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The Big Bang
Thursday, January 17
Doppler shift tells you if an object is
coming toward you or moving away.
Blueshift: distance decreasing.
Redshift: distance increasing.
All distant galaxies have redshifts.
But wait, there’s more!....
The amount by which
the wavelength is
shifted tells us the
radial velocity
of the object, in
kilometers/second.
A light source is at rest: it emits
light with a wavelength λ0.
If distance to light source is
changing, Doppler shift will
change the wavelength to λ ≠ λ0 .
Size of Doppler shift is
proportional to radial velocity:
  0 V

c
0
λ = observed wavelength
λ0 = wavelength if source isn’t at rest
V = radial velocity of moving source
c = speed of light
656.3 nm ↓
Hydrogen absorbs light
with λ0 = 656.3 nm.
You observe a star with a hydrogen
absorption line at λ = 656.2 nm.
Thinking locally: stars within
3 parsecs of the Sun.
Proxima Centauri
Equal numbers of
redshifts and
blueshifts.
Typical radial velocity
V = 30 km/second
(70,000 mph).
Thinking more globally: galaxies within
30 million parsecs of the Milky Way.
Almost all redshifts
rather than blueshifts.
Typical radial velocity
V = 1000 km/second
How do we know the distances
to stars and galaxies?
No sense of depth!
Climbing the
“cosmic distance ladder”.
Can’t use the same technique to find
distance to every astronomical object.
Use one technique within Solar System
(1st “rung” of ladder); another for
nearby stars (2nd “rung”), etc...
1st rung of the distance ladder:
distances within the Solar System.
Distances from Earth to nearby
planets are found by radar.
Radar distance measurement:
Send out a strong radio pulse, wait
until the faint reflected pulse returns.
Measured round-trip travel time = t
(typically several minutes)
One-way travel time = t/2
Distance = speed × one-way travel time
Since radio waves are a form of
light, distance = c t / 2
Using fancy technical methods,
round-trip travel time can be
measured with great accuracy.
Thus, we know distances within the
Solar System very well indeed.
1 astronomical unit (average distance
from Sun’s center to Earth’s center) =
149,597,870,690 meters
(plus or minus 30 meters).
2nd rung: distances to nearby stars
within the Milky Way Galaxy.
← Proxima Centauri
Distances from Solar System to
nearby stars are found by parallax.
Flashback slide!
1 parsec = distance at which a star
has a parallax of 1 arcsecond.
↓observed star
observer→
parallax angle
Not to scale
1 parsec = 206,000 astronomical units
= 3.26 light-years
Measured parallax angle is inversely
proportional to a star’s distance.
1 parsec
Distance 
p
(p = parallax angle,
in arcseconds)
First star to have its parallax angle
measured: 61 Cygni (in the year 1838).
Parallax angle =
0.287 arcseconds
Distance =
1 parsec / 0.287 =
3.48 parsecs
With the Hipparcos satellite,
astronomers measured parallax angles
with an accuracy of 0.001 arcseconds.
Parallax too small to measure for stars
more than 1000 parsecs away.
3rd rung: distances to galaxies
beyond our own.
Distances from Milky Way to nearby
galaxies are found with standard candles.
In the jargon of astronomers, a
“standard candle” is a light
source of known luminosity.
Luminosity is the rate at which
light source radiates away energy
(in other words, it’s the wattage).
Sun’s luminosity = 4 × 1026 watts
= 4 × 1033 ergs per second
When we measure the light from a star,
we aren’t measuring the luminosity.
To do that, we’d have to capture
all the light from the star.
When we measure the light from a star,
we are measuring the flux.
The flux is the wattage received per
square meter of our telescope lens.
At distance d from
star of luminosity L,
the luminosity is
spread over an area
4πd2.
Flux = luminosity / area
F=L/(4π
2
d )
What’s this got to do with
finding the distance?
You know luminosity (L) of a standard
candle. You measure the flux (F).
You compute the distance (d):
L
F
2
4πd
L
d
4F
Climbing the distance ladder.
1) Measure flux of two standard
candles: one near, one far.
2) Find distance to near standard
candle from its parallax.
3) Compute luminosity of near
standard candle: L = 4 π d2 F.
4) Assume far standard candle has
same luminosity as the near.
5) Compute the distance to the far
standard candle:
L
d
4F
A good standard candle:
Cepheid variable stars
Cepheid stars vary in brightness with a
period that depends on their average
luminosity.
Observe Cepheid.
Measure period.
Look up luminosity.
Measure flux.
Compute its distance!
L
d
4F
In 1929, Edwin Hubble looked at the
relation between radial velocity and
distance for galaxies.
Hubble’s result:
Radial velocity of a galaxy is linearly
proportional to its distance.
Modern data
1 Mpc = 1 million parsecs
Hubble’s law
(that radial velocity is
proportional to distance)
led to acceptance of the
Big Bang model.
Big Bang model: universe started in
an extremely dense state, but
became less dense as it expanded.