Unseen Astrometric Companions of Stars

The Gaia Mission and the Asteroids

“…Astrometric binaries are binary system for which both components are not observed separately (either the secondary is to faint to be detected in the instrument, or similarly it is too close to the bright primary), but instead one observes the photocentre of the system. This photocenter differs periodically from the centre of mass with an amplitude that depends on the mass ratio for the position of the barycenter, the brightness distribution and ratio for the position of the photocentre, and the inclination of the orbit [116,1]. What is observed is not the Keplerian orbit a but the photometric orbit α which are related by: f = α/a + β ; β = (1 + 10 0.4∆V )…”

In search of other planetary systems

“…Thus R increases with mass as M ~/3 until a maximum radius Rc is reached and degeneracy effects become important, whereupon R decreases with increasing mass as M 1/3. Zapolsky and Salpeter (1969) have attempted to determine Rc and the associated critical mass Mc for bodies of various compositions. Their results indicate that Mc ranges from 0.001 12M| for a pure helium body to 0.003 16Mo for a pure hydrogen body and to 0.005 89Mo for a pure iron body.…”

“…Two early analyses of the Sproul data have been given by van de Kamp (1963van de Kamp ( , 1969. The former showing that a single companion of mass comparable to the mass of Jupiter revolves about Barnard's star in an eccentric orbit (e = 0.6) with an orbital period of 24 yr. Van de Kamp's (1969) analysis showed that the Sproul data were equally consistent with the interpretation that the wobble in the motion of Barnard's star is due to two Jovian mass dark companions with orbits that are circular and coplanar, and with orbital periods of 12 yr and 24 yr. Two points should be made regarding the Sproul data shown in Figure 2. First, they reveal very little perturbation in the y-coordinate (Decl.…”

“…We will return to these two points later. The conditions of circular and coplanar orbits cited in van de Kamp's (1969) analysis were not derived from the data, but rather were input assumptions to the data analysis. Two of the key papers involving the controversial aspects of the Barnard's star story appeared in 1973, the first authored by Hershey and the second by Gatewood and Eichhorn.…”

“…The Gatewood-Eichhorn study clearly does not confirm the Sproul data, and if correct would vitiate previous interpretations concerning the nature and perhaps existence of any dark companion(s) to Barnard's star. In an attempt to address the documented discontinuities in the Sproul data, van de Kamp (1975) from the years . These data were also reduced using an improved plate measuring machine.…”