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Observed long-period multiple stars



 
 
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  #1  
Old October 25th 07, 02:32 PM posted to rec.arts.sf.science,sci.astro
Crown-Horned Snorkack
external usenet poster
 
Posts: 125
Default Observed long-period multiple stars

What is the longest period of any star system observed to be multiple
- that is, having a KNOWN eccentricity and inclination?

Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.

Why? Have a glimpse at the absolutely closest nearby stars, Alpha and
Proxima Centauri!

The distance between Alpha and Proxima is 15 000 AU - with uncertainty
of 700 AU.

This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.

Now, think of the stars just slightly farther than Alpha Centauri. The
uncertainty of distance is of course proportional to the square of
distance itself.

At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.

As for the peculiar motions, consider this: Proxima Centauri, at known
distance of 15 000 AU from Alpha would, if on a circular orbit, have a
speed of about 300 m/s. If it were on a low relative speed hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s, both
in proper motion and radial direction.

Or looking it another way, a star 1000 AU from a 1 solar mass primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of 1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of 1
km/s means the stars are at a low speed hyperbolic bypass.

So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out what
the inclination and eccentricity are.

What is the longest period of a star system possessing observed
inclination and eccentricity?

  #2  
Old October 26th 07, 10:02 AM posted to rec.arts.sf.science,sci.astro
Mike Dworetsky
external usenet poster
 
Posts: 715
Default Observed long-period multiple stars

"Crown-Horned Snorkack" wrote in message
oups.com...
What is the longest period of any star system observed to be multiple
- that is, having a KNOWN eccentricity and inclination?

Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.

Why? Have a glimpse at the absolutely closest nearby stars, Alpha and
Proxima Centauri!

The distance between Alpha and Proxima is 15 000 AU - with uncertainty
of 700 AU.

This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.

Now, think of the stars just slightly farther than Alpha Centauri. The
uncertainty of distance is of course proportional to the square of
distance itself.

At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.

As for the peculiar motions, consider this: Proxima Centauri, at known
distance of 15 000 AU from Alpha would, if on a circular orbit, have a
speed of about 300 m/s. If it were on a low relative speed hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s, both
in proper motion and radial direction.

Or looking it another way, a star 1000 AU from a 1 solar mass primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of 1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of 1
km/s means the stars are at a low speed hyperbolic bypass.

So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out what
the inclination and eccentricity are.

What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of long-period
orbiting pairs, the values are imprecisely known. But the best examples are
some of the longer period visual binaries with orbital elements. In these
cases the observational record spans more than 220 years (going back to Sir
William Herschel's systematic observations, or even further). It's usually
possible in favourable cases to calculate the elements of the orbit once
about 20-25% of the arc has been observed, so I'd guess that the answer is
periods of order 500-1000 years. Possible examples are the stars epsilon 1
and epsilon 2 Lyrae, each of which is a pair with partial observed arcs and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you search
using Simbad. Maybe you could dig into the most recent catalogue of VB
orbits and find something?

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

  #3  
Old October 26th 07, 05:13 PM posted to rec.arts.sf.science,sci.astro
Crown-Horned Snorkack
external usenet poster
 
Posts: 125
Default Observed long-period multiple stars

On 26 okt, 12:02, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message

oups.com...



What is the longest period of any star system observed to be multiple
- that is, having a KNOWN eccentricity and inclination?


Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.


Why? Have a glimpse at the absolutely closest nearby stars, Alpha and
Proxima Centauri!


The distance between Alpha and Proxima is 15 000 AU - with uncertainty
of 700 AU.


This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.


Now, think of the stars just slightly farther than Alpha Centauri. The
uncertainty of distance is of course proportional to the square of
distance itself.


At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.


As for the peculiar motions, consider this: Proxima Centauri, at known
distance of 15 000 AU from Alpha would, if on a circular orbit, have a
speed of about 300 m/s. If it were on a low relative speed hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s, both
in proper motion and radial direction.


Or looking it another way, a star 1000 AU from a 1 solar mass primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of 1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of 1
km/s means the stars are at a low speed hyperbolic bypass.


So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out what
the inclination and eccentricity are.


What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of long-period
orbiting pairs, the values are imprecisely known. But the best examples are
some of the longer period visual binaries with orbital elements. In these
cases the observational record spans more than 220 years (going back to Sir
William Herschel's systematic observations, or even further). It's usually
possible in favourable cases to calculate the elements of the orbit once
about 20-25% of the arc has been observed, so I'd guess that the answer is
periods of order 500-1000 years. Possible examples are the stars epsilon 1
and epsilon 2 Lyrae, each of which is a pair with partial observed arcs and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you search
using Simbad. Maybe you could dig into the most recent catalogue of VB
orbits and find something?

Thanks for hinting at Epsilon Lyrae. Something could indeed be found:

http://www.alcyone.de/SIT/doubles/SIT003301.htm

With the period of allegedly 1165,6 years, they dare give the
inclination (138 degrees) and eccentricity (0,19). This catalogue does
not include the true masses, though.

  #4  
Old October 27th 07, 07:59 AM posted to rec.arts.sf.science,sci.astro
Mike Dworetsky
external usenet poster
 
Posts: 715
Default Observed long-period multiple stars

"Crown-Horned Snorkack" wrote in message
ps.com...
On 26 okt, 12:02, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message

oups.com...



What is the longest period of any star system observed to be multiple
- that is, having a KNOWN eccentricity and inclination?


Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.


Why? Have a glimpse at the absolutely closest nearby stars, Alpha and
Proxima Centauri!


The distance between Alpha and Proxima is 15 000 AU - with uncertainty
of 700 AU.


This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.


Now, think of the stars just slightly farther than Alpha Centauri. The
uncertainty of distance is of course proportional to the square of
distance itself.


At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.


As for the peculiar motions, consider this: Proxima Centauri, at known
distance of 15 000 AU from Alpha would, if on a circular orbit, have a
speed of about 300 m/s. If it were on a low relative speed hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s, both
in proper motion and radial direction.


Or looking it another way, a star 1000 AU from a 1 solar mass primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of 1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of 1
km/s means the stars are at a low speed hyperbolic bypass.


So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out what
the inclination and eccentricity are.


What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of long-period
orbiting pairs, the values are imprecisely known. But the best examples
are
some of the longer period visual binaries with orbital elements. In
these
cases the observational record spans more than 220 years (going back to
Sir
William Herschel's systematic observations, or even further). It's
usually
possible in favourable cases to calculate the elements of the orbit once
about 20-25% of the arc has been observed, so I'd guess that the answer
is
periods of order 500-1000 years. Possible examples are the stars epsilon
1
and epsilon 2 Lyrae, each of which is a pair with partial observed arcs
and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you
search
using Simbad. Maybe you could dig into the most recent catalogue of VB
orbits and find something?

Thanks for hinting at Epsilon Lyrae. Something could indeed be found:

http://www.alcyone.de/SIT/doubles/SIT003301.htm

With the period of allegedly 1165,6 years, they dare give the
inclination (138 degrees) and eccentricity (0,19). This catalogue does
not include the true masses, though.


This would make a good exercise for a beginning astronomy course...

If you have a (arcsec) and P (years), look up the parallax with Simbad

http://simbad.u-strasbg.fr/simbad/


This gives 20.3 mas for Epsilon2, i.e., 0.0203 arcsec

Hence the true a is 2.78/0.0203 = 136.95 AU. Then use Kepler's Third Law

(M1+M2)P^2 = a^3 == (M1+M2) = 1.89 Msun. This seems pretty low to me.

The other pair, epsilon1, with P = 585 yr and a = 2.95 arcsec, parallax
0.0201, would give (M1+M2) = 9.24 Msun, which seems rather high to me for
two A3 main sequence stars, which ought to be around roughly 2.5 Msun each.

So my guess, with this limited data, is that the periods in particular are
wide of the mark (not surprising). Since 1955 there must be an extra
half-century of data, so I wonder if any improvement in the orbit is
possible.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

  #5  
Old October 27th 07, 09:51 AM posted to rec.arts.sf.science,sci.astro
Crown-Horned Snorkack
external usenet poster
 
Posts: 125
Default Observed long-period multiple stars

On 27 okt, 09:59, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message

ps.com...



On 26 okt, 12:02, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message


groups.com...


What is the longest period of any star system observed to be multiple
- that is, having a KNOWN eccentricity and inclination?


Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.


Why? Have a glimpse at the absolutely closest nearby stars, Alpha and
Proxima Centauri!


The distance between Alpha and Proxima is 15 000 AU - with uncertainty
of 700 AU.


This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.


Now, think of the stars just slightly farther than Alpha Centauri. The
uncertainty of distance is of course proportional to the square of
distance itself.


At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.


As for the peculiar motions, consider this: Proxima Centauri, at known
distance of 15 000 AU from Alpha would, if on a circular orbit, have a
speed of about 300 m/s. If it were on a low relative speed hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s, both
in proper motion and radial direction.


Or looking it another way, a star 1000 AU from a 1 solar mass primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of 1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of 1
km/s means the stars are at a low speed hyperbolic bypass.


So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out what
the inclination and eccentricity are.


What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of long-period
orbiting pairs, the values are imprecisely known. But the best examples
are
some of the longer period visual binaries with orbital elements. In
these
cases the observational record spans more than 220 years (going back to
Sir
William Herschel's systematic observations, or even further). It's
usually
possible in favourable cases to calculate the elements of the orbit once
about 20-25% of the arc has been observed, so I'd guess that the answer
is
periods of order 500-1000 years. Possible examples are the stars epsilon
1
and epsilon 2 Lyrae, each of which is a pair with partial observed arcs
and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you
search
using Simbad. Maybe you could dig into the most recent catalogue of VB
orbits and find something?


Thanks for hinting at Epsilon Lyrae. Something could indeed be found:


http://www.alcyone.de/SIT/doubles/SIT003301.htm


With the period of allegedly 1165,6 years, they dare give the
inclination (138 degrees) and eccentricity (0,19). This catalogue does
not include the true masses, though.


This would make a good exercise for a beginning astronomy course...

If you have a (arcsec) and P (years), look up the parallax with Simbad

http://simbad.u-strasbg.fr/simbad/

This gives 20.3 mas for Epsilon2, i.e., 0.0203 arcsec

Hence the true a is 2.78/0.0203 = 136.95 AU.


You are using instant "separation" though. The actual half axis may be
more (if the orbit is inclined or many other possibilities) or less
(if the stars are near apastron right now)

Then use Kepler's Third Law

(M1+M2)P^2 = a^3 == (M1+M2) = 1.89 Msun. This seems pretty low to me.

The other pair, epsilon1, with P = 585 yr and a = 2.95 arcsec, parallax
0.0201, would give (M1+M2) = 9.24 Msun, which seems rather high to me for
two A3 main sequence stars, which ought to be around roughly 2.5 Msun each.

So my guess, with this limited data, is that the periods in particular are
wide of the mark (not surprising). Since 1955 there must be an extra
half-century of data, so I wonder if any improvement in the orbit is
possible.

But you had not been using the alleged orbits.


  #6  
Old October 27th 07, 05:01 PM posted to rec.arts.sf.science,sci.astro
Mike Dworetsky
external usenet poster
 
Posts: 715
Default Observed long-period multiple stars

"Crown-Horned Snorkack" wrote in message
oups.com...
On 27 okt, 09:59, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message

ps.com...



On 26 okt, 12:02, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message


groups.com...


What is the longest period of any star system observed to be
multiple
- that is, having a KNOWN eccentricity and inclination?


Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.


Why? Have a glimpse at the absolutely closest nearby stars, Alpha
and
Proxima Centauri!


The distance between Alpha and Proxima is 15 000 AU - with
uncertainty
of 700 AU.


This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.


Now, think of the stars just slightly farther than Alpha Centauri.
The
uncertainty of distance is of course proportional to the square of
distance itself.


At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a
pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.


As for the peculiar motions, consider this: Proxima Centauri, at
known
distance of 15 000 AU from Alpha would, if on a circular orbit, have
a
speed of about 300 m/s. If it were on a low relative speed
hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s,
both
in proper motion and radial direction.


Or looking it another way, a star 1000 AU from a 1 solar mass
primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of
1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of
1
km/s means the stars are at a low speed hyperbolic bypass.


So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out
what
the inclination and eccentricity are.


What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of
long-period
orbiting pairs, the values are imprecisely known. But the best
examples
are
some of the longer period visual binaries with orbital elements. In
these
cases the observational record spans more than 220 years (going back
to
Sir
William Herschel's systematic observations, or even further). It's
usually
possible in favourable cases to calculate the elements of the orbit
once
about 20-25% of the arc has been observed, so I'd guess that the
answer
is
periods of order 500-1000 years. Possible examples are the stars
epsilon
1
and epsilon 2 Lyrae, each of which is a pair with partial observed
arcs
and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you
search
using Simbad. Maybe you could dig into the most recent catalogue of
VB
orbits and find something?


Thanks for hinting at Epsilon Lyrae. Something could indeed be found:


http://www.alcyone.de/SIT/doubles/SIT003301.htm


With the period of allegedly 1165,6 years, they dare give the
inclination (138 degrees) and eccentricity (0,19). This catalogue does
not include the true masses, though.


This would make a good exercise for a beginning astronomy course...

If you have a (arcsec) and P (years), look up the parallax with Simbad

http://simbad.u-strasbg.fr/simbad/

This gives 20.3 mas for Epsilon2, i.e., 0.0203 arcsec

Hence the true a is 2.78/0.0203 = 136.95 AU.


You are using instant "separation" though. The actual half axis may be
more (if the orbit is inclined or many other possibilities) or less
(if the stars are near apastron right now)


As far as I can tell from the orbital data table presented, the value a is
the semimajor axis, not the separation rho (gk letter), so I am using the
correct quantity in a formal sense.

Then use Kepler's Third Law

(M1+M2)P^2 = a^3 == (M1+M2) = 1.89 Msun. This seems pretty low to me.

The other pair, epsilon1, with P = 585 yr and a = 2.95 arcsec, parallax
0.0201, would give (M1+M2) = 9.24 Msun, which seems rather high to me for
two A3 main sequence stars, which ought to be around roughly 2.5 Msun
each.

So my guess, with this limited data, is that the periods in particular
are
wide of the mark (not surprising). Since 1955 there must be an extra
half-century of data, so I wonder if any improvement in the orbit is
possible.

But you had not been using the alleged orbits.


I don't understand your comment. In orbital parlance, "a" is the semimajor
axis. Observed a for a visual binary is in units of arcsec. An orbit
publisher presents a, e, i, node, longitude of periastron, P, and T(peri).
I did this correctly as far as I can tell. I used the elements represented
in the table you linked to.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

  #7  
Old October 29th 07, 03:45 PM posted to rec.arts.sf.science,sci.astro
Crown-Horned Snorkack
external usenet poster
 
Posts: 125
Default Observed long-period multiple stars

On 27 okt, 18:01, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message

oups.com...



On 27 okt, 09:59, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message


oups.com...


On 26 okt, 12:02, "Mike Dworetsky"
wrote:
"Crown-Horned Snorkack" wrote in message


groups.com...


What is the longest period of any star system observed to be
multiple
- that is, having a KNOWN eccentricity and inclination?


Just the stars seeming to be nearby in the sky and sharing similar
parallaxes, proper and radial motions does not show much.


Why? Have a glimpse at the absolutely closest nearby stars, Alpha
and
Proxima Centauri!


The distance between Alpha and Proxima is 15 000 AU - with
uncertainty
of 700 AU.


This 700 AU comes from the simple fact that the distance in radial
direction is a difference between two big and imprecise values close
to each other. The distances to both stars.


Now, think of the stars just slightly farther than Alpha Centauri.
The
uncertainty of distance is of course proportional to the square of
distance itself.


At 11 LY, you can expect distance uncertainties in the order of 4000
AU. At 88 LY, distance uncertainty would reach 280 000 AU - so a
pair
of stars which look close to each other and both at about 100 LY
distant to the precision of measurement may actually be as distant
from each other as Sun and Alpha Centauri.


As for the peculiar motions, consider this: Proxima Centauri, at
known
distance of 15 000 AU from Alpha would, if on a circular orbit, have
a
speed of about 300 m/s. If it were on a low relative speed
hyperbolic
bypass, the relative speed would be about 430 m/s. So, there is
absolutely no way of knowing one way or another unless the peculiar
motions of both components are known to the precision of 100 m/s,
both
in proper motion and radial direction.


Or looking it another way, a star 1000 AU from a 1 solar mass
primary,
with observed relative peculiar motion of 1 km/s, would be on a
circular orbit. But if the radial distance had an uncertainty of
1000
AU, which is true for all stars beyond Alpha Centauri, and the
distance is actually 2000 AU, that same relative peculiar motion of
1
km/s means the stars are at a low speed hyperbolic bypass.


So... the only way to actually see which stars are binary is observe
the orbital ACCELERATION. Over sufficient time period to find out
what
the inclination and eccentricity are.


What is the longest period of a star system possessing observed
inclination and eccentricity?


I don't have a concise answer because for "known" periods of
long-period
orbiting pairs, the values are imprecisely known. But the best
examples
are
some of the longer period visual binaries with orbital elements. In
these
cases the observational record spans more than 220 years (going back
to
Sir
William Herschel's systematic observations, or even further). It's
usually
possible in favourable cases to calculate the elements of the orbit
once
about 20-25% of the arc has been observed, so I'd guess that the
answer
is
periods of order 500-1000 years. Possible examples are the stars
epsilon
1
and epsilon 2 Lyrae, each of which is a pair with partial observed
arcs
and
periods of this order. I'd need to dig pretty hard to find the orbit
publications for you, but I think they are on the web via ADS if you
search
using Simbad. Maybe you could dig into the most recent catalogue of
VB
orbits and find something?


Thanks for hinting at Epsilon Lyrae. Something could indeed be found:


http://www.alcyone.de/SIT/doubles/SIT003301.htm


With the period of allegedly 1165,6 years, they dare give the
inclination (138 degrees) and eccentricity (0,19). This catalogue does
not include the true masses, though.


This would make a good exercise for a beginning astronomy course...


If you have a (arcsec) and P (years), look up the parallax with Simbad


http://simbad.u-strasbg.fr/simbad/


This gives 20.3 mas for Epsilon2, i.e., 0.0203 arcsec


Hence the true a is 2.78/0.0203 = 136.95 AU.



As far as I can tell from the orbital data table presented, the value a is
the semimajor axis, not the separation rho (gk letter), so I am using the
correct quantity in a formal sense.



Then use Kepler's Third Law


(M1+M2)P^2 = a^3 == (M1+M2) = 1.89 Msun. This seems pretty low to me.


The other pair, epsilon1, with P = 585 yr and a = 2.95 arcsec, parallax
0.0201, would give (M1+M2) = 9.24 Msun, which seems rather high to me for
two A3 main sequence stars, which ought to be around roughly 2.5 Msun
each.


So my guess, with this limited data, is that the periods in particular
are
wide of the mark (not surprising). Since 1955 there must be an extra
half-century of data, so I wonder if any improvement in the orbit is
possible.




I don't understand your comment. In orbital parlance, "a" is the semimajor
axis. Observed a for a visual binary is in units of arcsec. An orbit
publisher presents a, e, i, node, longitude of periastron, P, and T(peri).
I did this correctly as far as I can tell. I used the elements represented
in the table you linked to.

You are right - my mistake.

So, the masses do not make sense. And it cannot be mistake in distance
to both, because the masses are wrong in different directions. The
supposed orbits are clearly wrong.

 




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