Option D1 & D2: Measuring Stellar Distances https://www.youtube.com/watch?v=-QGU0m7T9Q4

Measuring Stellar Distances Various methods are used to determine the distances to stars and galaxies depending upon the distances involved In order of increasing distances, the four methods are Stellar Parallax* Absolute and Apparent Magnitudes Spectroscopic Parallax Cepheid Variables*

Parallax method As you move from one position to the other, objects change their relative position Near objects appear to move as compared to far objects Objects that are very far do not appear to move at all This apparent movement is known as PARALLAX and the effect can be used to measure the distance to some of the stars in our galaxy Stellar parallax is the apparent shifting of a star against a background of very distant fixed stars, when viewed from two different points

Parallax method Distance of the star from the Earth can be found by measuring the parallax angle and using trig Angle will be extremely small and is measured in seconds or arc-seconds One degree is equal to sixty minutes of arc and one minute is equal to sixty seconds of arc Word parsec comes from one parallax second and is abbreviated pc Parsec is defined as the distance from Earth of a star that has a parallax angle of one second (1pc = 3.26 ly)

Parallax method

Parallax method The two pictures taken at different times in Earth’s orbit are superimposed The background stars are used to match up the pictures The nearby star “moves” across the pictures Three superimposed pictures are shown:

Parallax method Using the small angle approximation and the correct units: d is distance from Earth to star in parsec p is parallax angle in arc-second EX: The nearest star to Earth is Alpha Centauri, which is at a distance of 4.37 ly. Calculate the parallax angle that must be measured to determine this.

Parallax method The more distant a star is from Earth, the smaller its parallax angle becomes Using photographic techniques with the most accurate equipment, the smallest parallax angle that can be currently measured is about 0.01 arc-second or about 100pc The limit on our ability to measure small angles means that the stellar parallax method can only be used to measure the distances of the closest stars, less than a few hundred parsecs form Earth

Cepheid Variables Quite rare but are very useful as there is link between the period of brightness variation and their average luminosity Astronomers can use them to help calculate the distance to the galaxies they are in Known as “standard candles”

Cepheid Variables Cepheid variables are stars of variable luminosity Luminosity increases sharply and falls off gently with a well-defined period Period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity The luminosity of Cepheid stars range from 103 to 104 times that of the Sun

Cepheid Variables The process of estimating the distance to a galaxy (in which the individual stars can be imagined) might be as follows: Locate a Cepheid variable in the galaxy Measure variation in brightness over a given period of time Use the luminosity-period relationship for Cepheids to estimate the average luminosity Use the average luminosity, the average brightness and the inverse square law to estimate the distance to the star EX: Pg. 654