Transcript The Scales of Things

The Cosmic
Distance Scale
Laura A. Whitlock / Sonoma State U Rohnert Park, CA
Outline
A quick review of notation and units
An examination of Distance
•
•
•
•
Measuring inside our solar system
Measuring to “nearby” stars
Measuring distant objects
Measuring the Universe
Remember:
Big or small, numbers are given meaning in our Universe!
Quick Review of Scientific
Notation
Powers of Ten
Scientific Notation
• 10n means 10 x 10 x 10 x 10 … [n times]
• 10-n means 1/(10 x 10 x 10 ….) [n times]
There are 1010 – 1011 stars in our Galaxy, and
a similar number of galaxies in the Universe
And remember...
To Multiply & Divide
10a •10b = 10 a + b
10a ÷10b = 10 a - b
How Many Grains of Sand?
If Earth were made of sand, would it contain more or less than a
googol (10100) grains of sand?
 Draw a 1 cm segment. Mark pencil points along the segment
to get an estimate of the number of tightly packed grains of
sand in 1 linear cm.
 Calculate the number of grains of sand in 1 cubic km.
(Remember: 100 cm = 1 m , 1000 m = 1 km)
 Earth’s radius is about 6400 km. Use the equation for the
volume of a sphere {V = (4/3)pr3} to calculate the number of
grains in a sandy Earth.
A Quick Tour from the
Unimaginably Tiny to the
Incomprehensibly Big
QuickTime™ and a
Intel Indeo® Video R3.2 decompressor
are needed to see this picture.
…an oldie, but a goodie!
Units for Time and Distance
Kilometer (km) = .621 miles
Light-year (lt-yr) = The distance light travels in one
year in a vacuum.
1 lt-yr = 9.5 x 1012 km
Parsec = 3.3 light-years (Mpc = 1,000 pc)
arc-second = (1 degree/3600)
 Radar (the replacement method for Kepler’s
Law, P2 ~ a3)
 Parallax
 Cepheid Period/Luminosity Relationship
 Supernovae
 Redshift and Hubble’s Law
Radar Measurements
• Beam travels at speed of light, c
• Measure the time it takes beam to leave Earth,
bounce off planet (or whatever), and return to Earth.
This represents the time for the beam, traveling at c,
to cover twice the distance between Earth and the
target object.
2d = c t
d = ct/2
d
But...
Radar techniques are only feasible for objects
inside our solar system.
The Nearest Stars
Distance to Alpha
or Proxima
Centauri is
~4 x 1013 km
(~4.2 light-years)
Distance between
Alpha and
Proxima Centauri
is ~23 AU
The Solar Neighborhood
Some stars are
within
about
2 x 1014 km
(~ 20 light-years)
Distances to Nearby Stars
Parallax : determined by the change of position of a nearby star
with respect to the distant stars, as seen from the Earth at two
different times separated by 6 months.
Parallax
Gold standard for astronomical distances. It is based on
measuring two angles and the included side of a
triangle
The parallax of a star is one-half the angle
parallax angle
Approximation!
D = Earth-Sun distance
parallax
Astronomers usually say the Earth-Sun distance is 1
astronomical unit, where 1 au = 1.5x1013 cm, and measure small
angles in arc-seconds. Arc-seconds are often denoted by , just
Historical Note
The first stellar parallax (of the star 61 Cygni) was measured by
Friedrich Wilhelm Bessel (1784-1846) in 1838. Bessel is also known
for the Bessel functions in mathematical physics.
Parallax
QuickTime™ and a
decompressor
are needed to see this picture.
Parallax to
Proxima Centauri
is only
0.76 
So...
Only the nearest stars to us have a measurable parallax.
Cepheids
Cepheid variable stars are pulsating stars, named after the brightest
member of the class, Delta Cephei.
Cepheids are brightest when they are hottest, close to the minimum
size. Since all Cepheids are about the same temperature, the size of a
Cepheid determines its luminosity.
Thus there is a period-brightness relationship for Cepheids.
Since it is easy to measure the period of a variable star and they
can be very bright, Cepheids are wonderful for determining distances
to galaxies!
Cepheid Variables
Henrietta Leavitt studied variable stars that were all at
the same distance (in the LMC or SMC) and found that
their pulsation periods were related to their brightnesses
L =K P1.3
Polaris (the
North Star)
is not
constant, it
is a Cepheid
variable!
Distances to Cepheids
Distance to closest Cepheid (Delta Cephei) in our Galaxy
can be found using parallax measurements. This determines
K in the period-luminosity relation (L = KP1. 3)
Since the period of a Cepheid is related to its absolute
brightness, if you observe its period and the apparent
brightness, you can then derive its distance
(to within about 10%)
Absolute Brightness
Apparent Brightness =
4 p distance2
If no Cepheids can be seen...
Life Cycles of Stars
QuickTime™ and a
Microsoft Video Utility decompressor
are needed to see this picture.
Supernova…
Going out with a Blast!
Crab Nebula
Observed by Chinese
astronomers in 1054 AD
Age determined by tracing
back
exploding filaments
Crab pulsar emits 30 pulses per
second at all wavelengths from
radio to TeV
QuickTime™ and a
Microsoft Video Utility decompressor
are needed to see this picture.
Crab Nebula
Radio/VLA
Infrared/Keck
Crab Nebula
Optical/Palomar
Optical/HST WFPC2
Crab Nebula and Pulsar
X-ray/Chandra
Distances to Supernovae
Brightest SN in modern times,
occurred at t0
Supernova 1987A in LMC
Measure angular diameter of
ring, q
Measure times when top and
bottom of ring light up, t2 and t1
Ring radius is given by
R = c(t1-t0 + t2-t0)/2
Distance = R / q
D = 47 kpc
Distances to Supernovae
Type Ia supernovae are “standard candles”
Occur in a binary system in which a white dwarf star
accretes beyond the 1.4 Mo limit and collapses and
explodes
 Decay time of light curve is correlated to absolute
luminosity
Good to 20% as a distance measure
But to really
“measure the Universe”...
Historical Note
Edwin Hubble
discovered
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.
Doppler Shift
Wavelength is shorter when approaching
Stationary waves
Wavelength is longer when receding
What It Looks Like
Comparison of laboratory to blue-shifted object
Comparison of laboratory to red-shifted object
Doppler Shift / Redshift
Redshift, z, is a non-relativistic
approximation to the Doppler shift
z
=
Dl
l
=
l - lo
lo
=
v
c
Hubble’s Law Revisited
v = Ho d = cz
where
v = velocity from spectral line measurements
d = distance to object
Ho = Hubble constant in km s-1 Mpc -1
z is the redshift
Space between
the galaxies expands
while galaxies stay
the same size
Example
A certain absorption line that is found at 5000Å in the lab is found at 5050Å
when analyzing the spectrum of a particular galaxy. We then conclude that this
galaxy is moving with a velocity v = (50/5000) * c = 3000 km/sec away from us.
Putting it altogether now, if the object is moving away from us at 3000 km/ sec,
its distance from us (according to the Hubble’s Law) is
d = v/Ho = 3000/65 = 46 Mpc or 1.4 x 108 light-years
And so the Universe is...
v = H0d and d =vt
Solving for t, we find the age of the Universe is:
t ~ 1/H0
If H0 = 65 km/s/Mpc, then the age of the Universe is
~ 16 x 109 yr or 16 billion years
Books and Slides
 Mitton, Jacqueline and Mitton, Simon, Scholastic Encyclopedia of Space,
Scholastic Inc., 1998.
 Fraknoi, Andrew, A Grand Tour of the Universe Slide Set, Astronomical
Society of the Pacific.
Videos
 Powers of Ten: $39.95 through the Astronomical Society of the Pacific
Catalog. http://www.aspsky.org/catalog/vt110.html
or
write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112
 Cosmic Voyage: $29.95 through the Astronomical Society of the Pacific
Catalog. http://www.aspsky.org/catalog
or
write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112
Web
 Cosmic Distance Ladder – 3 labs http://www.astro.washington.edu/labs/Distance_Ladder.html
 Extragalactic Cosmic Distance Scale ttp://www.uq.edu.au/~phjross/ph227/galaxy/candles.htm
 Cosmic Distance Ladder I: Parallax http://209.52.189.2/article.cfm/astronomy/11999
 Cosmic Distance Ladder II – Stars as Standard Candles http://209.52.189.2/article.cfm/astronomy/13217
More Web
 Seeing is Believing! – Determining the Distance to Venus
http://www.amtsgym-sdbg.dk/as/venus/ven-dist.htm
 Stellar Parallax Lab
http://einstein.uhh.hawaii.edu/spacegrant/lab2/lab2.html
More Web
 Cosmic Distance Scale
http://csep10.phys.utk.edu/astr162/lect/cosmology/cosmicd.html
 Cepheid Variables and the Cosmic Distance Scale Lab
http://einstein.uhh.hawaii.edu/spacegrant/lab4/lab4.html
Wrap Up…at long last!
Presentation will appear at
http://perry.sonoma.edu/nbsp/materials/distances.html