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Doppler Shift
Consider a stationary point source emitting light waves
Doppler Shift
If source moves away, light appears redder than it is.
If source moves towards us, light appears bluer.
Visible light
The shift in the light waves is proportional to
the relative speeds of the source and
observer
Doppler Shift
Wavelength is shorter when approaching
Stationary waves
Wavelength is longer when receding
Comparison of laboratory to blue-shifted object
Comparison of laboratory to red-shifted
object
Wavelength shift
Assume radial speed, v, of glowing object is
small compared to speed of light, c
v << c.
l0 is reference wavelength of medium at rest.
Dl
l
=
l - lo
lo
=
-v
c
Frequency shift
Df
f
=
f - fo
f
=
v
c
Example calculation
The star Vega has a hydrogen line of
656.255nm, which is shifted from the
reference value of 656.285 nm.
1. Is it moving towards us or away?
2. Calculate its speed
Red shifted to LONGER wavelength
so moving away.
Speed is –13.7 km/s.
Rotation Rate from Doppler Shift
Spectroscopic Binary Stars
Discovery of Planets Around Remote Stars
Rotation speed of galaxy from 21-cm spectral line of
Atomic hydrogen
Historical Note
Using the
Doppler shift,
Edwin Hubble
observed
that the
Universe is
expanding!
What Hubble Found
The Hubble constant
Ho = 558 km s -1 Mpc -1
is the slope of these graphs
Compared to modern
measurements, Hubble’s
results were off by a
factor of ten!
Hubble’s Law
v = Ho d
Ho is called the Hubble constant. It is generally
believed to be around 65 km/sec/Mpc…
plus or minus about 10 km/sec/Mpc.
Note: The further away you are,
the faster you are moving!
Implications of Hubble’s Law
Distance = velocity/(Hubble constant)
To get a rough idea of how far away a very distant
object is from Earth, all we need to know is the object's
velocity.
The velocity is relatively easy for us to measure using
the Doppler effect, or Doppler shift.
Caveat!
Space between
the galaxies expands
while galaxies stay
the same size
The Tools of All Astronomy
• Light Curves – examining how bright something is
as a function of time
• Images – examining what something
looks like spatially
• Spectra – examining how much energy an object
emits as a function of energy
Kinds of Spectra
Another Way to Look at a
Spectrum
The Atom’s Family
Bohr atom




Electrons in fixed orbits around…
Protons and neutrons in the nucleus
Only certain electron orbits are allowed
Electrons jump between orbits to make photons of
specific energies
Periodic Table
Electrons fill shells labeled s, p, d, f, etc. 
New shells are added 
The Atom’s Family
Quantum atom
Electrons are clouds of probability density
 No two electrons can have identical
quantum numbers  Pauli exclusion
principle
 Heisenberg Uncertainty principle limits
knowledge our simultaneous knowledge
of:
 position & momentum
>


energy & time
Dx Dp =
h/2
Gravitational Force
The gravitational force is weak, but very
long ranged. Furthermore, it is always
attractive, and acts between any two
pieces of matter in the Universe since
mass is its source.
Remember the Tortoise and the
Hare?
Gravity has basic properties that set it apart from the other
forces: (1) it is long-ranged and thus can act over
cosmological distances; (2) it always supplies an attractive
force between any two pieces of matter in the Universe.
Thus, although extremely weak, it always wins over
cosmological distances and is the most important force for
the understanding of the large scale structure and
evolution of the Universe.
So, let us deal with GRAVITY
We’ll need a bit of a history lesson:
•Brahe
•Kepler
•Newton
•Einstein
Pay close attention, gravity has
many
implications!
Tycho Brahe
1546 - 1601
A wild Dane, but he made
and recorded large
quantities of accurate
measurements of the
motions of the planets
around the Sun.
Began working with
Johannes Kepler in 1600.
Kepler’s Three Laws of Planetary Motion
Landmarks in the history for astronomy and mathematics,
for in the effort to justify them Isaac Newton was led to
create modern celestial mechanics. The three laws are:
1) The planets move abort the sun in elliptical orbits
with the sun at one focus.
2) The radius vector joining a planet
to the sun sweeps over equal areas
in equal intervals of time.
3) The square of the time of one compete
revolution of a planet about its orbit is proportional
to the cube of the orbit's semi-major axis
T12/ T22 =R13/ R23
or
T2=k.R3
The empirical discovery of these laws
from Tycho Brahe's mass of data
constitutes one of the most remarkable
inductions ever made in science.
Isaac Newton
He put the physics and
mathematics to
Kepler’s Laws!
Born 1642, the year
Galileo died
Loner, tinkerer,
paranoid
1665-1666 Plague was
very good for him
Suffered mental
breakdown 1675
Math, Chemistry,
Theology, Parliament
Died 1727
Has his picture on the
British pound note
Was there really an apple?
We know: he was
on a farm
We don’t know
anything else
Newton’s Laws of Motion
First Law
- A body remains in its state of motion unless acted upon by an
outside force
Second Law
- A body acted upon by an external force will change its
momentum in the direction of the force such that the greater the
force the greater the change in momentum (F= ma)
Third Law
- Forces always occur in pairs, i.e. for every action there is an
equal and opposite reaction
Universal Law of Gravitation
All objects in the Universe attract each
other with a force that varies directly as
the product of their masses and
inversely as the square of their
separation from each other.
F gravity
= G m 1m
r2
2
Albert Einstein
Besides having great hair,
he taught us a few fundamentally
important things:
E = m c2
• Energy can be neither created nor destroyed. It can just
change from one form to another. Light, heat, kinetic, potential,
etc. etc. etc.
• No object can move faster than the speed of light.
• Space and time are linked together.