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Units to cover: 55, 56, 59, 60
Homework 7
Unit 53. Problems 14, 18, 19, 20, 21, 22
Unit 26. Problem 12, 18, 20
If a new planet were found with a period of revolution
of 6 years, what would be its average distance from
the Sun?
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a. About 1AU
b. About 3.3 AU
c. About 6 AU
d. About 36 AU
In order of increasing wavelength the electromagnetic spectrum is
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a. gamma rays, blue light, red light, radio waves;
b. ultraviolet, gamma rays, blue light, radio waves;
c. red light, radio waves, X rays, blue light;
d. visible, ultraviolet, X-rays, radio
Light has properties
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a. of waves;
b. of particles;
c. none of the above;
d. both a. and b.
What is the Law of Inertia?
• A body at rest stays at rest unless acted on by an
outside force
• b. F=ma
• c. P^2=A^3
• d. Fg=mMG/R^2
Convert 742 km to millimeters
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a. 7.42 x10^8
b. 7.42 x10^5
c. 74.2 x10^8
d. 7.42 x10^6
What is retrograde motion?
• a. “backward moving”/ or interrupted movement of a
planet on the sky
• b. Clockwise rotation of the moon around the earth
• c. Rotation of planets around the sun
• d. Large elliptical movements of comets
This does not work for Light!
• If Galilean
Relativity worked
for light, we would
expect to see light
from a star in orbit
around another star
to arrive at different
times, depending on
the velocity of the
star.
• We do not see this
– light always
travels at the same
speed.
The Michelson-Morley Experiment
• Two scientists devised
an experiment to detect
the motion of the Earth
through the “aether”
– Light should move
slower in the direction
of the Earth’s motion
through space
– Detected no difference
in speed!
– No aether, and the
speed of light seemed
to be a constant!
The Lorentz Factor
• It was proposed that
perhaps matter contracted
while it was moving,
reducing its length in the
direction of motion
• The amount of
contraction was described
by the Lorentz factor
– At slow speeds, the effect
is very small
– At speeds close to the
speed of light, the effect
would be very
pronounced!
Einstein’s Insights
• Albert Einstein started from the
assumption that the speed of light
was a constant, and worked out the
consequences
– Length does indeed contract in the
direction of motion, by a fraction
equal to the Lorentz factor
– Time stretches as well, also by the
Lorentz factor
• Moving clocks run slow
• Moving objects reduce their length
in the direction of motion
Special Relativity
• Time dilation and length
contraction depend on the
observer!
– To an observer on Earth,
the spacecraft’s clock
appears to run slow, and
the ship looks shorter
– To an observer on the ship,
the Earth appears to be
moving in slow-motion,
and its shape is distorted.
• The passage of time and
space are relative!
Possibilities for Space Travel
• Example: A spacecraft leaves
Earth, heading for a star 70 lightyears away, traveling at .99c
– To an observer on Earth, it takes
the spacecraft 140 years to get to
the star, and back again
– To passengers on the ship, it only
takes 20 years for the round-trip!
• This means that high speed travel
to the stars is possible, but comes
at the cost of friends and family…
You see this every day!
• More distant streetlights appear
dimmer than ones closer to us.
• It works the same with stars!
• If we know the total energy output of a
star (luminosity), and we can count the
number of photons we receive from
that star (brightness), we can calculate
its distance
L
d=
4pB
• Some types of stars have a known
luminosity, and we can use this
standard candle to calculate the
distance to the neighborhoods these
stars live in.
Photons in Stellar Atmospheres
• Photons have a difficult time moving through a star’s atmosphere
• If the photon has the right energy, it will be absorbed by an atom and raise an
electron to a higher energy level
• Creates absorption spectra, a unique “fingerprint” for the star’s composition.
The strength of this spectra is determined by the star’s temperature.
Stellar Surface Temperatures
• Remember from Unit 23 that the peak
wavelength emitted by stars shifts with the
star’s surface temperatures
– Hotter stars look blue
– Cooler stars look red
• We can use the star’s color to estimate its
surface temperature
– If a star emits most strongly in a wavelength 
(in nm), then its surface temperature (T) is:
T=
2.9 ´106 K × nm
• This is Wien’s Law
l
Measuring Temperature using
Wein’s Law
T=
2.9 ´106 K × nm
l
Spectral Classification
• Around 1901, Annie
Jump Cannon
developed the spectral
classification system
– Arranges star
classifications by
temperature
• Hotter stars are O type
• Cooler stars are M
type
• New Types: L and T
– Cooler than M
• From hottest to coldest, they are
B-A-F-G-K-M
O-
– Mnemonics: “Oh, Be A Fine Girl/Guy,
Kiss Me
– Or: Only Bad Astronomers Forget
Generally Known Mnemonics
The Stefan-Boltzmann Law
• The Stefan-Boltzmann Law links a
star’s temperature to the amount of
light the star emits
– Hotter stars emit more!
– Larger stars emit more!
• A star’s luminosity is then
related to both a star’s size
and a star’s temperature
A convenient tool for organizing stars
• In the previous unit, we saw that
stars have different temperatures,
and that a star’s luminosity
depends on its temperature and
diameter
• The Hertzsprung-Russell diagram
lets us look for trends in this
relationship.
The H-R Diagram
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A star’s location on the HR diagram is
given by its temperature (x-axis) and
luminosity (y-axis)
We see that many stars are located on a
diagonal line running from cool, dim
stars to hot bright stars
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Other stars are cooler and more
luminous than main sequence stars
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The Main Sequence
Must have large diameters
(Red and Blue) Giant stars
Some stars are hotter, yet less luminous
than main sequence stars
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Must have small diameters
White Dwarf stars
The Family of Stars
Stars come in all sizes…
The Mass-Luminosity Relation
• If we look for trends in
stellar masses, we notice
something interesting
– Low mass main
sequence stars tend to be
cooler and dimmer
– High mass main
sequence stars tend to be
hotter and brighter
• The Mass-Luminosity
Relation:
L » M 3.5
Massive stars burn brighter!
Massive stars burn brighter
L~M3.5
Luminosity Classes
Stellar Evolution –
Models and Observation
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Stars change very little over a human lifespan, so it is impossible to
follow a single star from birth to death.
We observe stars at various stages of evolution, and can piece together
a description of the evolution of stars in general
Computer models provide a “fast-forward” look at the evolution of
stars.
Stars begin as clouds of gas and dust, which collapse to form a stellar
disk. This disk eventually becomes a star.
The star eventually runs out of nuclear fuel and dies. The manner of
its death depends on its mass.
Evolution of low-mass stars
Evolution of high-mass stars
Tracking changes with the
HR Diagram
• As a star evolves, its
temperature and luminosity
change.
• We can follow a stars
evolution on the HR
diagram.
• Lower mass stars move on
to the main sequence, stay
for a while, and eventually
move through giant stages
before becoming white
dwarfs
• Higher mass stars move
rapidly off the main
sequence and into the giant
stages, eventually exploding
in a supernova