Alternative Splash image; Double Star orbits

[t00fri]

You do not seem to read my posts well before answering. Sorry, if my English makes you suffer...

The english isn't making me suffer, its the maths... (well, maybe it's both. The fact you're not explaining things much in non-mathematical terms probably isn't helping)

Back up a bit though. If you can have a frame of reference where everything in the system orbits the barycentre, why does it have to be moving at all? Wouldn't the barycentre act as if it's an object that has the mass of the two stars, and everything else would follow an elliptical orbit around it?

You may always chose a frame of your liking. If you want to consider the movement for a fixed barycenter, that's fine. The main drawback is that this frame is unsuitable for binary star observations that provide the crucial input data! Here, you want to place the primary into the center of your micrometer view and measure the secondary's distance and polar angle relative to north, say. In this frame (where the primary is at rest in each observation, the initial conditions x(t0), v(t0) of the secondary at epoch t0 can easily be determined.
Sure enough, in this frame, the observer is moving

In your favorite frame, both the primary and the secondary are moving...

As I emphasized, the physics does not depend on the choice of frame. And different frames can be trivially transformed into each other by applying rotations and translations to the respective orthonormal basis vectors...

Bye Fridger

[granthutchison]

What is interesting is that the 6th catalog also uses 7 parameters:

Besides the ones that are obvious, and in agreement with what I discussed above,

--semi-major axis (a)
--eccentricity (e)

--inclination (i)
--node (Omega)
--longitude of periastron (w)
--time of periastron passage (T)

they quote as 7th parameter

--the period (P) in years.

Six parameters characterize the orbit's orientation and the position of the orbiting body at t(0). A seventh is required to indicate how the orbiting body moves with time.

Orientation of the plane relative to some reference plane (2 parameters)
Shape of orbit (1 parameter, selecting from the family of conics)
Scale of orbit (1 parameter)
Orientation of orbit within plane (1 parameter)
Position of orbiter at some reference time (1 parameter)
Evolution with time (1 parameter)

I'm guessing that your very general equations of motion yield six parameters that constrain the orbit and its evolution, but don't stipulate the t(0) position, which is after all arbitrary?

Grant

[t00fri]

...
Six parameters characterize the orbit's orientation and the position of the orbiting body at t(0). A seventh is required to indicate how the orbiting body moves with time.

This seems to match perfectly what I wrote above. Right?




Bye Fridger

[granthutchison]

This seems to match perfectly what I wrote above. Right?

It does, with some additional detail tagged on. I was hoping to learn where you thought your original six parameters fitted into the list of seven, and so I felt a reference list was required.
I have clarity issues.

Grant

[Evil Dr Ganymede]

And different frames can be trivially transformed into each other by applying rotations and translations to the respective orthonormal basis vectors...

See, this is a prime example of the mathematical gibberish that I'm talking about - you could have just left that at "transformed into eachother."

In your favorite frame, both the primary and the secondary are moving...

Yeah, but it's easier to figure things out that way, surely.

It seems to me your life is being made difficult by not having the mass there. You're trying to figure out the masses from a big list of data so you can figure out where the barycentre is, and it's very difficult to do that given the data you have. So it seems to me that either you have to use a fudge based on the masses derived from the evolution tables, or you have to enter the masses by hand, or precalculcate the masses of each binary system and hardwire that into Celestia, or just not calculate the barycentres of every multiple system in Celestia, or just have the option to enter the masses by hand.

It boils down to practicality I think. I really doubt that anyone is going to want to fart around with rotating barycentres and rotating reference frames in Celestia. Ideally, I think you should just be able to write down the position of the barycentre and then everything should revolve around that. Anything more complex takes the program further out of the hands of people who are not professional astrophysicists and who are just interested in astronomy and want to build their own systems.

[granthutchison]

I really doubt that anyone is going to want to fart around with rotating barycentres and rotating reference frames in Celestia.

None of that is necessary in Celestia. You specify a barycentre, you stick some stars in orbit around it. You specify a barycentre in orbit around that barycentre, and you stick some more stars around it. You can place a planet around any of the stars or barycentres. Isn't that what you wanted?
The other stuff is fun for Fridger and me to get straight, but nowhere is there a requirement within Celestia for anyone to solve the two-body problem from the ground up.

Grant

[Evil Dr Ganymede]

None of that is necessary in Celestia. You specify a barycentre, you stick some stars in orbit around it. You specify a barycentre in orbit around that barycentre, and you stick some more stars around it. You can place a planet around any of the stars or barycentres. Isn't that what you wanted?

Yes, it is - so why are you guys worrying about all the other stuff?! Aren't you just trying to figure out how to put the barycentres into Celestia here?

[granthutchison]

Yes, it is - so why are you guys worrying about all the other stuff?!

Because it's what we do ... we hack stuff around until we figure we understand it from as many directions as possible. Convincing ourselves that the orbital elements are unchanged when moving from body-centred elements (in the catalogues) to barycentric elements (which we'd like to use in Celestia) is part of the process.

Aren't you just trying to figure out how to put the barycentres into Celestia here?

We know how to do that ... Chris has already produced the code. We're just trying to hack together a way of transferring >1800 orbits as faithfully as possible from various catalogue resources into Celestia.
Anyone who wants to place one barycentre in Celestia can type the definitions in in a couple of minutes, once they learn how the new stc parameters work.

Grant