Stars fascinate us, but how do we measure their vast distances? Astronomers use clever techniques like parallax, which measures a star's apparent shift as Earth orbits the Sun. This method works best for nearby stars, giving us a cosmic yardstick.

For faraway stars, we need space telescopes and indirect methods. These include spectroscopic parallax and main-sequence fitting, which use a star's brightness and color to estimate its distance. Understanding these techniques helps us map our galactic neighborhood and beyond.

Measuring Stellar Distances

Triangulation for stellar distances

• Parallax measures the apparent shift in position of a nearby star relative to more distant background stars caused by Earth's orbit around the Sun (Proxima Centauri)
• Larger parallax angle indicates a closer star since the apparent shift is more noticeable for nearer objects (Alpha Centauri vs Betelgeuse)
• Parallax angle ($p$) is measured in arcseconds and relates to the distance ($d$) to the star in parsecs (pc) by the formula $p = 1/d$
• Parsec (pc) is a unit of distance equal to approximately 3.26 light-years, defined as the distance at which a star has a parallax angle of 1 arcsecond (distance to Sirius)

Ground vs space-based distance methods

• Ground-based methods are limited by Earth's atmosphere, which causes turbulence and distortion that affect the accuracy of measurements and can only determine distances up to about 100 parsecs (Barnard's Star)
• Space-based methods utilize telescopes in space, such as Hipparcos and Gaia, which are above Earth's atmosphere and provide clearer observations to measure parallax angles with higher precision for stars thousands of parsecs away (Pleiades star cluster)

Strategies for nearby star measurements

• Parallax method is the most direct and reliable for nearby stars but limited to those within a few hundred parsecs (61 Cygni)
• Spectroscopic parallax estimates distance using a star's spectrum and apparent brightness, requiring knowledge of its intrinsic luminosity (Vega)
• Main-sequence fitting compares a star cluster's color-magnitude diagram to a standard diagram and estimates distance by shifting the cluster's diagram to match (Hyades cluster)
• Statistical parallax uses the motion of groups of stars to estimate their average distance, assuming they have similar velocities and are roughly the same distance away (Ursa Major Moving Group)

Stellar Properties and Classification

• Luminosity is the total amount of energy emitted by a star per unit time
• Apparent magnitude is how bright a star appears from Earth, while absolute magnitude is how bright it would appear from a standard distance of 10 parsecs
• Stellar classification organizes stars based on their spectral characteristics and temperature
• Stellar spectra provide information about a star's composition, temperature, and other physical properties
• Stellar evolution describes how stars change over time, from formation to their final stages