
Some Notes on Orbital Mechanics - jessaustin
http://www.tjradcliffe.com/?p=1774
======
nkurz
Tangential to his point, but N-Body simulations like this are almost a perfect
fit for GPU computation. The power of modern GPU's is astonishing. It's
probable that he could get his "about a day" calculations down to a few
minutes, or alternatively, keep the runtime the same and dramatically improve
the accuracy or length of simulation.

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](http://arxiv.org/abs/1411.5234)

The GENGA Code: Gravitational Encounters in N-body simulations with GPU
Acceleration [http://arxiv.org/abs/1404.2324](http://arxiv.org/abs/1404.2324)

~~~
TheLoneWolfling
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.

------
leephillips
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!

------
enupten
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.

~~~
chm
So, explain to me who gets to live and who doesn't?

~~~
lisper
It doesn't have to be that way. Simply making it less fashionable to have kids
would make a big dent in the problem.

------
cdwhite
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](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.

~~~
reidacdc
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.

~~~
troubled5
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.

------
TheLoneWolfling
RK4 is not a good choice for periodic systems.

It may be better to use a symplectic integrator.

~~~
tjradcliffe
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.

~~~
TheLoneWolfling
Use an adaptive symplectic integrator and get the best of both worlds.

Also, I wouldn't call 10% error in an invariant "good accuracy".

------
lvs
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)

~~~
tjradcliffe
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!

------
CamperBob2
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.

~~~
tjradcliffe
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](https://en.wikipedia.org/wiki/Fundamental_attribution_error)

