1. Unit 10: Measuring the Properties of Stars
Mr. Ross Brown
Brooklyn School for Law and Technology

2. In this unit we will learn about:
How we measure stars’ distances using parallax
Why a star’s color indicates temperature & how to use Wien’s law to determine temperature
The difference between luminosity and brightness
How we can measure radius using temperature
The magnitude system of star brightness
Stellar spectra and how it indicates surface temperature
Luminosity classes
How we estimate stellar masses
The H-R diagram for inferring a star’s size and evolutionary state

3. How do we measure a star’s distance
7 March 2016
Do now: Why is it important to know a star’s distance from Earth? What other things can we calculate if we know the distance?

4. How do we measure a star’s distance
For nearby stars….
Triangulation
Lay out a right triangle, whose one side we know

5. How do we measure a star’s distance
Parallax
Method of triangulation that uses an apparent change in an object’s position as the observer’s position changes.

6. How do we measure a star’s distance
Parallax is small across such large distances. Rather than measure it in degrees, we measure it in fractions of degrees called “arc seconds” (1/3600 of a degree, 1/60 of an arc minute)

7. Homework #17
7 March 2016
How is a parsec defined? How big is a parsec compared to a light year?

8. How do we measure a star’s distance
We define a parallax (p) as ½ the angle by which it appears to shift. From this, we measure a star’s distance (d) as 1/p where p is in arc seconds and d is parsecs.
dpc=1/parc seconds
One parsecs = 3.26 light-years (3.09*1013 km)

9. How do we use a star’s light to learn about its properties?
14 March 2016 (Happy Pi Day!)
Do now: How can we tell how hot something is without using a thermometer or touching it?

10. How do we use a star’s light to learn about its properties?
Temperature
Stars are VERY hot
Hotter  blue, cooler  red

11. How do we use a star’s light to learn about its properties?
Using color more precisely
Wien’s Law: longer wavelength = cooler temperature

12. How do we use a star’s light to learn about its properties?
Luminosity: the amount of energy an object radiates
Lightbulb = watts
Sun = 4* 1026 watts
Luminosity measures how fast an object consumes its fuel

13. How do we use a star’s light to learn about its properties?
Luminosity measured via inverse-square law
Its distance and apparent brightness

14. How do we use a star’s light to learn about its properties?
Radius
If two stars have the same temperature but one is more luminous, the more-luminous star must have a larger surface area, thus a larger radius

15. How do we use a star’s light to learn about its properties?
Stefan-Boltzmann Law
If two stars have the same size but the surface of one is hotter, the hotter star will have greater luminosity

16. In what other ways can we measure a star’s properties?
15 March 2016 (Beware the Ides of March!)
Do now:
Which star is cooler and many
times brighter than Earth’s Sun?
a) Barnard’s Star b) Betelgeuse
c) Rigel d) Sirius

17. In what other ways can we measure a star’s properties?
Direct measurement of radius
(Yesterday we used luminosity and Stefan-Boltzmann Law to arrive at radius)
We can be more precise by using Angular Size

18. In what other ways can we measure a star’s properties?
Challenges to using angular size
Due to distance, fuzzy images, even with telescopes
Large ground-based telescopes get better images, but the atmosphere blurs them some
Computer can de-blur it a little

19. In what other ways can we measure a star’s properties?
We need a HUGE telescope
Or TWO telescopes, far apart, combined with computers

20. In what other ways can we measure a star’s properties?
Star radii differ greatly
Most are roughly the size of our Sun
Some, like Betelgeuse, are hundreds of times larger. These are Giants
Smaller stars, including our Sun, are Dwarfs, or Dwarves

21. In what other ways can we measure a star’s properties?
The Magnitude System of measuring brightness
150 BCE, Greek astronomer Hipparchus
Brightest is magnitude 1, dimmest is magnitude 6

22. In what other ways can we measure a star’s properties?
Is the Magnitude System the best system?
Apparent magnitude is a function of luminosity and distance
The scale is “backward,” with the lowest number representing the brightest stars
Magnitude differences represent ratios
Each magnitude represents a factor of 2.512

23. Homework #18
15 March 2016
What is the H-R Diagram? What are its axes?

24. How can we differentiate between classes of stars?
16 March 2016
Do now: What are dimensions across which we can differentiate one star from another?

25. How can we differentiate between classes of stars?
The Hertzsprung-Russell Diagram (H-R)
1912
If we plot stars according to luminosity and temperature, the follow a smooth curve

26. How can we differentiate between classes of stars?
The H-R Diagram
Bright stars on top, dim on bottom
Hot stars on left, cool on right
Blue on left, red on right
Temperature-wise, this is opposite other graphs
The curve on which most stars (90%) are depicted is the Main Sequence

27. How can we differentiate between classes of stars?

28. How can we differentiate between classes of stars?

29. How can we differentiate between classes of stars?
17 March 2016
Do now: On what factors does the luminosity of a star depend?

30. How can we differentiate between classes of stars?
Luminosity depends on a star’s surface area and temperature
If stars are the same temperature and one is brighter, it must have a larger radius
This is a Giant
Cool giants are Red Giants
Hot stars that are dim must have smaller radii
Dwarfs
If it’s hot yet dim, White Dwarf

31. How can we differentiate between classes of stars?
What can we surmise about mass and density and luminosity?
The Mass-Luminosity Relation
Larger mass = greater luminosity

32. How can we differentiate between classes of stars?
Luminosity Classes

33. How can we differentiate between classes of stars?
18 March 2016
Do now: What are the various methods we use for determining stellar quantities?

34. How can we differentiate between classes of stars?
Methods of determining stellar quantities
Distance
Temperature
Luminosity
Composition
Radius
Mass
Radial Velocity

35. How can we differentiate between classes of stars?
The Method of Standard Candles
Think about oncoming headlights as you drive

36. How can we differentiate between classes of stars?
Method of Standard Candles
If we know luminosity and brightness, we can calculate distance

37. How can we differentiate between classes of stars?