astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, the

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...

to a visual binary star may be estimated from the

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

es of its two components, the size of their

orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...

, and the period of their orbit about one another. A dynamical parallax is an (annual)

parallax Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects ...

which is computed from such an estimated distance. To calculate a dynamical parallax, the angular

semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...

of the orbit of the stars is observed, as is their

apparent brightness Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's lig ...

. By using Newton's generalisation of Kepler's Third Law, which states that the total mass of a binary system multiplied by the

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...

of its

orbital period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...

is proportional to the

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...

of its

, together with the

mass–luminosity relation In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. The relationship is represented by the equation: :\frac = \left(\frac\right)^a whe ...

, the distance to the binary star can then be determined.The Mass–Luminosity Relation
University of Tennessee, Astronomy 162: Stars, Galaxies, and Cosmology, lecture notes. Accessed July 18, 2006. 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 In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

, 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 magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...

s 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.

References

{{DEFAULTSORT:Dynamical Parallax - Astrometry

See also

References