Trinary system STC code check?

[Malenfant]

(I moved this from the P&A board, not sure where it's relevant but it's possibly better off here)

I'm wondering if someone can check this for me... previously I've made multiple star systems with circular orbits, this is the first one I've made with eccentric ones.

What I've got here is a trinary M V system, consisting of an M0 V with a close binary orbiting it:

The M0V (0.416 solar masses) and the binary barycentre (combined mass 0.486 solar masses) orbit the trinary barycentre, the separation between the two (semimajor axis) is 34.153 AU and the eccentricity of the orbit is 0.282.

The M3 V (0.278 solar masses) and M5V (0.208 solar masses) in the binary orbit the binary barycentre with a semimajor axis of 0.110 AU and an eccentricity of 0.778. (hrm, one issue with this might be that such a close binary is more likely to have a much more circular orbit, especially given that the system is 6.5Ga old...)

But anyway, does the code below make sense? Can anyone spot any major flaws with the code itself? I guess I'm wondering if I should be using the same eccentricities for each object orbiting a given barycentre. Is it even possible to have two stars orbiting a barycentre with different eccentricities?

I'm using this very useful paper to figure out the orbits, BTW:
http://arxiv.org/abs/astro-ph/9809315

(paste the code as a new .stc file)

Code: Select all

Barycenter "TrinaryABC"
{
RA         45
Dec       -45
Distance  100
}

Barycenter "TrinaryAB"
{
   OrbitBarycenter "TrinaryABC"

   EllipticalOrbit {             
      Period          210.16
      SemiMajorAxis   34.153 
      Eccentricity    0.282
      ArgOfPericenter 0
   }
}

"StarS"
{
OrbitBarycenter "TrinaryABC"
SpectralType "M0V"
AbsMag  8.78 # Luminosity = 0.026 Sol
Radius 375983

   EllipticalOrbit {               
      Period          210.16
      SemiMajorAxis   34.153
      Eccentricity    0.282
      ArgOfPericenter 180
   }
}

#-------------
"StarN1"
{
OrbitBarycenter "TrinaryAB"
SpectralType "M5V"
AbsMag  13.08 # Luminosity = 0.0005 Sol
Radius 157296

   EllipticalOrbit {               
      Period          0.052
      SemiMajorAxis   0.110
      Eccentricity    0.778
      ArgOfPericenter 0
   }
}

"StarN2"
{
OrbitBarycenter "TrinaryAB"
SpectralType "M3V"
AbsMag  10.60 # Luminosity = 0.0049 Sol
Radius 199056

   EllipticalOrbit {               
      Period          0.052
      SemiMajorAxis   0.110
      Eccentricity    0.778
      ArgOfPericenter 180
   }
}


[selden]

Code: Select all

Is it even possible to have two stars orbiting a barycentre with different eccentricities?

Remember that a barycenter is the center of mass of a system. When only two bodies are involved, they're both always on opposite sides of their barycenter with a distance inversely proportional to their masses. i.e. their orbits have the same eccentricity but different SMAs.

When more than two bodies are involved, things are somewhat more complicated. One simplified example might be two pairs of close stars, members of each pair orbiting around their mutual barycenters, and those barycenters orbiting around the barycenter of the whole system.

Your system doesn't look too outrageous to me, but I'm no expert in such things. I do think the SMAs need to be adjusted, though, since the stars with different luminosities would have different masses. Since they're coplanar, you might try to simulate the system using Tony Dunn's gravity simulator at http://www.orbitsimulator.com/

[t00fri]

The orbital elements from scientific publications usually have to be transformed into the Celestia frame (which also includes some unusual conventions). Has this been done in the above .ssc file?? I suppose not. What's the frame used in the above paper?

[selden]

Fridger,

The paper is about the long term stability of planetary systems in general.

These particular orbital parameters aren't from the paper.

[t00fri]

Fridger,

The paper is about the long term stability of planetary systems in general.

These particular orbital parameters aren't from the paper.

Well, since I am at work, I had not time yet to look into the paper. But my point remains valid: wherever these orbital elements are from, it is important to make sure that the frame is correct.

[Malenfant]

Code: Select all

Is it even possible to have two stars orbiting a barycentre with different eccentricities?

Remember that a barycenter is the center of mass of a system. When only two bodies are involved, they're both always on opposite sides of their barycenter with a distance inversely proportional to their masses. i.e. their orbits have the same eccentricity but different SMAs.

Ah, that's probably what was bugging me about this - the fact that the semimajor axes were the same within the binary!

When more than two bodies are involved, things are somewhat more complicated. One simplified example might be two pairs of close stars, members of each pair orbiting around their mutual barycenters, and those barycenters orbiting around the barycenter of the whole system.

That's what I've tried to account for here.

The orbital elements from scientific publications usually have to be transformed into the Celestia frame (which also includes some unusual conventions). Has this been done in the above .ssc file?? I suppose not. What's the frame used in the above paper?

The orbital elements aren't real or from a paper, they're randomly generated. The paper I linked to just describes how to find where the stable orbits are around each star in a binary system.

[Malenfant]

How does this look now? I fixed the orbital distances and lowered the eccentricity of the close binary...

(edit: oops, got the semimajor axes the wrong way round - corrected now)

Code: Select all

Barycenter "TrinaryABC"
{
RA         45
Dec       -45
Distance  100
}

#binary barycentre effective mass = 0.486 solar masses
Barycenter "TrinaryAB"
{
   OrbitBarycenter "TrinaryABC"

   EllipticalOrbit {             
      Period          210.16
      SemiMajorAxis   15.761
      Eccentricity    0.282
      ArgOfPericenter 0
   }
}

"StarS"
{
OrbitBarycenter "TrinaryABC"
SpectralType "M0V"
AbsMag  8.78 # Luminosity = 0.026 Sol, mass=0.416
Radius 375983

   EllipticalOrbit {               
      Period          210.16
      SemiMajorAxis   18.393
      Eccentricity    0.282
      ArgOfPericenter 180
   }
}

#-------------
"StarN1"
{
OrbitBarycenter "TrinaryAB"
SpectralType "M5V"
AbsMag  13.08 # Luminosity = 0.0005 Sol, mass=0.208
Radius 157296

   EllipticalOrbit {               
      Period          0.052
      SemiMajorAxis   0.063
      Eccentricity    0.432
      ArgOfPericenter 0
   }
}

"StarN2"
{
OrbitBarycenter "TrinaryAB"
SpectralType "M3V"
AbsMag  10.60 # Luminosity = 0.0049 Sol, mass=0.278
Radius 199056

   EllipticalOrbit {               
      Period          0.052
      SemiMajorAxis   0.047
      Eccentricity    0.432
      ArgOfPericenter 180
   }
}