29-03-2007, 01:33 AM
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The shortest binary star period is just under 6 hours, and is among the W UMa eclipsing binaries. Two stars here cannot get any closer than a roughly 800 000 km apart - core to core - based on the problem of the star's atmosphere's getting too intermixed. If I can recall my basic astrophysics, I think it’s called the "breaking distance" - meaning that stars below this would merge as one. Some speculate examples of these are R CrB's - anti-novae - whose light is blocked by carbon orbiting in an accretion disk. Other examples are the Supernova, where a white dwarf near 1.4 solar masses mergers into a red giant - causing the white dwarf to explode. However, such giant stars exceed many hundreds of million kilometres - so the periods of such stars would be in the order of a year or two.
For the largest doubles, the periods can be up to several hundred thousand years whose distance is less than 0.3 parsecs. Such binaries are unknown, mainly because the orbital period is so slow and there has been insufficient time for indications of true motion - hence association. Much of this is therefore based on theory, whose limits are influenced by many factors, such as the mass of the stars and the influence of the surrounding medium, which contains other stars. Gravitation at such distances are so weak, that the gravity of nearby stars may affect the trajectory of the orbit to the extent that the distant component is eject into interstellar space to become a single star. The distances of more stable binaries are in the order of 20000 to 50000 years, whose distances are roughly under 10000 A.U.
This binary period can be simply calculated by;
Period = sqrt (D^3) x (M1 + M2)
Where;
D is the Distance in A.U. and
M1 and M2 are the masses of the two Components.
Separation (max) = 10^(2.8-(0.2 x DeltaM))
Where;
Separation (max) is the likely maximum separation of two stars expressed in arcsec and;
DeltaM is the Difference in Magnitude
True Separation = sin (SO / 3600) * D
Where;
SO is the Observed Separation (in arcsec)
D is the Distance (in Parsecs - pc.)
To convert the True Separation into the units required multiply by;
light-years = 3.2616
AU = 63240
km. = 9.46 x10^12
From this you can estimate any maximum distance limit, based on the various calculated masses and an upper period of roughly around 500 000 years.
NOTE: This can be calculated far more exactly, but the general results can only be achieved using far more complicated maths (calculus) - and this is probably too much for a general discussion like this one.
Hope this helps.
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