# Stars

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```					           Stars

Chapter 8 Characterizing Stars
Page 257-
Distance to stars by parallax
Basic Questions
•   How far away
•   How bright
•   How hot
•   How big
•   How massive
Parallax
Friedrich Wilhelm
Bessel
1838
Stellar parallax angle
61 Cygni
1/3 arcsec, 3pc
Parallax Calculations
P (parallax angele) = ½ parallax angle
_1 AU_
tan P =
d = _1 AU_                    d
tan P
1 AU = 93,000,000 mi = 1.496 x 108 km
P = 1 second = 1/3600 o
tan P = 4.848 X 10-6
d= __ 1.496 x 108 km_ = 3.08572 X 10 13 km
4.848 X 10-6
Distance Units (Appendix H-1)
• Parsec the distance of an object with a parallax
angle = 1 arcsecond.
• Parsec = 3.08572 X 10 13 km
• 1AU (astronomical unit)= 1.5 X 108 km
• 1 ly (light year) = 9.46 X 1012 km
• = 365 days/year X 24 hrs/day X 3600 s/hr
• = 3.15 X 107 s X 3.00 X 105 km/s = 9.46 X 1012 km
• 1 parsec = 3.26 ly
Parsec
• As angle goes down the distance goes up
• 3 parsec = 1/3 arcsecond
• Measuring small angles is very difficult
• .01 arcsec is smallest with Earth-based
telescopes
• ie. 100pc
• Hipparcos (satellite) measured distance to 2.5
million stars up to 150 pc or 500 ly
Brightness
•   Hipparchus 200 BC and Ptolemy 200 AD
•   Classified and cataloged stars
•   Brightest were 1st magnitude
•   Faintest were 6th magnitude

• Problems
– Scale is backward High numbers fainter than low
– Human perception – logarithmic not linear
– Does not consider effect of distance
Apparent Magnitude
• Apparent magnitude – the brightness of a star
measured without regard to their distance
from Earth.
• lowercase “m”
• Vega m=0.0
• Sirius (brightest star in the sky) m= -1.44
• Venus m= - 4.4
• Moon m= -12.6
• Sun m= -26.7
Absolute Magnitude
• Absolute magnitude “M” is the
brightness each star would have at a
distance of 10pc
• Inverse-square law
• As light moves outward from a
source it spreads out over a larger
area and its brightness decreases.
Absolute Magnitude
• Range
• M= -10 for brightest stars
• Mid range star M= +3.5
• M= +17 for dimmest stars

• Absolute Magnitude of Sun = +4.8
–(apparent magnitude m= -26.7)
Luminosity
• Luminosity is the total amount of
electromagnetic power .
• Energy of Sun 3.83 x 1026W at the surface
• Mercury
• 9140 watts per square meter
• Earth
• 1370 watts per square meter
Luminosity Scale
•   Expressed as multiples of Sun luminosity
•   Brightest Stars
•   M= -10 then L= 106 Sun Luminosity
•   Dimmest Stars
•   M=+17 then L= 10-5 Sun Luminosity
Temperature
• Review Chapter 3
• Temperature can be determined by the
wavelength of the most intense light waves given
of by a star.
• Temperature can also be determined by
observing spectral absorption lines.
– Absorption lines are produced when an electron
absorbs energy of a particular wavelength and this
energy causes an electron to move to a higher energy
level.
Star Temperature
Why aren’t the types in order?
• Originally the spectral types were assigned
due to the strength of specific absorption lines
of hydrogen.
• A-P early 1900’s
• 1920 Cecilia Payne and Meghnad Saha
• Associated temperature with the different
spectral types.
• Temperature scale and Balmer Line scale did
not match.
Hertzsprung-Russell Diagrams
• Independently
• Plotted Luminosity (Absolute Magnitude)
against Temperature (Spectral Type)
• Temperature and Luminosity are coorelated
H-R Diagram
Trends
• Patterns of behavior are valuable clues to
understanding properties and their causes.
• Bright stars near top, dim stars near bottom.
• Hot stars to the left, cooler stars to right.
• Diagonal band in center- Main Sequence Stars
• White Dwarfs
• Red Giants
Distance Determination P268
• Parallax limited to near by stars- up to 100PC
or 326 light years.
• Method for more distant stars
1. Observe apparent magnitude and spectrum
2. From spectrum determine temperature
3. Determine class- Main, White, Red
4. Read Absolute Magnitude from HR graph
5. Determine distance from distance magnitude
relationship.
Basic Questions

•   How far away
•   How bright
•   How hot
•   How big
•   How massive
Measuring Mass (P269)
• Mass is important because it determines the
amount of energy each star has available.
• Mass cannot be determined directly by
observing isolated stars.
• Can use Newton’s law of gravity to determine
gravitational effect on other objects.
• Fortunately 1/5 of the stars we see are
actually pairs of stars orbiting each other.
Determine Mass of Stars
• Double Stars- stars that appear at nearly the
same position
• Optical Binaries (apparent binaries) are not
actually close to each other but appear close
in the sky
• Binary Stars are pairs of stars that orbit each
• Visual Binaries can be distinguished by
telescope.
Newton and Kepler’s 3rd Law
•   P 2=   a 3
true for planets in the solar
system. P = period, a= semi major axis
• Newton
• For any object orbiting another.
• Planet-star, moon-planet, star-star
• Sum of masses =       a 3/   P 2
Mizar in Ursa Major
Visual Application
• Determine the period
• Determine the separation

• Determine the sum of the masses
• If we can determine the center of
mass of the pair, we can determine
the ratio of the masses.
• Determine individual mass- 2
equations, 2 unknowns.
Determining Center of Mass
• To find the center of mass, we must know the
plane of the orbit.
• We can do this by observing the light emitted
by the star.
Page 272
Main Sequence
Spectroscopic binaries (P273)
• Some binaries cannot be observed visually
because they are either too close to each other
or too far from us to “resolve” with telescopes.
• But we can observe the spectra (absorption) of
the stars.
• Two hydrogen lines- A and B
• Doppler effect
– Shift toward the red (right) moving away
– Shift toward blue (left) moving toward.
Next Chapter we
will search for an
explanation for
the trends on the
H-R Diagram

H-R Diagram
Schedule
•   Thursday 2/11 Work on Study Guide
•   Friday 2/12 Work on Study Guide
•   Monday 2/15 No School
•   Tuesday 2/16 Answers to Study Guide
•   Wednesday 2/17 Test on Chapter 8

• Monday 2/22 @7:00PM GWU Williams
Observatory
– Follow Rt 150 South of Downtown Boiling Springs
– Turn right onto Stadium Dr just south of Hardees
– Observatory is the building with a dome

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