Ternary Star System?

[MKruer]

Ternary Star System

Close binary pair with distant third star

I am working on a project and I would like some confirmation that this is physically possible. My idea for the system is as follows:

Mass:
Star A: 0.8 Solar Masses
Star B: 0.7 Solar Masses
Star C: 1.5 Solar Masses

Distance:
Stars A and B are within 0.1AU of each other, in roughly circular orbits
Star C is in a highly elliptical orbit and once in a while comes within 3 light months of Stars A and B

Both stars should be able to have planets around them, but the proximity of the between Stars AB and C would tend to toss out planets further out from both stars or so I would think.

Questions:
Is such a system possible, and Stars A and B form that close together with out merging with each other?
Can an orbit around the AB binary be stable enough to support life?

Thanks

-Matt-

[Malenfant]

It's not only possible but there systems known to be that close and also systems that are even closer than that.

you won't get planets around A or B, but you can get planets orbiting the barycentre of the pair. Planetary orbits should be stable beyond about 0.25 AU of the barycenter, if you want to be conservative about it call it 0.4 AU.

Star C is going to be interesting though - it's pretty massive, and if it's on an inclined orbit relative to the AB and their planets then they can cause some pretty crazy cyclic eccentricity and inclination variations via the Kozai mechanism - though they'd be on the order of billions of years probably.

[MKruer]

I guess my big concern is how close can you get the AB pair with out them adversely affecting each other. What I mean at some point they are going to be so close that the stars will become heavily distorted by the gravitation pull of each other and begin to have mass transference. In which can any increase or decreased in solar output would have adverse effects on and inhabited planets around the stars.

Also on C star, I might reduce the mass to a more conservative 1 solar mass. Is there any reason why you could not have larger more massive star outside the binary pair. I believe that most Ternary system tend a massive central star and the other smaller stars orbit the main one. Any reason why the mass could not be equally split?

[MKruer]

Can someone double check my math on the first part of the system? For the given mass of the stars, they seem to be orbiting very slowly, Perhaps I am wrong. Also the orbital distance between both stars is equal to the distance between the Sun and Mercury. Is it possible to get these stars closer without any adverse tidal effects? Right now I calculated the Roche Limit to be about 2 million kilometers from the surface of each star.

Sekgnai.stc

Code: Select all

Barycenter "Sekgnai AB"
{
   RA 0
   Dec 0
   Distance 1000
}

"Sekgnai A"
{
   OrbitBarycenter "Sekgnai AB"
   SpectralType "K1"
   #Mass 1.75032E+30
   Radius 668590.000 # KM



   EllipticalOrbit {
      Period          0.1822235   # Years
      SemiMajorAxis   0.192446207 # AU / 28789542.857 KM
      Eccentricity    0.0
      Inclination     0.0
      AscendingNode   180.0
      ArgOfPericenter 0.0
      MeanAnomaly     180.0
   }
}

"Sekgnai B"
{
   OrbitBarycenter "Sekgnai AB"
   SpectralType "K2"
   #Mass 1.73043E+30
   Radius 666505.000
   
   EllipticalOrbit {
      Period          0.1822235   # Years
      SemiMajorAxis   0.194658233 # AU / 29120457.143 KM
      Eccentricity    0.0
      Inclination     0.0
      AscendingNode   0.0
      ArgOfPericenter 0.0
      MeanAnomaly     0.0
   }
}

Thanks -Matt-

[chris]

Can someone double check my math on the first part of the system? For the given mass of the stars, they seem to be orbiting very slowly, Perhaps I am wrong.

It does seem to slow . . .

Shouldn't the period be r^1.5 * (Msun/(M1+M2)) years?
. . . where SMA is the sum of the semi-major axes in au, and M1+M2 is the total mass? I get ~0.13 years.

--Chris

[Malenfant]

AFAIK the binary orbital period (in years) around the barycentre should be:

P = SQRT(R^3/M1+M2)

where R is the separation in AU, and M1 and M2 are the masses of the stars in MSol.

With R=0.4 AU, M1=0.8 and M2=0.7, I get a binary orbital period of 0.21 years. the 0.8 MS star should be 0.187 AU from the barycentre, and the 0.7 MS star should be 0.213 AU from the barycentre.

[MKruer]

Hum?€¦ Maybe I made a mistake on the Berycenter. I use a distance of 57,910,000,000 meters between stars A and B. Star A has a mass of 1.75032E+30 kg and Star B has a mass of 1.73043E+30

Berycenter for Mass1
Distance = (Mass1/(Mass1+Mass2))*Distance

For the Orbital Period
P = 2*PI*SQRT(Distance^3/(G*(Mass1+Mass2)))

EDIT: I think I know what I did wrong. I calculated the berycenter distance for each object and then assigned the distance between both stars, not to the berry center.

BTW How do the Mass to Radius look for the stars. I was trying to keep them at the same density as out sun 1.41 Density (g/cm??)

EDIT2: @Chris In the future release do you plan on using different orbit colors to differentiate between stars and planets orbits?

Thanks

-Matt-

[Hungry4info]

EDIT2: @Chris In the future release do you plan on using different orbit colors to differentiate between stars and planets orbits?

Yeah, it would be nice if they were given different coloured orbits. White perhaps?

[MKruer]

Small update: I found the original formula that I was using.

Code: Select all

       4 pi^2
T^2 = -------- * a^3
       G(M+m)

G = 0.0000000000667
M = 1.75032E+30
m = 1.73043E+30

M a = 29,828,571,429
m a = 30,171,428,571
    = 60,000,000,000

Now If I use the equations above I run into a problem because of the slight orbital distance form the barycentre. The more massive star orbits about a half day faster (24.6 vs 25.0). This should not be the case the only way to correct this problem is to use the distance between both stars. The question is that the full distance or the half?

[chris]

Now If I use the equations above I run into a problem because of the slight orbital distance form the barycentre. The more massive star orbits about a half day faster (24.6 vs 25.0). This should not be the case the only way to correct this problem is to use the distance between both stars. The question is that the full distance or the half?

It's the full distance . . . Consider the case where one mass is much larger than the other, e.g. the Earth/Sun system. The period is determined by the distance between the two, not half the distance. It's no different when the masses are more similar.

--Chris

[MKruer]

Thanks Chris, I never had to calculate with a barycentre before.