Simulation method

[Tony]

I expect that Celestia simulates the motion of orbs only according to Keplerian laws. Am I right? If yes, does anybody know some real gravity simulator, which provides the simulation according to Newton's gravity law (or even realtivistic laws)?

[Apollo7]

For the Mac there is an old program called Gravitation that did something like this in 2D. There is also an app called Newtons Aquarium that is out for Mac and I believe is coming out for PC as well. I've used both of them and they are pretty cool. You can also use the website to visualize a primitive (but interesting) 4 planet system (again in 2D). Anyway hope this helps.

Cheers.

[marc]

I've created a gravity mod for celestia previously.


http://mostlyharmless.sourceforge.net/p ... orysml.jpg

Follow the link below and have a look at the most recent Celestia patch.

[ElPelado]

there is also a program called orbit explorer(or orbitX)

[t00fri]

I just want to add a few "semi-serious" words about the general problem of including more sophisticated gravity phenomena. Inclusion of some mutual gravity force effects into /game/ engines is no major problem whatsoever, since these are not supposed to simulate reality in any serious way. Celestia is NOT meant to be a game engine and is so far distinguished by amazingly high precision w.r.to the physics that has been included already.

The problem with the gravity effects that we are talking about is that these are /very/ complicated. Every massive body acts as the source of a gravitational force field. The form of the /total/ field and thus the reaction of another body (e.g. spaceship) moving in this effective field depends on the distribution and sizes of these masses in a most complicated way. Gravitational forces are also of relatively long range so that in many interesting cases other 'disturbing' masses cannot be neglected.

Bye Fridger

[Tony]

marc, I respect you for your ambitious project, Elite was a great game. I think you calculate only gravity force acting to spaceship, that is better for game, but not exactly what I thought.

t00fri, I must agree with you. But there are few situations, where Keplerian laws does not function. The best example is our Moon. I have simulated it's motion, which is very strongly affected by the gravity of the Sun - the Moon's orbit is dissimilar to ellipse.

Thank you all.

[selden]

Tony,

I think you are saying the same thing that Fridger did, just in different words.
The moon''s orbit in Celestia is not modelled using a Keplerian orbit.
All of the planets (except Pluto) follow trajectories calculated using what is known as the "VSOP 87 Theory" The positions of most planets' moons also are calculated using high-precision formulas.

[chris]

t00fri, I must agree with you. But there are few situations, where Keplerian laws does not function. The best example is our Moon. I have simulated it's motion, which is very strongly affected by the gravity of the Sun - the Moon's orbit is dissimilar to ellipse.

Celestia does not use ellipses to model the orbits of the major planets and satellites of our solar system. Instead series with up to a a thousand terms are used to compute the positions of these bodies. The series are derived from decades of ground-based and spacecraft measurements of planet positions combined with very accurate integration.

--Chris

[t00fri]

Tony,

I think you are saying the same thing that Fridger did, just in different words.
The moon''s orbit in Celestia is not modelled using a Keplerian orbit.
All of the planets (except Pluto) follow trajectories calculated using what is known as the "VSOP 87 Theory" The positions of most planets' moons also are calculated using high-precision formulas.

Tony:

In addition it is worth mentioning that the sophisticated VSO87 expansion effectively takes into account gravitational perturbations of the orbits through hundreds of terms. I am sure Tony, you have realized that all this sophistication is incorporated in Celestia for practically all planets (except Pluto).

As Selden has pointed out, we are certainly not talking about simple Keplerian orbits;-)

But in any case, its comforting to read that "you must agree with me";-)

Bye Fridger

[marc]

marc, I respect you for your ambitious project, Elite was a great game. I think you calculate only gravity force acting to spaceship, that is better for game, but not exactly what I thought.
Thank you all.

Tony, Yup my mod was pretty simple, I gave masses to all the large objects in celestia then used the sum of the accelleration vectors to each to apply to the observer. No doubt ill have to cut a few corners once more spaceships start happening. It is fairly accurate though, as far as newtonian maths goes.

[Guest]

Tony,

I think you are saying the same thing that Fridger did, just in different words.
The moon''s orbit in Celestia is not modelled using a Keplerian orbit.
All of the planets (except Pluto) follow trajectories calculated using what is known as the "VSOP 87 Theory" The positions of most planets' moons also are calculated using high-precision formulas.

Tony:

In addition it is worth mentioning that the sophisticated VSO87 expansion effectively takes into account gravitational perturbations of the orbits through hundreds of terms. I am sure Tony, you have realized that all this sophistication is incorporated in Celestia for practically all planets (except Pluto).

As Selden has pointed out, we are certainly not talking about simple Keplerian orbits;-)

But in any case, its comforting to read that "you must agree with me";-)

Bye Fridger

VSOP 87 Theory seems to be very sophisticated and interesting. Could you send or recomend me some description with more details? I wonder how far to the future it can work.
In Celestia, I watched the motion of the Moon, but the orbit was still the same one (probably it wasn't actualized, because the Moon was't orbiting on painted orbit - a bug?).

[t00fri]

...

VSOP 87 Theory seems to be very sophisticated and interesting. Could you send or recomend me some description with more details? I wonder how far to the future it can work.
In Celestia, I watched the motion of the Moon, but the orbit was still the same one (probably it wasn't actualized, because the Moon was't orbiting on painted orbit - a bug?).

Yes, indeed. Here is the URL
http://cdsweb.u-strasbg.fr/htbin/Cat?VI/81

The original papers with the theory, all VSOP87 coefficients (including the moon) as well as subroutines are to be found there.

If next time you sign with your name or better register in the forum, I will be glad to continue communicating if you like;-)...

Bye Fridger

PS: Sorry, but as a matter of principle I deny communicating with cyber robots, shell scripts or the like. I am human.

[Gibfish]

I'm working on a project that would do generic simulation of unsteady systems - essentially it is works, but I need to package it.

If this is still something you need, I can dop back in later (a month or so) and post the details. I'm going to wait until after my finals to complete it...

[Guest]

I'm working on a project that would do generic simulation of unsteady systems - essentially it is works, but I need to package it.

If this is still something you need, I can dop back in later (a month or so) and post the details. I'm going to wait until after my finals to complete it...

I'm working on a very similar problem. I have used Runge-Kutta's method (without an extrapolation). Could you recommend me some more available method or how to do the extrapolation?
I have also read about your problem with getting vector data. Have you solved it? I haven't found any program capable to transform orbital elements to state vectors for more than one planet.

[Sum0]

Google's Space Simulation section (woo! Celestia's in second place!) has a few gravity-oriented programs, but none of them seem to be exactly what you're looking for. Gravel seems close, though.

[t00fri]

I'm working on a project that would do generic simulation of unsteady systems - essentially it is works, but I need to package it.

If this is still something you need, I can dop back in later (a month or so) and post the details. I'm going to wait until after my finals to complete it... 8)

I'm working on a very similar problem. I have used Runge-Kutta's method (without an extrapolation). Could you recommend me some more available method or how to do the extrapolation?
I have also read about your problem with getting vector data. Have you solved it? I haven't found any program capable to transform orbital elements to state vectors for more than one planet.

Runge-Kutta is nothing but a standard algorithm to numerically solve differential equations. So, what are you really doing, (astro-)physicswise?...

Bye Fridger

[Falck]

As a numerical integration method, isnt Runge-Kutta itself an extrapolation technique? Or do you mean that youre not integrating both acceleration and velocity in the same timestep?

All the NASA orbital propagation tools that I can think of that do Cartesian position integration use Runge-Kutta of some sort, and most of them use an adaptive-step method, such as RK45 or RK78.

As for Keplerian-to-Cartesian transformations, here's the algorithm: http://astronomy.swin.edu.au/~ahughes/c ... lerian.htm

[Guest]

As a numerical integration method, isnt Runge-Kutta itself an extrapolation technique? Or do you mean that youre not integrating both acceleration and velocity in the same timestep?

All the NASA orbital propagation tools that I can think of that do Cartesian position integration use Runge-Kutta of some sort, and most of them use an adaptive-step method, such as RK45 or RK78.

As for Keplerian-to-Cartesian transformations, here's the algorithm: http://astronomy.swin.edu.au/~ahughes/c ... lerian.htm

Thanks for the transformation, it's exactly what I needed.
First, I calculate n accelerations to the future (there are later used in method), where n is Runge-Kutta's order. For this calculation, I expect the acceleration to be zero - that causes the main error. It would be better to extrapolate the acceleration from accelerations I have already calculated. Good extrapolation method is Burlisch-Stoer, but I need some good text to understand it, I have only basic knowledge of differential equations.

[Gibfish]

I'm using the R-K technique as of yet. It can be reasonably computationally intensive, but like anything you get what you pay for - error is of the order of the R-K level IIRC.

I don't know much about the Stoer-Burlisch method, but from what I've heard it's a trapezoid rule with extrapolation, with quite small error - polynomial in h^2 (time step size = h).

[Tony]

Thanks to all for help.
I have just found a great colection of numerical recipes on
http://www.library.cornell.edu/nr/nr_index.cgi
I have enough information now and I'm going to study them.