Final answer:
Binary stars detectable by direct observation of their proper motion are called visual binaries. Measurements to determine whether two stars form a visual binary include monitoring their changes in position relative to each other and checking for periodic changes in radial velocities. An example of a visual binary is Castor in the constellation of Gemini.
Step-by-step explanation:
Binary stars detectable by direct observation of the proper motion are called visual binaries. To determine if two stars observed close together in the sky form a visual binary, one would need to make several measurements using a good observatory. You would examine the changes in position relative to each other over time to assess if they are gravitationally bound and orbiting each other - this change is known as proper motion. Additionally, you would check for periodic changes in their radial velocities, which can be indicative of orbital motion. This method is used in identifying spectroscopic binaries. However, in this case, you'd be focusing on whether the stars can be visually resolved through a telescope as a visual binary.
For stars that are too close to resolve individually, but which reveal their binary nature through periodic variations in radial velocity due to orbital motion, the term spectroscopic binary is used. Notably, every binary star has the potential to eclipse if the orbital plane is aligned with our line of sight, but few are oriented in such a way to be observed as eclipsing binaries from Earth. An example of a visual binary is Castor in the constellation Gemini, where one component orbits the other. A historical record of its proper motion provided the first evidence of gravitational interactions outside the solar system. The detection of binary stars plays a crucial role in astronomical research and our understanding of stellar evolution.