1. ASTR 1020 – January 28 Second Homework Due Thursday (Feb 9)
Next Observatory opportunity tomorrow (Feb 7pm
Planetarium on Feb 14
First Exam Feb 21
Today: Stars
Website

2. Stars are grouped in Galaxies
Sun and all the stars we see are part of the Milky Way Galaxy
We all orbit a common center
Sun is 3x1020m from center of MW
You are here
Each star orbits
center
Disk Stability Again

3. Distances to the Stars
Closest Star, Proxima Centauri is 4.2x1016m away.
(Alpha Cen ~4.3x1016m)
Need a more convenient unit

4. The Light Year
Light Travels at 300,000km/s (186,000miles/s = 3x108m/s)
That’s one foot per nanosecond
One Year is 3.15x107 seconds long
In one year light travels 3.15x107x3x108 = 1016m
This is the definition of a light year. Prox Cen is at 4ly.

5. Question
There’s a big black hole in the Center of the Milky Way at a distance of 3x1020m. How long does it take for its light to reach us?
A) 3years
B) 30 years
C) 300 years
D) 3000 years
E) 30,000 years

6. Answer
There’s a big black hole in the Center of the Milky Way at a distance of 3x1020m. How long does it take for its light to reach us?
A) 3years
B) 30 years
C) 300 years
D) 3000 years
E) 30,000 years

7. The Parsec
Astronomers use the parsec as a measure of distance
1pc  3ly
1pc = 3x1016m
Origin of parsec comes from method of measuring distance

8. Each Star Orbits the Center

9. How Long does that Take?
Takes about a hundred million years to circumnavigate the galaxy

10. Star Names Arabic Names Constellations
Antares, Capella, Mira, etc.
Constellations
a Orionis, b Cygni, … then 49 Ori, 50 Ori, etc.
Catalogues HD80591, SAO , etc
RA and Dec – just position in the sky

11. Proper Motion 2003 All stars move Nearby stars move faster
Appear to move against fixed field
Can Take Many Years
Use Old Photographic Plates
1900

12. Parallax
I year cycle

13. The Parsec 1 parsec 360 degrees in circle 60 arcminutes per degree
1AU
1 arcsecond
360 degrees in circle
60 arcminutes per degree
60 arcseconds per arcminute
200,000AU = 1 parsec = 3x1016m
parsec parallax second

14. Question
Based on the definition of a parsec , if star A has a parallax of 0.5 arcseconds and star B has a parallax of 0.75 arcseconds which one is farther from the Earth?
A. Star B is farther away because it has a higher parallax
B. Star A is farther away because it has a lower parallax
C. All stars are the same distance away from the Earth
D. It is impossible to tell from this information.

15. Answer
Based on the definition of a parsec , if star A has a parallax of 0.5 arcseconds and star B has a parallax of 0.75 arcseconds which one is farther from the Earth?
A. Star B is farther away because it has a higher parallax
B. Star A is farther away because it has a lower parallax
C. All stars are the same distance away from the Earth
D. It is impossible to tell from this information.

16. Measure Parallax
distance to a star in parsecs = 1/(parallax in arcseconds)
e.g. measure .04” parallax, then distance is 25pc
Measuring Parallax was first successful way to measure
distances to stars after centuries of trying
Took high speed photography in 1890’s to do it.

17. Question
The parallax of an observed star is 0.1 arcseconds, how many light years is it away from Earth?
a. 1 light year
b. 3 light years
c. 10 light years
d. 30 light years
e. 75 light years

18. Question
The parallax of an observed star is 0.1 arcseconds, how many light years is it away from Earth?
a. 1 light year
b. 3 light years
c. 10 light years
d. 30 light years (10parsecs)
e. 75 light years

19. Brightness Around the sky stars vary in brightness and in color.
Brightness is the result of two factors
1. Intrinsic Luminosity
2. Distance
Each Sphere has
area A=4d2 d
Brightness is
Star Emits N photons
per second
photons/m2/s

20. Brightness (2) Brightness e.g. 10-12 Watts/m2
Simple and easy to understand
If your eye is 10-4m2, then it collects 10-16W
4 stars at 10-12W/m2 together have 4x10-12W/m2
But this would be too easy for astronomers.
We use a brightness system invented by Ptolemy in the 400’s

21. Question
If the distance between Earth and the Sun were cut in half, how much brighter would the sun appear in our sky?
a. 2x brighter
b. 4x brighter
c. 8x brighter
d. 16x brighter

22. Answer
If the distance between Earth and the Sun were cut in half, how much brighter would the sun appear in our sky?
a. 2x brighter
b. 4x brighter
c. 8x brighter
d. 16x brighter
Brightness is a function of the inverse square of distance, so if distance was cut by half it would get brighter by 4x=1/(.5)2

23. The Magnitude System Ptolemy Broke Stars into 5 magnitude groups
m=1 the brightest, m=5 the faintest
In 1700’s it was found this was a logarithmic scale, as that is how the naked eye responds. Also, faintest were about 100x fainter than
brightest.
Break the factor of 100 into 5 equal factors:
Start with Vega m=1
Polaris 2.51x fainter m=2
2.5x fainter than Polaris m=3
2.5x fainter than that m=4
etc

24. Magnitudes (2) Every 5 magnitudes is a factor of 100
m=5 is 100 times fainter than m=0
m=10 is 100x100 =10,000 times fainter than m=0
m=15 is (100)3 = 1million times fainter than m=0
Sun m=-26.5
Full Moon m=-13
Venus m=-4
Sirius m=-1.5
Vega m=1
Polaris m=2
Faintest Visible m=6
Faintest Detected m=28
Works only in the visible.
Really inconvenient in modern astronomy because we
observe across the spectrum from radio to gamma rays.

25. Absolute Magnitude The magnitude a star would have were it at 10pc
We see a star of magnitude m=10 at 100 pc.
What would be its magnitude (M) if it were at 10 pc instead of 100pc?
At 10 times closer the star would be 100x brighter = 5 magnitudes
M = 10-5 = 5

26. Question
A 5 magnitude difference means a factor of 100 in flux. By what factor do the fluxes differ between two stars of 20 magnitudes difference?
2.51 20
400
10,000
100,000,000

27. Answer
5magnitudes difference is a factor of 100. By what factor do the fluxes differ between two stars of 20 magnitudes difference
2.51 20
400
10,000
100,000,000
20 magnitudes is four factors of 102, which is 108

28. Nature of Light Light is a flux of particles called photons
Each photon is both a particle and a wave (a packet of waves)
250 years after Newton we still don’t understand it
Electromagnetic Theory (Maxwell’s Equations) 1860’s
Quantum Electrodynamics 1948 Feynman
Each photon has:
direction
wavelength
polarization

29. Light Waves l lambda is lower case Greek L stands for length
Each photon is a sine wave moving at the speed of light
Wavelength is usually measure in Angstroms
1Å = 10-8cm =10-10m
about the diameter of an atom.
And 10Å = 1nm
Electric and Magnetic
Fields Sloshing Back
And Forth

30. Color RED 7000Å YELLOW 5500Å VIOLET 4000Å
Wavelength Determines Color of Light
Color is the eye’s response to different wavelengths
Color is a physiological effect
A photon can have any wavelength
RED 7000Å
YELLOW 5500Å
VIOLET 4000Å

31. Electromagnetic Spectrum
visible is tiny chunk of em spectrum

32. Parts of EM Spectrum Radio l > 1mm (107A)
Infrared 1mm> l > 10000A
Visible 10,000A > l > 3500A
Ultraviolet 3500A > l > 100A
X-ray 100A > l > 0.1A
Gamma-ray 0.1A > l

33. Question
What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above

34. Answer
What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above Answer: C

35. Speed of Light Speed of Light c = 3x108m/s That’s a very odd statement
2 cars at 65mph
1 car at 130mph
Cover same distance in same amount of time
The Relative speeds are the same

36. Relativity NO!!! .8c .8c Clearly Approaching each other at 1.6c
v always less than c
if velocities << c, then v=v1+v2
per Einstein
(Concept of time and space changes)

37. Frequency l l l l Moves l during each cycle
Frequency is the number of cycles per second, n
Greek “nu”
Moves distance l for each of n cycles each second

38. Frequency (2)
300MHz = 1m wavelength
Yellow Light = 600 trillion Hertz

39. Question An x-ray has a wavelength of 100Å
(10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz)
A. 3x1016
B. 1.5x1016
C. 3x1013
D. 1.5x1013

40. Answer
An x-ray has a wavelength of 100Å (10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz)
A. 3x1016
B. 1.5x1016
C. 3x1013
D. 1.5x1013
Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz

41. Energy of a Photon h = 6.63x10-34 J s Planck’s Constant
energy of yellow photon
Sunlight is 104 W/m2
Outside we have 1023 photons/m2/s hit us

42. Question
How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light).
A. Ten times as powerful.
B. A hundred times more powerful.
C. A thousand times more powerful.
D. 1x1012 (a trillion) times more powerful.
E. 1x1015 (a quadrillion) times more powerful.

43. Answer
How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light).
A. Ten times as powerful.
B. A hundred times more powerful.
C. A thousand times more powerful.
D. 1x1012 (a trillion) times more powerful.
E. 1x1015 (a quadrillion) times more powerful.
Answer: C. 10,000nm/10nm = 1000

44. Spectroscopy
Spectrum is plot of number of photons as a function of wavelength
Tells us huge amounts about nature of object emitting light.

45. Thermal Radiation Planck’s Law
Temperature Determines Where Spectrum Peaks
Position of Peak Determines Color

46. Blue is Hotter than Red Optically Thick, But hot
Sun almost “white hot”
Burner “red hot”
Desk “black hot”
Ice Cube “black hot”

47. Question
A star with a temperature of 100,000K has what color to the naked eye?
White
Yellow
Orange
Red

48. Wien’s Law Å As T rises, l drops Bluer with temperature (T in Kelvin)
300K 100,000A Earth
Sun
X-ray source

49. Question
How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K)
A. Twice as long
B. Half as long
C. Four times as long
D. A fourth as long

50. Answer
How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K)
A. Twice as long
B. Half as long
C. Four times as long
D. A fourth as long
Answer: B. Since peak wavelength is a function of the inverse of temperature, doubling the temp of a star would cause it's peak wavelength to cut in half.

51. Stefan-Boltzman Law s = 5.67x10-8 W/m2/K4 A is area in m2 T in Kelvins
Example: The Sun
L = 5.7x10-8 x 4 x 3.14 x (7x108m)2 x (5500K)4 = 4 x 1026 W
4x1026 Watts = 100 billion billion MegaWatts!!

52. Question
If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8 16 32

53. Answer
If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8
16 = 24 32

54. Emission Lines Electron Drops Energy Levels of H Photon Escapes
Can Only Happen Between
Certain Pre-determined orbitals
Spectrum of Hydrogen
Each Element Has Different Orbitals
So Each Element Has Different Lines

55. Absorption Lines Light moving through cold
gas can have photons removed.
Creates dark wavelengths
called absorption lines

56. Question
A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only
B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

57. Answer
A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only
B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

58. Stars Come in Different Colors