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If the companion is sufficiently massive to cause an observable shift in position of the star, then its presence can be deduced. From precise Astrometric measurements of the movement of the visible star over a sufficiently long period of time, information about the mass of the companion and its orbital period can be determined.


MATHEMATICAL FORMULATION


Even though the companion is invisible, the characteristics of the system can be determined from the observations using Kepler 's laws. The following equation gives the relation between the masses and the amount of motion observed:

:(m_1 + m_2) \cdot \left( rac{m_2}{m_1 + m_2} ight) ^3 = rac{a_1^3}{p^3 \cdot P^2}

where:
  • m1 = mass of the star in Solar Mass es.

  • m2 = mass of the hidden companion in solar masses.

  • a1 = Semi-major Axis of the star's orbit about the mass-center in Seconds Of Arc .

  • p = Parallax of the binary system in seconds of arc.

  • P = orbital period in Year s.



METHODS OF OBSERVATION


In Friedrich Bessel used observations with a Meridian circle Telescope to infer that Sirius has a hidden companion, due to the motions of the star. The mass of the hidden companion was determined using the formula above. After improved telescopes became available, Alvan G. Clark was able to directly observe the companion star 'Sirius B' in 1862 . This companion was later determined to be a White Dwarf by Kurt F. Bottlinger in 1923 . Similar means were used to infer the presence of a companion orbiting Procyon .

This method of detecting binaries is also used to locate Extrasolar Planet s orbiting a star. However the requirements to perform this measurement are very exacting, due to the great difference in the mass ratio, and the typically long period of the planet's orbit.

Detection of position shifts of a star is a very exacting science, and it is difficult to achieve the necessary precision. Various facto. Space telescopes can avoid the blurring effect of the Earth's Atmosphere , resulting in more precise resolution. In 2010 the ESA has proposed to launch the Gaia Probe , the successor to the Hipparcos spacecraft. Gaia will be placed at the Earth L2 Lagrange Point ,