Determining the orbits in a binary star relationship

[Guest guest]

To the list. I've posted this elsewhere. I need some help finding one

resource that I had found but have now lost.

 

As I consider the binary star relationship between our Sun and Sirius,

it seems helpful to have a sense of the orbital nature of each star. I

haven't yet found anything helpful on the Internet for anything

similar to two stars with a 8.7 light year separation, unlike the

close together binary setup such as between Sirius A and Sirius B

which are quite close to each other. The following steps in

calculating the Sol-to-Sirius relationship seem reasonable. If anyone

can correct or suggest something different, please do so.

 

** The combined mass of Sirius A and B relative to our Sun will have a

balance point much like two dissimilar children on a see-saw. The

heavier Sirius side of the equation will move the gravitational

balance point closer to Sirius.

 

** The balance point will form one focus-point of the two focus points

that make up an elliptical orbit. Each ellipse has two focus points

along its major (longest) axis.

 

** The distance to Sirius will determine the length of the major axis.

 

** The observed wanderings of Sirius over the sky, as logged over time

by various cultures, will define the total arc of movement as seen

from here in our orbital view. Given the distance to Sirius and the

observed total arc of movement, we can determine the distance of the

minor arc (across the shortest axis of the ellipse) of Sirius. The

ONLY PROBLEM WITH THIS is that I didn't keep the web-address of the

site where Sirius was observed to be over a few thousand years of

time. IF ANYONE KNOWS OF, OR HAS, THIS DATA I WOULD REALLY APPRECIATE

HAVING IT.

 

** I believe, but don't know for sure, that the width of the semi-arc

of our Sun's orbit will be proportionate to the same value used to

determine the gravitational balance between the two Suns.

 

** From this data I might be able to determine the eccentricity of our

orbit and its second focal point relative to the 8.7 light year length

of the major axis.

 

** The sum of the distance from one focal point to the width of the

orbit and from there to the other focus point is a constant value when

we define the orbital path at any point on the ellipse. So, we can

plot the ellipse path.

 

** We can test this ellipse path and axis locations because the Sun in

its orbital path covers an equal area of space as swept by its

movement along its orbit --- no matter where you measure it.

 

** Finally, because the two stars in a binary system always are

opposite each other along a line drawn through the common gravity

balance point (also a focus point on each Sun's orbit's major axis) we

can determine Sirius orbit.

 

If anyone can comment on this, and if it looks appropriate, I'll try

to plot out the possible orbits of the Sun and Sirius in a binary

relationship. Of course, this might have already been done somewhere

on the Internet. Oh well, its an interesting exercise. Dave

[Guest guest]

I've been in touch with a NASA physicist who believes that the

distance between our two Suns precludes a binary relationship due to

the likelihood that other nearby stars might have enough influence to

degrade the orbital path of our Sun such that a long term (very long

term) relationship would not be stable.

 

Given the scale of time (millions and billions of years) and the

likely complete orbit time (24,000 years) it might be that such a

binary relationship would be " short term " (several million years,

perhaps) or perhaps longer, or perhaps not at all.

 

I've contacted also the Sirius Research Group to see 1) what orbital

work/calculations they might have done, and 2) to see if they can

point me to records of Sirius arc of motion across the sky. This

latter information is needed to estimate an orbit's minor axis. If

anyone does come across the records that I've seen once on the

Internet (but can not now re-locate) about Sirius' historical

positional records in the sky, please contact me. Meanwhile, I will

continue to explore this fascinating subject. Dave