The distance to the nearest stars to Earth varies, but the closest star system to our solar system is the Alpha Centauri system. Alpha Centauri is a triple star system consisting of three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri.
Proxima Centauri, which is the closest individual star to us, is located about 4.24 light-years away from Earth. Alpha Centauri A and Alpha Centauri B are slightly farther at a distance of about 4.37 light-years. These distances are approximate and can vary slightly due to the stars' motion through space.
Now, as for how we determine the distances to these stars in light-years, astronomers use a method called parallax. Parallax is a technique that takes advantage of the Earth's motion around the Sun. When observing a star from two different points in Earth's orbit, the star appears to shift its position against the background of more distant stars.
By measuring this apparent shift in position over a six-month period, astronomers can calculate the angle of the parallax. This angle, combined with the known distance between the two observing points on Earth's orbit, allows astronomers to determine the distance to the star using trigonometry. The unit of distance most commonly used in astronomy for such vast distances is the light-year, which is defined as the distance light travels in one year (approximately 9.46 trillion kilometers or 5.88 trillion miles).
In summary, the nearest stars to Earth, such as those in the Alpha Centauri system, are several light-years away, and we determine their distances using the parallax method.