TEST 1B MATERIAL – JANUARY 31, 2013
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Learning Objectives – Apparent Magnitudes (Sections 18.1.1 and 18.1.2)
Recognize the mathematical form of the inverse square law
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 𝐵𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 = 𝑑2
a. Calculate how much fainter or brighter a star would appear if its distance
changed; i.e., doubled or tripled, etc.
 Original Distance = 2 Feet, Original Brightness = 1/4
 Doubled Distance = 4 Feet, Doubled Brightness = 1/16
 Tripled Distance = 6 Feet, Tripled Brightness = 1/36
Describe the difference between intrinsic brightness and apparent brightness
 Intrinsic Brightness – The actual brightness of a star
 Apparent Brightness – How bright an object appears on Earth
a. How are they related to distance?
 Apparent brightness takes distance into account whereas intrinsic brightness
does not
List how many magnitude groups are visible to the naked eye
 Six
a. What is the faintest group visible?
 Six (m=6)
b. Given apparent magnitudes of two stars, identify which on is brighter or
fainter than the other
 M = 3.5 is fainter than M = 2.1
c. Explain how there came to be negative magnitudes
 Some objects are brighter than the first-magnitude stars on Hipparchus’ scale
Be able to calculate the brightness ratio of two stars given their apparent
magnitudes
 𝐵𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 = 2.512∆𝑚
 b1 = 2.5, b2 = 4, Δm = 1.5
 𝐵𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠 𝑅𝑎𝑡𝑖𝑜 = 2.5121.5 = 3.98
Learning Objectives – Brightness Transparency
Describe how the number of photons received by the eye relates to brightness
 Light is visualized as bundles of energy (photons)
 The more photons, the more energy and the brighter the star appears
List the four terms we use to describe brightness
 Intensity and Brightness (everyday meaning), Magnitude and Luminosity (special
meaning/technical terms)
Define energy flux
 The amount of energy passing through a surface each second
 Measured in joules/s/cm2 or watt/cm2
Distinguish between “magnitude difference” and “brightness factor”
 Magnitude Difference = Adding/Subtracting magnitudes
 Brightness Factor = Multiplying/Dividing magnitudes
9. If two stars differ by one magnitude, how many times brighter is the brighter of
the two?
 2.512 times brighter
Learning Objectives – Change in Magnitude Transparency
10. Calculate a difference in brightness if two stars differ in magnitude by more than
5
 M=7
 2.5127 = 630 OR (Δm=5) + (Δm=2) 100 x 6.3 = 630
Learning Objectives – Distance (Sections 18.2.1 and 21.1)
11. Define parsec, light-year, and parallax
 Parsec – A parallax of one second of arc, the fundamental unit of distance, 3.26 lightyears
 Light-year – How far light travels in one year, 9.4 x 1012 km
 Parallax – the angle sun/star/earth, measured in seconds of arc, when a star
appears to move relative to more distant/background stars
a. Which directly tells us travel times?
 Light-years
12. Demonstrate your understanding of the parallax distance technique by
calculating the distance to a star given its parallax in arc seconds
206265" 𝑥 1 𝐴𝑈
206265"
 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = (
) = ( 𝑝" ) 𝐴𝑈
𝑝"
13. Explain how astronomers measure parallax
Astronomers record a star’s position at least twice a year by taking photos
Using a filar micrometer on the eyepiece of the telescope, astronomers can measure
the distances between stars
a. How the distance depends on the value of the measured parallax angle
 See equation in objective #12
b. What is the critical factor that makes the measurement of parallax
possible?
 The base of the triangle (the distance between the sun and Earth) is constant
(1 AU)
14. Recognize the distance to the nearest star in…
a. AU’s
 267,900 AU
b. Light-years
 4.3 light-years
c. Parsecs
 1.3 PC
d. The numerical value of its measured parallax
 .77” or 1/4675 of a degree
15. List the maximum distance determinable with parallax measurements and
explain why a limit exists (related to objective #13)
As you extend the distance that the star is away from Earth, the parallax angle
becomes harder to measure
From Earth = 0.01”/326 light-years/100PC, From Space = 0.005”/650 lightyears/200 PC
Learning Objectives – Parallax Transparency
16. Explain how seconds of arc, minutes of arc, and degree are related
1 degree = 60 minutes of arc, 1 minute of arc = 60 seconds of arc
1 degree = 3600 seconds of arc
17. List the general limit to the size of parallax angles (fraction of a degree), the
largest ever recorded, and the smallest
General limit = 0.01” from earth, 0.005” from space
Largest ever recorded = 0.76” (Alpha Centauri)
Smallest ever recorded = ???
18. Explain how the thumb experiment describes parallax
When you switch the eye that you are looking with, your thumb appears to move in
comparison to the background objects just like stars appear to move compared to
more distant/background stars
19. Explain how the thumb experiment relates the parallax angle to distance
The farther away that your thumb is away from your face, the less it appears to
move compared to the background
20. Define the astronomical unit (AU)
The distance between the Earth and the Sun
21. Explain how light-year is both a time and a distance
The distance that light travels in a year
22. Convert light-years to parsecs and vice versa
1 parsec = 3.26 light-years
23. Calculate the distance in parsecs given a parallax in seconds of arc
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𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑝" 𝑝𝑎𝑟𝑠𝑒𝑐𝑠
Learning Objectives – Radiation Laws (Section 18.3)
24. Identify the color of a star (reddish or bluish) given the wavelength of their peak
intensities.
Blue – about 3500 A, Yellow – about 6000 A, Red – about 7500 A
25. Describe Planck curves
the way that astronomers represent the supply of photons emitted by a star
throughout the electromagnetic spectrum
a. Explain what they represent – what is it the temperature of?
 Represent the supply of photons emitted, the temperature of the star
26. Describe what properties of Planck curves indicate temperature
The energy flux depends on the temperature
A hotter star has a higher energy flux because it emits more energy at every
wavelength than a cooler star
27. Determine the relative temperatures of stars given the wavelength of their peak
intensities
Wien’s law – 𝑇 =
2.9 𝑥 10−3 𝑚
𝜆𝑚𝑎𝑥
28. Describe what property/characteristic of the Planck curve is used to determine
stellar temperature using the Wien’s Law or the Stefan-Boltzmann Law
Temperature???
29. Recognize the mathematical equation for Wien’s Law and the Stefan-Boltzmann
Law
Wien’s Law – see #27
Stefan-Boltzmann Law – 𝐹 = 𝜎𝑇 4
Learning Objectives – Planck Curves Transparency
30. Describe how Planck curves change for stars of different temperatures – see also
Figure 18.11 in the textbook
Planck curves are higher in intensity for the hotter the star
Learning Objectives – Wien’s Law Transparency
33. Describe the temperature measured in Wien’s law
The temperature of the radiating surface (EMR) of the star
34. Define λmax
The wavelength of the maximum/peak intensity (Planck curve)
35. Convert angstroms to meters
1A = 10-10 m
36. Calculate the temperature of a star given λmax
See transparency for examples
Learning Objectives – Stefan-Boltzmann Law
37. Define F(total)
The radiant energy (EMR – photons) summed over all wavelengths passing through
1 cm2 every second
38. Distinguish between the units of energy (watts) and F(total)
?????
Learning Objectives – Spectra (Sections 18.4, 18.2.1, 21.2, M2.4)
39. Describe atoms in terms of particles and orbitals
The positive charge is in the middle, it is wrapped by orbitals with negatively
charged electrons, the electrons move around the orbitals
40. Identify the fundamental property of the atoms of elements that allows
astronomers to identify elements in the spectra of stars
Their excited state ??
41. Describe absorption and emission
Absorption – when dark lines (representing individual wavelengths due to an
absence of photons at those wavelengths) show on the continuous spectrum
Emission – when colorful, bright lines appear on the non-continuous spectrum
Both are a result of the interaction of photons and atoms in a star’s outer layers
a. What limitations do atoms place on these processes
42. Define excitation and ionization