Suppose a double star system. What about Kepler 3rd law. See details?

Question

ID Stars: A&B.
A=Sun mass.
B=2A
AB distance = Sun/Earth
Radius both very small, or zero

Orbit shape: circular both (eccentricity zero).
period must be the same, but...

I think the semi axis is different, yes? so...
How the Kepler's 3rd Law must be written for both stars ?

Answer 1

I think you can use the equation on this site http://imagine.gsfc.nasa.gov/YBA/cyg-X1-mass/binary-formula.html to derive the information you need.

Answer 2

Both stars orbit a common center of mass around one another. The orbital track looks somewhat like a figure eight track.

Any planets would ALSO orbit this center of mass of the two stars, causing some WEIRD eccentricities in their orbits.

The center of mass would be approximately 2/3 of the way to the larger star, NOT in the center between them (due to the difference in masses). This would probably cause loops in the orbits of any/all planets, as they pass near the stars.

Due to the eccentricities in the orbits, it has a high probability of not being able to support life as we know it, except for high temperature bacteria that could lie dormant during the colder periods.

Answer 3

The period is NOT the same as earth's orbit around the sun, because the mass of the two bodies is 3x greater than the mass of the Sun-Earth system. Therefore the orbital speed must be sqrt(3) times greater, so the period must less by 1/sqrt(3) times.

Answer 4

In this case, both stars need to be calculated from the center of mass - not the center of the larger star (B).

Both stars will orbit the center of mass based on Kepler's 3rd law.

Answer 5

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