The Continuous Spectrum of Light
•Stellar Parallax
•The Magnitude Scale
•The Wave Nature of Light
•Blackbody Radiation
•The Quantization of Energy
•The Color Index
Stellar Parallax
• Trigonometric Parallax:
Determine distance from
“triangulation”
tan q = B /d
d = B /tanq
• Parallax Angle: One-half the
maximum angular
displacement due to the
motion of Earth about the
Sun (excluding proper
motion)
1AU 1
d=
» AU
tan p p
With p measured in radians
PARSEC/Light Year
•
•
•
1 radian = 57.2957795 = 206264.806”
Using p” in units of arcsec we have:
206,265
d»
AU
p"
Astronomical Unit of distance:
PARSEC = Parallax Second = pc
1pc = 2.06264806 x 105 AU
•
The distance to a star whose parallax
angle p=1” is 1pc. 1pc is the distance at
which 1 AU subtends an angle of 1”
d»
•
•
1
pc
p"
Light year : 1 ly = 9.460730472 x 1015 m
1 pc = 3.2615638 ly
•Nearest star proxima centauri has a
parallax angle of 0.77”
•Not measured until 1838 by Friedrich
Wilhelm Bessel
•Hipparcos satellite measurement
accuracy approaches 0.001” for over
118,000 stars. This corresponds to a a
distance of only 1000 pc (only 1/8 of
way to centerof our galaxy)
•The planned Space Interferometry
Mission will be able to determine
parallax angles as small as 4
microarcsec = 0.000004”) leading to
distance measurements of objects up
to 250 kpc.
Parallax determination of
distance to Venus
http://venustransit.nasa.gov/2012/articles/ttt_75.php
The Magnitude Scale
• Apparent Magnitude: How bright an object appears.
Hipparchus invented a scale to describe how bright
a star appeared in the sky. He gave the dimmest
stars a magnitude 6 and the brightest magnitude 1.
Wonderful … smaller number means “bigger”
brightness!!!
• The human eye responds to brightness
logarithmically. Turns out that a difference of 5
magnitudes on Hipparchus’ scale corresponds to a
factor of 100 in brightness. Therefore a 1
magnitude difference corresponds to a brightness
ratio of 1001/5=2.512.
• Nowadays can measure apparent brightness to an
accuracy of 0.01 magnitudes and differences to
0.002 magnitudes
• Hipparchus’ scale extended to m=-26.83 for the
Sun to approximately m=30 for the faintest object
detectable
Flux, Luminosity and the Inverse Square Law
•
Radiant flux F is the total amount of
light energy of all wavelengths that
crosses a unit area oriented
perpendicular to the direction of the
light’s travel per unit
time…Joules/s=Watt
•
Depends on the Intrinsic Luminosity
(energy emitted per second) as well
as the distance to the object
•
Inverse Square Law:
L
F=
2
4pr
Absolute Magnitude and Distance Modulus
•
•
Absolute Magnitude, M: Defined to
be the apparent magnitude a star
would have if it were located at a
distance of 10pc.
Ratio of fluxes for objects of
apparent magnitudes m1 and m2 .
F2
= 100(m1 -m 2 )/ 5
F1
•
Taking logarithm of each side
æ F1 ö
m1 - m2 = -2.5log10ç ÷
è F2 ø
•Distance Modulus: The connection
between a star’s apparent magnitude, m ,
and absolute magnitude, M, and its
distance, d, may be found by using the
inverse square law and the equation that
relates two magnitudes.
2
100
(m-M )/ 5
F10 æ d ö
=
=ç
÷
F è10 pc ø
Where F10 is the flux that would be received
if the star were at a distance of 10 pc and d
is the star’s distance measured in pc.
Solving for d gives:
(m-M +5)/ 5
d =10
pc
The quantity m-M is a measure of the
distance to a star and is called the star’s
distance modulus
æ d ö
m - M = 5log10 (d) - 5 = 5log10 ç
÷
10
pc
è
ø
The Continuous Spectrum of Light
•The Nature of Light
•Blackbody Radiation
•The Color Index
Speed of Light
•
Ole Roemer(1644-1710) measured the
speed of light by observing that the
observed time of the eclipses of Jupiter’s
moons depended on how distant the Earth
was from Jupiter. He estimated that the
speed of light was 2.2 x 108 m/s from
these observations. The defined value is
now c=2.99792458 x 108 m/s (in vacuum).
The meter is derived from this value.
•
Measurement of speed of light is the same
for all inertial reference frames!!!
Special Relativity
(will come back to this topic..soon)
Takes an additional
16.5 minutes for light
to travel 2AU
The Nature of Light
•
•
Newton believed that like was “corpuscular”, particle-like in nature…due
to sharpness of shadows.
Christian Huygens (1629-1695) believed that light was wave-like, with a
distance between succesive peaks (troughs) of wavelength and that
the number of waves per second that pass a point in space is the
frequency of the wave. The speed of light is then given by :
c = ln
•
Particle and wave models could explain reflection and refraction of
light…wave nature of light demonstrated by Thomas Young’s double slit
experiment…
The Wave Nature of Light
• Light impinging on
double slit
• Exhibits Inerference
pattern
Interference condition
ì nl
ï
d sinq = í
1
ïî(n - )l
2
(n=0,1,2,…for bright fringes)
(n=1,2,…for dark fringes)
INTERFERENCE
http://vsg.quasihome.com/interfer.htm
WAVE
What is Light?
And God said…let there be light
Maxwell’s Equations in
Free space
and there was light….
Electromagnetic
Wave equation
Wavelike Nature of light
•
Light is an electromagnetic
phenomenon
Heinrich Hertz’s Apparatus for the
production and detection of radio waves
Deutsches Museum Munich
Changing electric field
Propagates through free space
Changing Magnetic Field
Nothing is waving!!!!
EM waves created by accelerating charges
Accelerating Charge
causes Electromagnetic Waves
• Electric Field
emanates from
electric charges
• What happens to
field when charge is
accelerated?
• “Kink” in electromagnetic field
propagates with
finite velocity
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=322.0
Electromagnetic Waves
Electromagnetic Wave speed
Light is indeed an
Electromagnetic Wave
Waves are Transverse
Electromagnetic Spectrum
Region
Gamma Ray
X-Ray
Wavelength
nm
1 nm<10 nm
Ultraviolet
10 nm<400 nm
Visible
400 nm<700 nm
Infrared
700 nm<1 mm
Microwave
Radio
1mm<10 cm
10 cm<
Radiation Pressure
and the Poynting Vector
Poynting Vector
•The rate at which energy is carried by a light
wave is described by the Poynting vector.
•Instantaneous flow of energy per unit area per
unit time (W/m2) for all wavelengths.
•Points in the direction of the electromagnetic
wave’s propagation.
•Radiant Flux: Time average (over one period) of
the Poynting vector
1
S =
2m0
E 0 B0
•Because an electromagnetic wave carries
momentum it can exert a force on a surface hit by
light…
Radiation Pressure
Frad =
S A
cos q
c
absorption)
2S A
reflection)
cosq
c
Radiation Pressure is significant in
Frad =
–
–
extremely luminous objects such as:
• early main-sequence stars
• red supergiants
• Accreting compact stars
Interstellar medium dust particles
Photon Flux Densities
Light Source
Photon Flux Density
Photons/(sec m2)
Laserbeam (10 mW,He-Ne 20um)
10 26
Laserbeam (1 mW,He-Ne )
Bright Sunlight
10 21
1018
Indoor Light Level
1016
Twilight
1014
Moonlight
1012
1010
Starlight
Particle-like nature of light
Photons
• Photon = “Particle of
Electromagnetic “stuff””
Light is absorbed and emitted in
tiny discrete bursts
• Blackbody Radiation
Failure of Classical Theory
Radiation is “quantized”
• Photo-electric effect (applet)
Color/Temperature Relation
Betelguese(3100-3900K)
What does the color of a
celestial object tell us?
Rigel (8000-13,000K)