Some Notes on Orbital Mechanics(tjradcliffe.com)
tjradcliffe.com
Some Notes on Orbital Mechanics
http://www.tjradcliffe.com/?p=1774
7 comments
I don't think that that is a good fit for this case.
Remember - he's using only ~11 bodies. The problem remains mainly sequential for that number of bodies.
Remember - he's using only ~11 bodies. The problem remains mainly sequential for that number of bodies.
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This is a really good article. I've only had time to skim so far, but it's impressive.
I happen to be a physicist too, and my stance on climate change is identical to yours. I don't think we'll ever have a climate model with detailed predictive ability: the system is too complex and the initial conditions too uncertain. But we really need to stop changing the composition of the atmosphere; mainly, we need to move quickly away from burning coal, for several reasons. I agree that we should do this through incentives and development of alternatives, not through a "revolutionary" approach.
It was refreshing to read something rational about climate. Everything I've seen lately (although this isn't my field) is either "we can't predict climate so we should stop worrying and just keep burning coal" or "it's already too late because the models are true and we have to shut everything down now or we're all going to die."
On your orbital simulations: you seem to be using physical units. Often people avoid some of the very big or small numbers by using, say, the Earth-Sun distance as the unit of length or the Earth mass as the mass unit. Do you just prefer physical units, or are you doing this and I missed it? Either way, very interesting demonstration of the effect of the Moon on the Earth orbit - would not have guessed this result.
P.S.: Go gnuplot!
I happen to be a physicist too, and my stance on climate change is identical to yours. I don't think we'll ever have a climate model with detailed predictive ability: the system is too complex and the initial conditions too uncertain. But we really need to stop changing the composition of the atmosphere; mainly, we need to move quickly away from burning coal, for several reasons. I agree that we should do this through incentives and development of alternatives, not through a "revolutionary" approach.
It was refreshing to read something rational about climate. Everything I've seen lately (although this isn't my field) is either "we can't predict climate so we should stop worrying and just keep burning coal" or "it's already too late because the models are true and we have to shut everything down now or we're all going to die."
On your orbital simulations: you seem to be using physical units. Often people avoid some of the very big or small numbers by using, say, the Earth-Sun distance as the unit of length or the Earth mass as the mass unit. Do you just prefer physical units, or are you doing this and I missed it? Either way, very interesting demonstration of the effect of the Moon on the Earth orbit - would not have guessed this result.
P.S.: Go gnuplot!
I certainly agree with the author's conclusions. Frankly, I think the discussion on Anthropogenicity of Global warming is irrelevant.
We are in an era, aptly called the Anthropocene, where Humans, while spreading like cancer, are basically taking crucial breathing space away from our co-habitants.
I wish there were some sort of joint efforts underway to curb populations, in countries like India, and at the same time curb consumption in the Western world.
Sadly, the debates are all extremely partisan, and play by old - petty- rules of geopolitics.
We are in an era, aptly called the Anthropocene, where Humans, while spreading like cancer, are basically taking crucial breathing space away from our co-habitants.
I wish there were some sort of joint efforts underway to curb populations, in countries like India, and at the same time curb consumption in the Western world.
Sadly, the debates are all extremely partisan, and play by old - petty- rules of geopolitics.
> I wish there were some sort of joint efforts underway to curb populations, in countries like India, and at the same time curb consumption in the Western world.
The best way to curb a population is to accelerate a Third World country into the First World consumption you so denigrate.
Suddenly, female fertility drops below replacement when being a female doesn't suck.
The best way to curb a population is to accelerate a Third World country into the First World consumption you so denigrate.
Suddenly, female fertility drops below replacement when being a female doesn't suck.
What sort of joint effort do you have in mind? Force works of course; that's an option (as in China) is it?
Curbing consumption? Same again. Love to know what you have in mind to stop the buyers and how to re-employ the producers?
Finally, 'all' debates? You're that positive?
Curbing consumption? Same again. Love to know what you have in mind to stop the buyers and how to re-employ the producers?
Finally, 'all' debates? You're that positive?
I'm given to believe, that given, all the comments, the one who espouses the Middle path is equally demonized by both camps in the Manichean's world.
I will not deign fools with answers.
I will not deign fools with answers.
I'm curious about his use of Runge-Kutta. IANA numerical methods expert, but it seems like this is exactly what symplectic integrators (https://en.wikipedia.org/wiki/Symplectic_integrator) are for. Looks like he gets very good results, but how trustworthy is Runge-Kutta?
From his perspective, of course, using Runge-Kutta makes perfect sense. This is "Huh: I have this tool, and applying it to this problem wouldn't be too hard; would the tool work?", not "I should create a new tool."
ETA: couple of forgotten words.
From his perspective, of course, using Runge-Kutta makes perfect sense. This is "Huh: I have this tool, and applying it to this problem wouldn't be too hard; would the tool work?", not "I should create a new tool."
ETA: couple of forgotten words.
I agree in general, and it would have been nice to see some plots of some of quantities that should be conserved, e.g. how well does his simulation preserve the initial energy and angular momentum?
Having said that, it is an adaptive RK scheme, and it seems to work pretty well, the article shows that the results match some reference data quite well, and it even captures some quite subtle effects, most notably the influence of the moon.
Having said that, it is an adaptive RK scheme, and it seems to work pretty well, the article shows that the results match some reference data quite well, and it even captures some quite subtle effects, most notably the influence of the moon.
He mentions a 10% error in energy conservation, so not too great.
Probably he should have done research before he started, he would have found one of the several lecture notes that tell you how to integrate orbits. They tell you that symplectic methods are great for time reversible problems.
Or he would have found one of the public codes for integrating the solar system very far into the future.
Probably he should have done research before he started, he would have found one of the several lecture notes that tell you how to integrate orbits. They tell you that symplectic methods are great for time reversible problems.
Or he would have found one of the public codes for integrating the solar system very far into the future.
Initial energy is conserved at the 10% level, which is not great.
I really didn't expect the RK4 thing to work at all, and once it was clear it kind of did decided to push on for fun.
I really didn't expect the RK4 thing to work at all, and once it was clear it kind of did decided to push on for fun.
That was precisely my logic. Maybe I'll build a symplectic integrator in future, but this was a case of "Hey, I've got this hammer, maybe I can drive this screw with it!"
RK4 is not a good choice for periodic systems.
It may be better to use a symplectic integrator.
It may be better to use a symplectic integrator.
A number of people have suggested this and I've now looked into the question a bit.
Curiously, the comparisons I've seen between RK4 and symplectic integrators all use fixed step sizes. I used RK4 with adaptive step size because I had the code around, having written it for a different project about ten years ago that involved mostly smooth motion with a few tight turns that required a very small time step. By making the step size adaptive I could get decent run-time performance while retaining good accuracy.
I'm tempted now to write a symplectic integrator and see how it performs against adaptive RK4.
Curiously, the comparisons I've seen between RK4 and symplectic integrators all use fixed step sizes. I used RK4 with adaptive step size because I had the code around, having written it for a different project about ten years ago that involved mostly smooth motion with a few tight turns that required a very small time step. By making the step size adaptive I could get decent run-time performance while retaining good accuracy.
I'm tempted now to write a symplectic integrator and see how it performs against adaptive RK4.
Use an adaptive symplectic integrator and get the best of both worlds.
Also, I wouldn't call 10% error in an invariant "good accuracy".
Also, I wouldn't call 10% error in an invariant "good accuracy".
The following paper is a better read than OP's, and it also shows some academic refinements in the main number used here. This article is (obviously) referenced, as science should be, and makes clear that these points are clearly not ignored by models or unknown in the field.
http://onlinelibrary.wiley.com/doi/10.1029/2010GL045777/full
http://onlinelibrary.wiley.com/doi/10.1029/2010GL045777/full
Thanks. I've added a link to this. I should hope it's a better read: it reports on more than a week's part-time work written up in a couple of days for a blog post!
Interesting article, inappropriate title. If you want to discuss the physics of climate models, don't bury the real title in an attempt to appear objective. It will have the opposite effect.
I've changed the title to "Some Notes on Orbital Mechanics and Climate Change". My actual motive for the original title was that I thought putting both in was clumsy and ugly, and felt that "Some Notes on Climate Change" would be misleading, as the bulk of the content is about orbital mechanics even though the motivation is related to climate change (which is spelled out clearly in the first sentence.)
I forgot, as I often do, how common the fundamental attribution error is: https://en.wikipedia.org/wiki/Fundamental_attribution_error
I forgot, as I often do, how common the fundamental attribution error is: https://en.wikipedia.org/wiki/Fundamental_attribution_error
Here's a couple of recent papers:
Using Graphics Processing Units to solve the classical N-body problem in physics and astrophysics http://arxiv.org/abs/1411.5234
The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration http://arxiv.org/abs/1404.2324