Final answer:
The distance to a star with a parallax of 25.0 milliarc-seconds is 130.4 light years. This is calculated by first converting the milliarc-seconds to arc-seconds, then using the reciprocal to find the distance in parsecs, and finally converting parsecs to light years using the conversion factor.
Step-by-step explanation:
The question is asking how to determine the distance to a star in light years given its parallax angle in milliarc-seconds. The key to solving this problem is understanding the relationship between parallax and distance, and the conversion between parsecs and light years. Using the given parallax angle of 25.0 milliarc-seconds, we first convert it to arc-seconds by dividing by 1000 (for 1000 milliarc-seconds = 1.0 arc-second). Thus, we get a parallax of 0.025 arc-seconds.
According to the formula, the distance (D) to a star in parsecs is the reciprocal of its parallax (p) in arc-seconds, which gives us D = 1/p. Using the parallax of 0.025 arc-seconds, the distance to the star would be D = 1/0.025 parsecs, which is 40 parsecs. We can then convert this distance to light years using the conversion factor that 1 parsec equals 3.26 light years. Therefore, the distance to the star is 40 parsecs × 3.26 light-years/parsec, which equals 130.4 light years.