Gravity simulator [flash] - try "Generate proto disk"

http://www.nowykurier.com/toys/gravity/gravity.html

by 8ren • 16 years ago

89 39 16 years ago

nowykurier.com

wlievens2• 16 years ago

Reminds me of Osmos. Neat game for the iOS.

borism2• 16 years ago

dude, it's cross-platform http://en.wikipedia.org/wiki/Osmos

wlievens2• 16 years ago

dude, I know.

I played the demo on my PC a year ago.

I did only buy it for my iPod Touch though. It fits the touch platform really well. I played through every single level except the last arcade level which I can't seem to beat. Damn gravity!

brown9-2• 16 years ago

Available on Steam for Mac and Windows for $9.99: http://store.steampowered.com/app/29180/

I picked up Osmos during Steam's xmas sale, the game is a lot of fun and really original.

maushu• 16 years ago

Is that a solar system I see there? It can also be a galaxy if each dot is a solar system. Makes me wonder if the galaxies are actually orbiting around something and that something is orbiting around something and so on. Turtles all the way down.

carbocation• 16 years ago

I was under the impression that whether or not the universe had nonzero angular momentum was still open, in which case, yeah, could be.

umibozu• 16 years ago

You're onto something...

http://en.wikipedia.org/wiki/Supermassive_black_hole#Superma...

revjx• 16 years ago

Interesting diversion for a few minutes.

I wish there was a website that made the maths for all this kind of thing accessible to idiots who don't have any formal maths education (like me). I've bought a few books, but even those seem to skip a stage or two.

borism2• 16 years ago

Wikipedia.org?

cheald• 16 years ago

The math is actually really easy. Every two objects exert a force on each other of (mass 1 * mass 2) / (distance ^ 2). Pseudocode to step gravity in a simulation would be something like:

  foreach(object as o1) {
    foreach(object as o2) {
      if(o1 != o2) {
        force = (o1.mass * o2.mass) / (o1.pos - o2.pos).length
        o1.vector *= unit_vector_from_o1_to_o2 * force
      }
    }
  }

Obviously this is O(n^2), which is why it's so slow when you have a lot of objects in the system, but it's pretty straightforward.

_corbett• 16 years ago

there are various algorithms to reduce the complexity via physically motivated approximations, see http://www.cs.cmu.edu/~scandal/alg/nbody.html for an older but accessible introduction

Simucal• 16 years ago

Once you get the basic Euler setup working it is worth it to try out a more accurate integration method.

Anytime someone posts a simulation using Euler Integration someone usually links to the following[1]. It describes why Euler integration isn't good enough (with the famous line, "If you are use Euler then you are a bloody idiot"). It then proceeds to show how to implement RK4 or Runge Kutta order 4.

This method will evaluate the derivative at four points in between the previous and current timestep to detect the curvature of an objects velocity. It will then take a weighted average to get the best approximation of the derivative for that timestep. This accounts for acceleration in between timesteps rather than assuming a constant velocity between them.

[1] http://gafferongames.com/game-physics/integration-basics/

Slashed• 16 years ago

http://www.khanacademy.org/

arethuza2• 16 years ago

It's a shame that lots of maths education can actually completely miss what you can practically do with things like integration, differential equations and numerical techniques for integration.

This simulation is built around Euler integration - which is pretty much the easiest numerical integration technique:

http://en.wikipedia.org/wiki/Euler_method

Even with fairly simple differential equations and numerical integration techniques you can model some really interesting stuff.

phreeza• 16 years ago

Trying to put something on a lagrange point of a 3 body system. No luck yet though.

sgt2• 16 years ago

I think there's something wrong with it. Why do I get something of mass '1' to affect something with a mass of '1000000000' to such a large degree?

arethuza2• 16 years ago

What did you do? I can't seem to get a "tiny" to do anything to an OMFG no matter how high the velocity of the former.

sgt2• 16 years ago

I went into the game again and now it behaves properly! Very strange.. perhaps it was due to a bug in the game?

fhars2• 16 years ago

The simulation is quite bad numerically. If I start with a proto disk and then put an non-moving OMFG particle immediately to the left of it, the whole system that is initially at rest will end a with a considerable momentum to the left, even though no or almost no particles carry any momentum to the right. That is not only not to physical scale, generating momentum out of nothing is completely unphysical.

hartror• 16 years ago

It looks right in my tests, the particles accelerate towards the OMFG with a large proportion hitting the OMFG in what looks like a perfect inelastic collision, that is they merge and the velocity and mass is added to OMFG. This creates a movement to the left of the OMFG particle.

Deleted my other comment as you replied sorry, it is 12 am and I am not explaining myself to my satisfaction.

Retric• 16 years ago

Take two masses A and B, place them at rest near each other. They should collide and be at rest at some point between them. However, based on the inaccuracy in the way the simulation works if one of those particles is really huge they sometimes gain a lot of energy and fly past each other.

fhars2• 16 years ago

As I said in my reply to your deleted comment, this is plain wrong. Momentum is conserved. Unlike kinetic energy (which gets transformed into heat), it is even conserved in inelastic collisions.

harshpotatoes• 16 years ago

It's hard to tell if momentum is being conserved or not with so many particle, but in the example you mention there is one particle moving to the right, which is the OMFG.

So to make the test simpler, let's start with a single particle. This particle is initially at rest, just as with the protodisk, and nothing happens if we wait for a while. Adding in another particle of the same mass, we see the two particles move towards each other and meet in the middle, implying momentum is conserved. So I am thinking momentum is probably conserved for all cases, to some degree of accuracy

grogers3• 16 years ago

It says it uses Euler integration, what do you expect? At least the really bad interactions are mostly handled by absorbing the planets into one another, even though not all of them are.

8ren2• 16 years ago

Nice observation. The inaccuracy is greatest when masses are near, so absorbing close masses limits how near they can get. When I wrote one of these simulators, I had masses zinging off everywhere when they "collided".

Question: does this inaccuracy systemically affect the development of a "solar system" from a "proto disk"? I think, by increasing randomness, it would actually tend to work against it somewhat.

Also, the odd effect of the proto disk expanding after the sun forms is caused (I think) by masses falling into the sun, and thus further away from the rim of the disk. This greater distances reduces the gravitational force on the rim, and so their velocity ("centrifical" force) can carry them away.

prawn• 16 years ago

The smaller items whipping around a larger body remind me of the footage you see on docos about the discovery of Sgr A* in our galaxy. It's mesmerising.

hook2• 16 years ago

Probably a stupid question, but does this take into account the speed of light?

pavel_lishin• 16 years ago

How do you mean?

hook2• 16 years ago

The force of gravity is not instantaneous. It "travels" at the speed of light. The Earth is not attracted to where the Sun is "now", it is attracted to where the Sun was approx. 8 minutes ago (the length of time it takes for light to travel from the Sun to the Earth), and vice versa.

teamonkey3• 16 years ago

No, it doesn't take special relativity or general relativity into account. It's purely Newtonian physics.

8ren2• 16 years ago

protip: it goes faster if you move your mouse cursor out of the window.

hernan7• 16 years ago

Paging Dr Velikovsky...

jewbacca• 16 years ago

Dear god, there was a solar system simulation on the macs in my middle-school library (c. 1998) that I sunk absolutely inordinate, ridiculous amounts of time into. I think it had a 10-body limit and may have been much older (was definitely monochrome, and possibly used lines of varying density for shading). I can't remember what it was called and I haven't been able to find any information about it. It may be my favourite single piece of software ever and I am certain it had some nontrivial effect on the course of my life[0].

Can anybody help me out?

  [0] Including nurturing several destructive habits and attitudes, such as on the acceptability of spending grade-school lunch hour on the computer every day.

Gravity simulator [flash] - try "Generate proto disk"

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