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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? |
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"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) |
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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. |
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"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) |
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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. |
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"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) |
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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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