Let's consider the art of Astrometry. This is what the SIM mission is all about. Astrometry is the method by which one determines the positions of stars, and other celestial objects, in the sky. It is an ancient practice. The most famous of the ancients who devised star maps is the Greek astronomer Hipparchus who lived in the 2nd century B.C.
However, stars are not stationary. They "drift" through space, or more properly, are in orbit about the center of the Milky Way galaxy. Modern astrometry utilizes the measurement of stars' positions as they change with time. In other words, modern astrometry produces a very accurate record of a star's motion through space. If a star is a solitary object, with no planets or sibling stars, then it should be traveling in an absolutely straight line. However, if the star has companions, then their mass will cause the path of the star to follow a curved path. The larger the mass of the companion, and the closer it is to the central star, the more pronounced the curvature.
Let's look at one famous example of this technique, the discovery of Sirius B, the White Dwarf star that orbits around Sirius A. While we can easily see Sirius A on any winter's night, Sirius B, while massive, is very dense and is invisible to the naked eye. In 1844, Friedrich Bessel noticed that the path of Sirius deviated from a perfect straight line. He attributed this to the presence of an unseen companion. The existence of Sirius B was confirmed about 20 years later when it was detected visually.
The diagram below shows the orbits of Sirius And B, as well as the curved paths of both stars. One can imagine a straight line passing between those curved paths. That straight line is the path of the center of gravity, or barycenter, of the system.
SIM uses the technique of interferometry to determine the positions of stars with unprecedented accuracy.
The image above shows how the Sun moves around its barycenter, or center of gravity. One can see how complicated would be the curved path of our Sun through space.