Help! Orbit problems!

[ajtribick]

I'm trying to create an add-on for the Epsilon Eridani system. So far I've managed to get the planets I want in there, a few moons and the like.

Unfortunately, I'm not sure what half these terms mean, and the internet sources I've come across seem to presume university level knowledge.

Examining solarsys.ssc, I find the following terms:

SemiMajorAxis
Eccentricity
Inclination
AscendingNode
LongOfPericenter
MeanLongitude

Of these, I understand fully SemiMajorAxis and Eccentricity. Inclination I understand as the tilt of the plane of the orbit, but I'm not sure relative to what or in what direction.

AscendingNode seems to rotate the orbit around the star. The others completely confuse me.

So some definitions of these terms would be very much welcomed.

Thanks in advance,

Chaos Syndrome.

[selden]

chaos syndrome,

A while ago I created the Web page http://www.lns.cornell.edu/~seb/celestia/orbital-parameters.html, which includes a crude picture showing the relationships of the angles.

Does this help?
If the web page doesn't clarify things adequately, please ask some questions about any of the things it describes. I'll try to improve it.

[Evil Dr Ganymede]

Mean Longitude is a bugger to explain. It's equal to (Mean Anomaly + Longitude of Pericentre), and since Mean Anomaly doesn't really have a simple geometric explanation (i.e. you can't really draw it on a diagram), that makes Mean Longitude somewhat hard to visualise.

No disrespect to Selden, but this might be a slightly easier to read diagram than the one he has on his page (the key is on the second page).

(Note: my 'capital gamma' should really be a 'capital omega').

[selden]

Hey, I never claimed to be an artist!

I note, however, that you've got straight lines indicating some of the angles. That makes tham a bit hard to recognize. My understanding is that the convention is to use arcs.

It seems to me that it'd be appropriate to have some kind of model for Celestia. That might make the angles easier to visualize.

[Evil Dr Ganymede]

Hey, I never claimed to be an artist!

I note, however, that you've got straight lines indicating some of the angles. That makes tham a bit hard to recognize. My understanding is that the convention is to use arcs.

Yeah, I do - that's purely because it's a pain to try and draw short curvy lines in a graphics program by hand .

[ajtribick]

And the winner of the contest between diagrams is...

no, I wouldn't be that harsh. For a newbie though, selden's is slightly more friendly as it has nice full labels all over it rather than trying to remember greek letters (even though I studied this magnificent language remembering loads of arbitrary letters of a diagram does my head in...)

Anyway I think I understand this much better now.

So anyway, further queries.

I take it that the AscendingNode parameter means "Longitude of Ascending Node".

Is there any way to specify Argument of Pericenter independent of AscendingNode in Celestia, or must I use the Longitude of Pericenter combination?

Similarly, is there a simple way of putting in Time since Pericenter without calculating angular velocities and stuff to get to the mean anomaly?

What does Celestia take as the reference plane? Does the program store each star's axial tilt and use that?

All help much appreciated.

[Evil Dr Ganymede]

And the winner of the contest between diagrams is...

no, I wouldn't be that harsh. For a newbie though, selden's is slightly more friendly as it has nice full labels all over it rather than trying to remember greek letters (even though I studied this magnificent language remembering loads of arbitrary letters of a diagram does my head in...)

Most of those letters aren't arbitrary (in the sense that I just made them up anyway) - they're the letters that are generally used to refer to those parameters (e.g. in Murray and Dermott's 'Solar System Dynamics' book. I only used GAMMA because I'd used OMEGA for something else elsewhere (that diagram is from my PhD thesis).

[ajtribick]

And the winner of the contest between diagrams is...

no, I wouldn't be that harsh. For a newbie though, selden's is slightly more friendly as it has nice full labels all over it rather than trying to remember greek letters (even though I studied this magnificent language remembering loads of arbitrary letters of a diagram does my head in...)

Most of those letters aren't arbitrary (in the sense that I just made them up anyway) - they're the letters that are generally used to refer to those parameters (e.g. in Murray and Dermott's 'Solar System Dynamics' book. I only used GAMMA because I'd used OMEGA for something else elsewhere (that diagram is from my PhD thesis).

Sorry, I should have said "seemingly arbitrary".

No offence was intended. I hope none was taken.

[selden]

I take it that the AscendingNode parameter means "Longitude of Ascending Node".

Yup

Is there any way to specify Argument of Pericenter independent of AscendingNode in Celestia, or must I use the Longitude of Pericenter combination?

The ArgOfPericenter and the Longitude of the Ascending Node are completely independant of one another. You need to specify the Longitude of the Ascending Node, but (to fully define an orbit) you can specify either the Arg. of the Pericenter or the Long. of Pericenter.

If you specify both, Celestia uses the Arg; if you specify the Long. of Pericenter, Celestia will calculate the Arg: ArgOfPericenter = Long. of Pericenter - Long. of Ascending Node

Similarly, is there a simple way of putting in Time since Pericenter without calculating angular velocities and stuff to get to the mean anomaly?

Tch. You didn't read the table on my page

When the object is at Pericenter, by definition its mean anomaly = 0.
So if you choose and specify an Epoch which is the time of a particular Pericenter passage, you don't have to calculate the Mean Anomaly: it's 0. Since Celestia doesn't implement orbital precession, for a given set of Keplerian elements and corresponding planetary positions, changing the Epoch only changes the value of the Mean Anomaly.

To put it another way, except for having to specify a corresponding Mean Anomaly, the value of Epoch only matters if you're going to define different orbital elements at different Epochs. i.e. if the object's orbit changes with time.

It'd probably be simplest to specify a different Epoch for each planet's orbit, using the date that the planet is closest to its sun.

What does Celestia take as the reference plane?

The solar system's ecliptic plane. So if you're going to have different orbital tilts around different stars, you have to do some spherical trig.
Grant Hutchison wrote a spreadsheet that might help. See http://www.lns.cornell.edu/~seb/celestia/hutchison/spreadsheets.html

Does the program store each star's axial tilt and use that?

Nope.

Don't forget that the axial tilt of a star does not necessarily correspond exactly to any of the planes of the orbits of its planets. The sun is tilted by about 7 degrees from the ecliptic, for example.

Does this help?

[Evil Dr Ganymede]

No offence was intended. I hope none was taken.

None taken. I just didn't want you to think I'd picked random letters out of a hat for my diagram