Final answer:
The greatest Doppler shift is observed from Star B, and the smallest from Star A. Parallax measures distances to stars by their apparent positional changes. Different temperatures of objects correspond to different types of electromagnetic radiation for observation.
Step-by-step explanation:
The Doppler effect is produced only by a motion toward or away from the observer, which is known as radial velocity. Among the three stars mentioned, the observer will observe the greatest Doppler shift from Star B, which is moving directly away from Earth. Conversely, the smallest Doppler shift will be observed from Star A, which is moving across our line of sight, and thus has no radial component of motion concerning the observer. Star C, with its movement at a 30° angle to the line of sight, will have a Doppler shift that is less than that of Star B but greater than that of Star A.
Parallax is a technique used to measure the distances to the nearest stars and is based on the apparent shift in position of a star when viewed from different points along Earth's orbit. For a star that is 4.0 ly directly above the Sun, the angles ₁ and 2 would be the angles subtended by the parallax motion relative to the plane of the Earth's orbit.
Concerning the type of electromagnetic radiation used to observe various astronomical objects: A star with a temperature of 5800 K, like the Sun, is best observed in the visible spectrum. A gas heated to a temperature of one million K would emit primarily in the X-ray spectrum. For observing a person on a night, infrared radiation would be most appropriate.