Inversion Formula for Determining the Parameters of an Astrometric Binary

@article{Asada2004InversionFF,
  title={Inversion Formula for Determining the Parameters of an Astrometric Binary},
  author={Hideki Asada and Toshio Akasaka and Masumi Kasai},
  journal={Publications of the Astronomical Society of Japan},
  year={2004},
  volume={56}
}
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental owing to the Kepler's equation. Such a common sense, however, is not true; we discover an analytic inversion formula, in which the original orbital parameters are expressed as elementary functions of the observable quantities such as the location of four… 

Figures from this paper

An exact method for orbit determinations of an astrometric binary
Here we present an exact method for orbit determinations of an astrometric binary for which the primary star can be seen but the companion is unseen like a black hole or an extra-solar planet. Since
Improving the Moment Approach for Astrometric Binaries: Possible Application to Cygnus X-1
A moment approach for orbit determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). With
Note on an Inversion Formula to Determine Binary Elements by Astrometry
Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004, PASJ, 56, L35), and therefore require neither iterative nor
Moment Approach to Determining the Orbital Elements of an Astrometric Binary with a Low Signal-to-Noise Ratio
A moment approach to the orbit determination of an astrometric binary with a low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with
Prospects of Application of Semi-Definite Programming to Determine Orbital Parameters of the Binary Systems Observed at Bosscha Observatory
Most methods of orbit determination are often difficult for numerical implementations since they are developed before the computer era. The recently developed mathematical technique of semi-definite
Simplified Solution to Determination of a Binary Orbit
We present a simplified solution to the orbit determination of a binary system from astrometric observations. An exact solution was previously found by Asada and coworkers by assuming no
Uncovering the identities of compact objects in high-mass X-ray binaries and gamma-ray binaries by astrometric measurements
We develop a method for identifying a compact object in binary systems with astrometric measurements and apply it to some binaries. Compact objects in some high-mass X-ray binaries and gamma-ray
Post-Newtonian Equilibrium Solutions to the Three-Body Problem in General Relativity
Recently, many projects of the second generation gravitational wave detectors including Advanced LIGO (USA), Advanced VIRGO (France and Italy), and KAGRA (Japan) and of the highprecision astrometric
An exact solution to determination of an open orbit
We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion. In solving this problem, we extend the method employed by Asada,

References

SHOWING 1-9 OF 9 REFERENCES
Visual Binary Orbit Calculation with the Help of a PC: One Possible approach
TLDR
A computer program, based on the original method (Olevid 1989), is interactive which means that the calcu lator of the orbit makes the final decision about the choice of the best orbit.
Orbits of 10 interferometric binary systems calculated by using the improved Koval'skij method
Orbital elements are presented of 10 interferometric binary systems with no previous orbit determination: WDS 07143-2621 (FIN 323), WDS 12064-6543 (FIN 367Aa), WDS 12446-5717 (FIN 65), WDS 13320-6519
An improved algorithm for the determination of the system parameters of a visual binary
Une methode est presentee pour la determination des parametres du systeme des binaires visuelles a partir des coordonnees relatives observees, sur la base d'un algorithme propose anterieurement par
Fundamentals of celestial mechanics
Orbital Motion (Bristol: Institute of Physics Publishing
  • Fundamentals of Celestial Mechanics (VA: William-Bell) Roy A. E
  • 1988
Classical Mechanics (MA: Addison-Wesley
  • Olevic D., Cvetkovic Z. 2004,
  • 1980
Fundamentals of Celestial Mechanics Orbital Motion (Bristol: Institute of Physics Publishing) Catovic Z. and Olevic D
  • IAU Colloquim 135, ASP Conference Series
Classical Mechanics (MA: Addison-Wesley) Olevic D., Cvetkovic Z
  • Classical Mechanics (MA: Addison-Wesley) Olevic D., Cvetkovic Z
  • 1980