Poutnik wrote:

I performed analysis of circular orbit case of twin binary stars.

I have realized the semi major axis in context of the 3rd Kepler law
must be surprisingly considered wrt the other star
and not wrt their barycentre, as I expected.

Otherwise formula of the 3rd Kepler law
does not match circular case requirement
of equality of gravitational and centripetal acceleration. […]

(“twin binary stars” contains redundancy as both “twin” and “binary” refer
to the number 2. Also, one system of a pair of stars orbiting each other is
called a “binary _star_”.)

Kepler’s laws (1609–1619 CE) are laws of *planetary* motion. They were
never intended for binary star systems [Johannes Kepler did not know that
such systems existed; the telescope had just been improved for planetary
observation by Galileo Galilei in 1609, and it was William Herschel who
first came up with the idea of a binary star in 1802]. They do not consider
that the star a planet is orbiting is also moving, as they do not consider a
system star–planet with a barycenter around which both star and planet are
moving. [Kepler may not even have considered Sol merely a star of many
others as that thought – worded as “the doctrine of the infinite universe
and the innumerable worlds” – was formulated at first by Giordano Bruno in
1584, which was considered one heresy of several of Bruno’s by the Catholic
Church, for which he was burned at the stake in 1600.]

Therefore, as Isaac Newton (1687) showed already, Kepler’s laws are only an
approximation of the observed planetary motion.

We now know that even Newton’s laws are only a better approximation as (so
far) only general relativity (GR), postulated by Albert Einstein in 1915,
fully describes gravitational effects, including planetary motion. (GR
could explain and predict the perihelion precession of Mercury to great
precision; Kepler’s laws and Newtonian gravity could not.)

As we have seen again recently with GW150914, effects predicted by GR become
important when large masses like of that of stars are involved.

Therefore, ISTM your calculations using Kepler’s laws to describe a binary
star are mere cyclosophy.


F'up2 sci.physics.relativity

PointedEars
--
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The officer asks him "Do you know how fast you were going?"
Heisenberg replies "No, but I know where I am."
(from: WolframAlpha)