Calculating Velocity & Axes of Planetary Orbits

[smize]

As my state (Indiana) has removed Astronomy from the curriculum, my school no longer offers it. I have taken AP Physics B and that is my best knowledge provided by the modern school system, so I apologize ahead of time for any low-level or simple questions.

I am wanting to know the equations for determining:

1. The velocity of an entity orbiting another (i.e. a planet around a star)
2. The two axis (major and minor)

I'm wanting to build a rudimentary PHP program for creating a basic planetary system, so this will help me become one step closer, thank you!

 

[Drakkith]

I think all the equations you need are here: http://en.wikipedia.org/wiki/Orbit
Or here: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c1

 

[DaveC426913]

And you might want to look up orbital simulator algorithms to see some of the better - and poorer - ways of writing it. For example, you likely won't need major and minor axes.

 

[smize]

Thank you very much! This will help a lot!

 

[smize]

And you might want to look up orbital simulator algorithms to see some of the better - and poorer - ways of writing it. For example, you likely won't need major and minor axes.

I will be wanting to create a coordinate system where you can tell the specific location of the planet at a given time, which I would denote p(t). I would need to know either the eccentricity or semi-minor axis. Is there any pattern to semi-minor axes/eccentricity of planets?

 

[DaveC426913]

I will be wanting to create a coordinate system where you can tell the specific location of the planet at a given time, which I would denote p(t). I would need to know either the eccentricity or semi-minor axis. Is there any pattern to semi-minor axes/eccentricity of planets?

Well, I'll leave it you how you do the simulation. When I programed my simulator, I simply needed distance, mass and force of gravity, updating positions and velocities iteratively. Whether they actually formed ellipses at all was a totally emergent property. And in a star system with more than one planet, you should not be getting ellipses anyway, since they'll perturb each other. That's usually the point of a simulation.

 

[smize]

Do you have advice on what physical laws I should integrate into my system?

 

[DaveC426913]

Do you have advice on what physical laws I should integrate into my system?

Only those three factors. Mass of the bodies, distance between them and force of attraction. Oh, and initial velocity.

 

[smize]

Alright, thank-you. I really want to create a star system generator someday.

 

[Drakkith]

Alright, thank-you. I really want to create a star system generator someday.

Have you seen Universe Sandbox?

 

[smize]

No. What is it programmed with?

 

[smize]

No. What is it programmed with?

Nevermind; I have found it. What I'm wanting to do is be able to generate, for example, 1000 systems in a matter of minutes and collect them in a database using PHP. It could be the basis for a game engine for text-based or browser-based games (which are more realistic).

 

[DaveC426913]

Nevermind; I have found it. What I'm wanting to do is be able to generate, for example, 1000 systems in a matter of minutes and collect them in a database using PHP. It could be the basis for a game engine for text-based or browser-based games (which are more realistic).

Oooooh! You're not interested in simulating systems over time, you're interested in generating static examples of stable systems!

Sorry - I misunderstood.

That's complEEEtly different!

And not something I can help you with.

 

[smize]

Oooooh! You're not interested in simulating systems over time, you're interested in generating static examples of stable systems!

Sorry - I misunderstood.

That's complEEEtly different!

And not something I can help you with.

Correct. As I get the basics of each system down, I will then make it more complex. (Adding the orbits of systems around a central mass, etc.). What is an example you were thinking of though? I think what I'm going for is the ability to actually do both, but mostly the latter.

 

[DaveC426913]

Correct. As I get the basics of each system down, I will then make it more complex. (Adding the orbits of systems around a central mass, etc.). What is an example you were thinking of though? I think what I'm going for is the ability to actually do both, but mostly the latter.

Both wouldn't make sense. It'd take millions or billions of orbits to see stable orbits materialize.

You either simulate it in time, or you model it statically using principles of orbital mechanics.

 

[smize]

Alright, I believe I comprehend now. I'm just curious but how do you personally go about the former?

 

[solarblast]

Try <http://orca.phys.uvic.ca/~tatum/celmechs.html>. It is well written and has some nice chapters on what you are looking for.