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Chapter 2
Read Pages 7-17
Continuous Radiation
from Stars
2.1 Brightness of Starlight


What two major factors determine how
bright a star appears to us?
Answers:
power output
distance from us
What quantities are used to describe
how bright a star is?
m = Apparent Magnitude
 M = Absolute Magnitude
 L = Luminosity
 f = Energy Flux

Ptolemy - 150 AD


Ptolemy divided the
stars visible to the naked
eye into six classes of
brightness call
magnitudes.
The magnitude scale is a
logarithmic scale.
 Energy
flux (f) is the energy per unit
area per unit time received from a
star.
 A difference of five magnitudes
corresponds to a factor of 100 in
energy flux.
f1
( m 2  m1 ) / 5
 100
f2
2.2 The Electromagnetic Spectrum
Thomas Young - wave nature of light
 Albert Einstein - photons
 James Maxwell - electromagnetic theory

The Electromagnetic Spectrum
(Seven Forms of Light)
Radio Waves - communication
 Microwaves - used to cook
 Infrared - “heat waves”
 Visible Light - detected by your eyes
 Ultraviolet - causes sunburns
 X-rays - penetrates tissue
 Gamma Rays - most energetic

The Visible Spectrum
Wave Speed = Frequency  Wavelength
c=n l
m/s
Hz
m
Questions
 In
which of the seven forms of light….
…does our Sun have its peak
intensity?
…does our eyes have the greatest
sensitivity?
…is the Earth’s atmosphere fairly
transparent?
2.3 Colors of Stars
2.3.1 Quantifying Color
I(l) = Intensity Function versus Wavelength
I(n) = “
“
“
Frequency
2.3.2 Blackbodies

...objects that are ideal radiators when hot

...perfect absorbers when they are cool

Blackbody Examples:
light bulb filament
stove or horseshoe
stars (not perfect blackbodies)
Wien’s Law
 “Hotter
bodies radiate more strongly
at shorter wavelengths.”
l maxT  2.9 10 A K
7
 Star
temperatures range from
about 3000K to about 50,000K.
Star Colors
Reddish
 coolest star
Orange-ish
Yellowish
White
Bluish
 hottest star

 Stefan-Boltzmann
Law - a star of
temperature T radiates an amount of
energy each second equal to sT4 per
square meter
 Luminosity - the amount of energy
per second (or power) given off by a
star
L  4R sT
2
4
What is the luminosity of the Sun?
T = 5800K
 R = 7 x 1010 cm
 s = 5.7 x 10-5 erg/(cm2 K4 s)

2.4.1 Planck’s Law

Rayleigh-Jeans Law
I(n, T)  2kTn / c
2
2
k  Boltzmann constant

Planck’s Equation
2hn / c
I ( n, T ) 
exp( hn / kT)  1
3
2
h  Planck' s constant
2.4.2 Photons

Photon energies are proportional to their
frequencies.
E  hn
2.5 Stellar Colors

Color Index allows astronomers to
quantify color.
m2  m1  2.5 log( f1 / f 2 )
B  V  2.5 log( f (l V ) / f (l B ))

Negative values for the color index
(B-V) correspond to blue stars.
2.6 Stellar Distances
Parsec - the distance from our Sun at which
the angle between the Earth and the Sun
subtends an angle of one arcsecond
 1 arcsecond = 1/3600 degrees
 1 parsec = 3.26 light years
 Light-year - the distance that light travels
in one year

Measuring A Star’s Brightness

Inverse-Square Law - the apparent
brightness of a star decreases with
increasing distance from Earth
L
f
2
4d
Measuring a Star’s Distance
Parallax - the apparent change in the
position of a star due to the motion of the
Earth
 Nearby objects exhibit more parallax that
remote ones.

1
Distance in Parsecs =
Parallax Angle in Arcseconds
1
d
p
2.7 Absolute Magnitudes

Distances to stars can be found from the
distance modulus,
m  M  2.5 log( d / d o )
2
m  M  5 log( d / 10pc)