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H205 – Cosmic Origins
Exploration Packet 2: Making Sense of the Universe
Your Name _____________________________
Due March 25, 2009
Other Group Members (if appropriate):
_________________________
_________________________
_________________________
Part 1: Basic Assumptions about the Universe
Discuss with a partner what assumptions might be reasonable for scientists to make about the
Universe. List three or four. For each describe why this is a reasonable assumption for our universe,
and what the assumptions might imply for the origin, evolution, or structure of our universe.
a)
b)
c)
d)
The boxes below are meant to represent small portions of very large two-dimensional universes.
Using small “”symbols to represent galaxies. An astronomer, located on a galaxy somewhere in
the box, is trying to understand the structure and important properties of her/his universe.
For each universe, sketch in a distribution of galaxies that would represent the caption given.
The universe appears isotropic to the
observer.
The universe appears isotropic but
not homogeneous to the observer.
The universe appears homogeneous
to the observer.
The universe appears homogeneous
but not isotropic to the observer.
Part 2: Making predictions from models: Two basic models for our universe are the “Steady
State” model and the “Big Bang” model. What would each model predict we would find as we explore
the Universe at greater and greater distances?
Steady State Universe:
Big Bang Universe:
Part 3: The Cosmic Microwave Background Radiation – Suppose the CMBR did not come from
the nearly uniform, evenly distributed, hot, 3000 K gas at the end of the Era of Nuclei, but rather from
many individual stars and galaxies that first formed in the early Universe. How would the spectrum of
the CMBR differ from the spectrum we observe?
Part 4: How much has the Universe expanded since the end of the Era of Nuclei?
a) The temperature of the gas when atoms formed from free electrons and nuclei was about 3000K.
What would be the wavelength at which a gas of that temperature would emit the most energy? (Hint:
Remember Wien’s Law, λmax = 2.9 x 106 / T(K), with in nanometers.)
b) The peak wavelength for the CMBR observed today is 1.1 millimeters (= 1.1 x 106 nm). Verify
using Wien’s Law that this corresponds to the observed temperature of the CMB of 2.7 K.
c) The increase in wavelength of the CMBR since the end of the Era of Nuclei until now is caused by
the expansion of space in our universe. By what factor has space stretched since the Era of Nuclei?
Part 5: Spatial Variation of the CMBR: The spatial variation in the temperature of the CMBR was
measured by the Wilkinson Microwave Anisotropy Probe (WMAP). Astronomers can study the
distribution of matter at the end of the Era of Nuclei by looking at how the temperature varies from
point to point in the sky. We will construct our own “temperature fluctuation spectrum” from WMAP
data. A temperature fluctuation spectrum relates how much temperature changes across different
length scales across the sky.
Use your “angular ruler” to determine the temperature at 10 points in a small region of the sky from
WMAP data. The angular ruler has a total length of 36 degrees (this is equivalent to about 70 times
the diameter of the full Moon) when placed on the WMAP section.
 Place the angular ruler anywhere on the WMAP section so that all of the little circles fall on the
image. Tape down both ends.
 Using the temperature scale on the side of the image, estimate the temperature deviation from
the average CMB temperature for the starting circle and for each small circle from 2 degrees
to 36 degrees from the starting circle.
 Record your temperatures in the chart below – remember the + or – sign!
Temperature
Starting Circle
2 degrees
4 degrees
6 degrees
Temperature
10 degrees
16 degrees
20 degrees
25 degrees
Temperature
30 degrees
36 degrees
We will collect the data from the whole class to produce our own fluctuation spectrum.
For Wednesday, March 25
Motion Due to Gravity: Although gravity is the weakest of the known forces, it dominates the
Universe on large scales. The strong and weak forces work only over very small distances, and the
electromagnetic force is weak because most mass in the Universe is electrically neutral.
Understanding gravity is essential to understanding the Universe.
In the exploration, use the simulations and applets available from the University of Colorado at:
http:solarsystem.colorado.edu/home/lowRes.html. Visit the website, click on "modules," and select
the "Kepler's Laws" modules. Be sure to explore the "Give me a hint" links for further information.
Part 6: Kepler’s First Law
Take a look at the Kepler's First Law applet. The applet draws each planet as if the semi-major axis
of its orbit is one astronomical unit, but with the correct eccentricity for each planet’s orbit. Use the
Applet to answer the following questions.
1. Which object has the smallest eccentricity? How do the perihelion to aphelion distances compare
for this planet? (Perihelion is the point where the planet is closest to the Sun; aphelion is the point
furthest from the Sun.
3. Which object has the largest eccentricity? How do the perihelion and aphelion distances compare
for this object?
Part 7: Kepler's Second Law
1. Select the planet Mercury in the Kepler's Second Law applet. What is the highest speed that
Mercury has during its orbit (expressed in AU per year)? What is its slowest speed?
Highest speed ___________________
Slowest speed _______________________
Where in its orbit does Mercury move the fastest?
Where in its orbit does Mercury spend the most time?
1. Select Pluto from the pull-down menu. Determine its orbital speed and distance from the Sun at
aphelion and at perihelion. Compute the produce of speed and distance at each location. How do
they compare? Try this again for 3 other eccentricities larger than Pluto’s
Eccentricity
Aphelion
Distance
Speed
Product
Perihelion
Distance
Speed
Product
e=0.25 (Pluto)
Part 8: Kepler’s Third Law – This applet explores the relationship between a planet’s orbital period
and its semi-major axis. The relationship is known as Kepler’s Third Law. The graph plots the
measured orbital period (p) and semi-major axis (a) of each planet in the Solar System. Click the
“up/down” buttons to explore what mathematical relationship that will fit the orbits of planets in the
Solar System.
1. Which combinations of exponents for the period and semi-major axis give you a good fit to the
data? (You can also explore decimal exponents. Try setting the exponent of the period to 0.5 and
1.0. What exponents of the semi-major axis are then needed to fit the true orbits of the planets?)
2. Why do you think Kepler chose to phrase his third law as he did, in view of the fact that there are
many pairs of exponents that seem to fit the data equally well?
Part 9: 'Dial-an-Orbit' Applet - Explore planetary orbits in more detail. Can you find an orbit that
does not crash the planet into the Sun? Give the X, Y, Vx and Vy values you find to produce an orbit
that does not impact the Sun.
Part 10: Beyond the Solar System – Gravity dominates not only the planets of the Solar System, but
all of the bodies of the Universe – stars, galaxies, even clusters of galaxies. Each small group will
consider ONE of the following problems to discuss with the class. Circle the number of the problem
you think about, and describe the solution below.
Remember, according to Newton’s formulation of Kepler’s 3rd Law: P2 = a3/(m1+m2) where the
period (P) and the semi-major axis (a) are given in solar masses and astronomical units.
1. Black hole in the center of the Milky Way – A massive black hole can be found at the center of
the Milky Way. The black hole has a mass of about 4 million times the mass of the Sun. Many
young stars orbit around this massive black hole. “S2,” the star that passes closest to the black
hole, has an orbital period of about 15.6 years, and a semi-major axis of about 1000 AU. What is
the mass of the black hole? (S2 approaches to within 150 AU of the black hole!)
2. Binary Neutron Stars – Two neutron stars, with masses of 1.6 and 2.4 solar masses,
respectively, orbit each other in a circular orbit with a period of 3 hours (3.5 x 10-4 years!). What is
the semi-major axis of the orbit? How does the semi-major axis of their orbit compare to the
diameter of the Sun (1.4 x 106 km)?
3. Orbit of the Sun around the Galaxy – The Sun orbits around the center of the Milky Way with an
orbital speed of 220 km s-1. Assume it follows a circular orbit, and the distance from the Galactic
Center is a mere 26,000 light years (2.4 x 1017 km or 1.7 x 109 AU). How many times has the Sun
circled the Galaxy since the Sun formed 4.6 billion years ago? Estimate the mass of the Milky
Way from the Sun’s orbit.
4. The Impact of Andromeda and the Milky Way - The Andromeda and Milky Way galaxies are
moving toward each other at a speed of 300 km s-1. The two galaxies are currently separated by
2.54 x 106 LY (2.4 x 1019 km = 1.6 x 1011 AU). The eccentricity of the Milky Way’s orbit around
Andromeda is not known. However, if the orbit were circular, and if the orbital speed were 300 km
s-1, how long would one complete orbit take? Assume both galaxies have masses of 1011 solar
masses. Would the two galaxies have completed one full orbit during the age of the Universe?
5. Falling toward Virgo - The Local Group of galaxies, including the Milky Way and the Andromeda
Galaxy, are falling toward the Virgo Supercluster of Galaxies at a speed of 600 km s-1. The
distance to the Virgo Supercluster is about 50 x 106 light years (about 5 x 1020 km = 3 x 1012 AU).
If the Local Group is following a circular orbit around the Virgo Supercluster, how long would one
orbit take? Assume the mass of the Virgo Supercluster is 1015 times the mass of the Sun.
Part 11: Reflection (5 minutes, max) – Write a short statement (no more than 5 sentences) what, if
anything, this packet helped to clarify or helped you to learn.