Dynamical parallax

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In astronomy, the distance to a visual binary star may be estimated from the masses of its two components, the size of their orbit, and the period of their orbit about one another. [1] A dynamical parallax is an (annual) parallax which is computed from such an estimated distance.

To calculate a dynamical parallax, the angular semi-major axis of the orbit of the stars is observed, as is their apparent brightness. By using Newton's generalisation of Kepler's Third Law, which states that the total mass of a binary system multiplied by the square of its orbital period is proportional to the cube of its semi-major axis, [2] together with the mass–luminosity relation, the distance to the binary star can then be determined. [3]

With this technique, the masses of the two stars in a binary system are estimated, usually as the mass of the Sun. Then, using Kepler's laws of celestial mechanics, the distance between the stars is calculated. Once this distance is found, their distance from the observer can be found via the arc subtended in the sky, giving a preliminary distance measurement. From this measurement and the apparent magnitudes of both stars, the luminosities can be found, and from the mass–luminosity relationship, the masses of each star. These masses are used to re-calculate the separation distance, and the process is repeated. The process is iterated many times, and accuracies within 5% can be achieved. [4]

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9 Puppis is a binary star system in the southern constellation of Puppis. It was originally designated 9 Argus, being part of the now defunct Argo Navis constellation. The system is faintly visible to the naked eye as a point of light with a combined apparent visual magnitude of 5.16. The magnitude difference between the two stars is 0.65. Parallax measurements yield a distance estimate to 9 Puppis of approximately 54 light years from the Sun, with the dynamic and trigonometric parallaxes for the system being in close agreement. It is drifting closer with a systemic radial velocity of –21 km/s. The motion of the system through space is predicted to bring it as close as 42.2 light-years in about 292,000 years.

References

  1. Patrick Moore (2002). Philip's Astronomy Encyclopedia (revised and expanded ed.). London: Philip's. p.  120. ISBN   0-540-07863-8.
  2. "dynamical parallax". Astronomy Knowledge Base. Archived from the original on 2006-07-05. Retrieved 2006-07-18.CS1 maint: discouraged parameter (link)
  3. The Mass–Luminosity Relation, University of Tennessee, Astronomy 162: Stars, Galaxies, and Cosmology, lecture notes. Accessed July 18, 2006.
  4. Mullaney, James (2005). Double and multiple stars and how to observe them . Springer. p.  27. ISBN   1-85233-751-6.