSP math.
- TeMPOraL 12y ago
  Thankfully, we only used KSP math, and not KSP engineering.
- titanomachy 12y ago
  Aren't Lagrange points present in Newton's model? Why would they be missing from the game?
  - Rumford 12y ago
    They're missing from KSP not merely because it uses Newtonian physics, but because it only uses two-body gravitational physics at any given time. The planets and moons are on rails and you are in only one gravity well at a time. Lagrange points exist in the intersections between two gravity wells.
- theothermkn 12y ago
  > Yes we sent astronauts to the moon using KSP math. I'm almost positive that we did not. While patched conics would have been used very early on for rough mission analysis and design, we had a very good understanding of perturbation theory at the time. Wikipedia tells me that the restricted 3-body problem was also essentially solved in 1917. I've seen very detailed plots of the free return trajectories that the Apollo missions followed, too. Using patched conics for the earth moon system would have resulted in an error on the scale of lunar escape velocity upon entering the sphere of influence of the Moon.
  - valarauca1 12y ago
Lutin 12y ago
Well if you're still interested in following the ongoing work to change that check out Principia :) http://forum.kerbalspaceprogram.com/threads/68502-WIP-Principia-N-Body-Gravitation-and-Better-Integrators-for-Kerbal-Space-Program http://forum.kerbalspaceprogram.com/threads/68502-WIP-Princi... https://github.com/mockingbirdnest/Principia https://github.com/mockingbirdnest/Principia
- titanomachy 12y ago
  I thought for a second you were facetiously referring to Philosophiae Naturalis Principia Mathematica... "hey, check out this cool new work on orbital mechanics" :P

Florin_Andrei 12y ago

Well, it's a different parameter space, that's all. We tend to operate in the usual 6-dimensional parameter space for everything we do (3 position vectors, 3 speed vectors), but there are equivalent parameter spaces that do the job just as well. In some cases, the alternate spaces are more useful - polar coordinates are the most common example. The paper quoted in the article found a parameter space where very interesting transformations and symmetries take place.

gohrt 12y ago
This is exacly right, and it's a shame that article pushes the "woo, magic" perspective, instead of using the opportunity to highlight the little-known fact (among the lay public and students) of theoretical phyisics: it's a about model-building, "dimensions" aren't real except in the sense that a certain mathematical model (with N dimensions) is (a) consistent with experiment, and (b) has a lot of symmetry and simplicity relative to its explanatory/predictive power.
- Florin_Andrei 12y ago
  TBH, when you stumble upon a really useful parameter space, it does seem like magic. Also, these days I'm reading Max Tegmark's "Our Mathematical Universe" and, being immersed in that argumentation, the whole "real vs unreal" dichotomy seems a bit transparent. Anyway, having formerly played a bit with computational physics, I'm primarily after what's useful.
  - sonoffett 12y ago
    General semantics helped me be aware of how easy it is to confuse the map for the territory, as well as adopt models based on their usefulness. As a great philosopher once said, reality is what you can get away with.

TeMPOraL 12y ago

With barely 200 hours of flight under my belt, I think I haven't played the game enough, because I haven't reached that intuition yet to see this article's insight as obvious. What this means, of course, is that I need to go back playing more KSP :). Seriously, it's amazing how this game can let you understand space travel and make you want to know the math behind it.

fixermark 12y ago
Here's the shortest, sweetest "a-ha" I've yet learned in KSP. So you're piloting ship A and you want to rendezvous with ship B in a stable orbit. Let's assume that A and B are on identical, basically circular orbits, and A is behind B, so your distances from each other aren't really changing much. The maneuver you're looking for is.... Point retrograde (i.e. "away from the direction that will take you to where B is now") and burn. In the short run, you increase your distance from B (of course), but you also dropped your orbital altitude and therefore the area of the arc swept between your ship and your center of orbit over time... and by Kepler's second law, you are now orbiting faster (more full revolutions per unit of time). So you'll swing under B and eventually come up "in front" of it; time your burns right, and you come up epsilon distance in front of B; rendezvous successful. It's totally counter-intuitive to accelerate away from something to approach it, except you're basically on a sphere. :-p
- hobs 12y ago
  Agreed, and I had played over 200 hours of KSP before I really got a handle on rendezvous, and had many failed attempts before intuitively getting it, and it becoming easy. After that point no maneuver was daunting in KSP, just something that was a matter of time and making sure I quick save occasionally.

troubled5 12y ago

How can you subtract gravity from an orbit and end up with a circle? If you have no gravity the particle will simply move in a straight line, and that's not a motion I would call an orbit.

claar 12y ago
You're absolutely right, of course. I was talking about the "time-gravity" component they subtract in the article to circularize the orbit, not all of gravity. During an orbit, gravity is of course stronger when you're near the planet, and weaker when you're away from the planet. So they equalize the gravity by subtracting the relative time/gravity differential and calling it a separate dimension. This leaves a constant gravity force and velocity, making certain calculations and transformations more natural in this model.