Astrometric Detection of Planets

A planet and star will orbit about their common center of mass. Because the mass of the planet is so small compared to the mass of the star, and the great distance to a typical nearby star, the reflex motion of the star is very small. Astrometry is the measurement of the angles between stars in the sky with very high precision. With sufficient accuracy, an astrometric instrument can measure the motion of a star caused by an orbiting planet.

While a Sun-Jupiter system at 10 parsec would have an astrometric signature of 1 mas p-p, most of the planets discovered to date have much smaller astrometric. The astrometric signature is fully determined by the mass of the star, the mass of the planet, the distance between the planet and the star, and the distance between the planet and our solar system. Below is a graph with planet mass on the Y axis and semi-major axis (orbital radius) on the X axis. The distance to the planetary system is assumed to be 10 parsec.The graph below shows the position of several planets that have been discovered with the radial velocity technique. The two slanted lines with 10, 50 microarcsec (uas) show the astrometric detection limits for astrometric instruments with 10 and 50 uas accuracy.