1. Option D1 & D2: Measuring Stellar Distances

2. 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*

3. 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

4. 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)

6. Parallax method

7. 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:

8. 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.

9. 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

10. 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”

11. 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

14. 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