Ground Based Limits to Astrometry

Conventional ground based telescopes with ~ 1 meter apertures measuring stars over a ~0.5 degree field of view are limited by atmospheric turbulence to a few milliarcsec(mas) accuracy for a ~ 1hr measurements. Atmospheric turbulence will cause the position of a star to fluctuate with time. However if two stars are sufficiently close together in the sky, the motion of the two stars will be almost identical because the light from the two stars traverse almost identical paths through the atmosphere.

For small telescopes (or interferometer) the amount of atmospheric inudced motion is independent of the size of the telescope. But when the size of the telescope or interferometer baseline grows to be larger than the separation of the two stellar beams at the top of the troposphere (~10km altitude) the behavior changes. For sufficiently large telescopes/interferometer, the angular motion of the stars becomes smaller for larger interferometer baselines.

As can be seen from the graph above, differential astrometric measurements with 10~30 uas are possible over a ~20 arcsec field of view with interferometers (or telescopes) ~ 100 meters in diameter at an excellent site like Mauna Kea. In early 1992 data was taken at the Mark III interferometer on Mt Wilson (show above) to validate the theoretical calculations. The Palomar Testbed is designed to observe two stars simultaneously to measure the angle between them with extremely high precision. But in addition to verifying the atmospheric limit for a 100m interferometer, there is an additional goal of identifying and removing instrumental errors as well. Lastly, the interferometer is to be used to conduct a modest survey of nearby stars, stars with known planets (from the radial velocity surveys) as well as new stars.

If one wishes to make measurements with significantly higher accuracy than 10 uas, the only solution is to go to space. The need to do this comes from the very small astrometric signatures of Earth like planets. While a Jupiter-Sun system has a signal of 1 mas, an Earth-Sun system has a very small 0.6 microarcsec signal. When an Earth-like planet is discovered, the only technique that can be used to unambiguously measure it's mass, is astrometry.