Astronomy 100
3/4/2009 8:31:00 PM
What is Astronomy?
 The study of the Universe in which humans live
 Involves long and short time scales
o Planck time=0.0000000000000000000000000000545
 Smallest measurable unit of time
o Age of the Universe= 12,000,000,000 years
 Small size scales and vast distances
o Parsec=3.26 light years=31,000,000,000,000 km
o Radius of an atom=~1 Angstrom=0.0000000001 meters
Scientific Notation
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Used as a simple short hand for very large or small numbers
o Number written in the form of a x 10b
 A is the mantissa, b is the exponent
 1 is greater than or equal to a, a is less than 10
o Remember: 10-x=1/10x
o Examples
 1.9891x1033gm=198910000000000000000gm
 1.67x10-24gm= 0.000000000000000167 gm
o Exponent
 Positive numbers move decimal right
 Negative number move decimal left
Write 43,000,000,000,000 km, the distance to the nearest star, in
scientific notation
o 43,000,000,000,000km=4.3x10,000,000,000,000
=4.3x1013km
Write 0.0000005m, a typical wavelength of optical light, in scientific
notation
o 0.0000005m=5x0.0000001
=5x10-7m
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Earth, Venus, and Mercury are planets, small and non-luminous
bodies that shine by reflected light
1 AU=98 million miles or 150,000,000km
o Distance from the earth to the sun
Light travels between earth and sun in 8 minutes
Distance from Venus to sun is 0.7 AU
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Distance from Mercury to sun is 0.39 AU
Orbits of planters are not perfect circles
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To express distances so large
o One light-year (ly) is the distance that light travels in one
year, roughly 1013 km or 63,000 AU
o The nearest star to the sun, Alpha Centauri, is 4.2 ly from
Earth
o Light from Alpha Centauri’s light takes 4.2 years to reach
Earth
o Alpha Centauri can only be seen by the southern most parts
of the US on occasion
o Found nearly 200 planter orbiting other stars
Scale of the Universe
 Galaxies are commonly grouped together in such clusters
o Some of these galaxies have beautiful spiral patterns like our
own galaxy, but others do not
o Most galaxies appear as large fuzzy patches of light with no
structure
o Clusters can have thousands of members with a range of
sizes and masses
Coma Cluster of Galaxies
 Much like our galaxy most of the mass is not visible except at other
wave lengths
o X-ray image of Coma Clusters of galaxies shows distribution
of intracluster gas
On the outskirts of the Virgo Cluster of Galaxies
 The Virgo cluster is about 20,000,000 pc (20Mpc) distant.
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Seen in the arms of the constellation Virgo.
We are on the very edge of the Virgo Cluster
Slowly accelerating towards this cluster
Contains M87
o Observed jet from core
o AGN
Scale of the Universe
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If you again expand your field of view, you see that the clusters of
galaxies are connected in a vast network
o Clusters are grouped into superclusters—clusters of clusters—
and the superclusters are linked to form long filaments and
walls. They outline voids that seem nearly empty of galaxies
o These appears to be the largest structure in the Universe.
Were you to expand you field of view another time, you would
probably see a uniform fog of filaments and voids
o When you puzzle over the origin of these structures, you are
at the frontier of human knowledge
o Reach the observable size of the Universe
Units
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A number is meaningless without units
Often use shorthand
o m=meters: 1 gram=1g, or 1gm
o in=inches; ft=feet
o s=second
Unit systems
o MKS=meters-kilograms-second
o CGS=centimeter-gram-second
 Preferred by astronomers
o Prefixes
 See page 503
Angle Units
o Degrees
 1 rotation=360 degrees ()
 1=60 minutes (‘)
 1’=60 seconds (“)3600”=1
o Radians
 1 rotation=2 radians=360
 1 radian=57.3
o Right angle=90=/2 radians
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Astronomical Unit (AU)
o Average distance between the Earth and the Sun
o 98,000,000 miles=1.5x10” km
Light Year (ly)
o A unit of distance not time
o Distance light travels in one year
 Speed of light (c)=3x105km/s
 1 ly=9.5x1012km
 Parsec (pc)
o 3.26 light years of 206265 AU
o 1pc=3.09x1013km
The Night Sky
 Stars are scattered in the void all around you, most very distant
and some closer
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Each rotates on its axis once a day. So, from your viewpoint, the
sky appears to rotate once around you each day.
 Not only does the sun rise in the east and set in the west, but do
the stars
Ancient Astronomers
 Stonehenge
o Located in England
o Several construction episodes
o Thought to be used for ceremonial purposes and establishing
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a calendar
o Marked the summer solstice
Mayans in Mexico
o Used temples as observatories
o Kept a keen eye on the heavens
o Knew the mechanics of the sky well
o Bighorn medicine wheel (in WY)
 Used to tell when to plant crops and begin the harvest
 Marked summer solstice and several bright stars
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Used the rising of stars to determine time of the year
Numerous examples across the states and Canada
The heavens viewed as intangible, sacred
The ancient astronomers organized what they saw by naming
stars and groups of stars
 gods
 heroes
 mythical creatures
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told stories for posterity
Constellations
 To the ancients, a constellation was a loose grouping of stars
o Many of the fainter stars were not included in any
constellation. Regions of the southern sky, not visible to the
ancient astronomers of northern latitudes, were not identified
with constellations
 Had we defined constellations today, they might be something
completely different
 Some of the constellations named with in the western culture
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originated in the Mesopotamia over 5,000 years ago
o Other constellations were added by
Constellation boundaries, when they were defined at all, were only
approximate
o So, a star like Alpheratz could b thought of as part of Pegasus
or part of Andromeda
o Areas of the sky which couldn’t be associated with a
constellation
In order to correct these gaps and ambiguities, astronomers in
recent centuries have added 40 modern constellations to fill gaps.
In 1928, the International Astronomical Union (IAU) established 88
official constellations with clearly defined boundaries.
o This, a constellation now represents not a group of stars, but
an area of the sky
In addition to the 88 official constellations the sky contains a
number of less formally defined groupings called asterisms
o The Big Dipper, for example, is a well-known asterism
Although constellations and asterisms are named based on what is
visible in the sky, it is important to remember that most of these
groups are made up of stars that are not physically related to each
other.
The Celestial Sphere
 As you study the sky, 3 important points
o Sky appears to rotate westward around Earth, but that is a
consequence of the eastward rotation of the earth. Produces
day and night
o Astronomers measure distances across the sky as angles and
express them in degrees, minutes and seconds
o What you can see of the sky depends on where you are on
earth
o
 Alpha Centauri
 In southern sky and not visible from most of the
US
 Only a glimpse about the southern horizon in
Miami
 Easily seen in Australia
 Sky above us appears as a sphere rotating from east to west,
continuously
o Stars and planets appear fixed on that sphere
o We call this model of the sky The Celestial Sphere
 The celestial sphere is an example of a scientific model, a common
feature to scientific thought
o Model doesn’t have to be true to be useful
The Names of Stars
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Way to identify stars is to assign Greek letters to the bright stars by
the order of brightness
o Brightest star is designated alpha (), 2nd brightest  (beta)
and so on
o Some exceptions apply
Star’s bayer (Greek Letter) designation is the Greek letter followed
by the genitive (possessive) form of the constellation name
o Brightest star in constellation Canis Major is  Canis Major.
Identifies the star and constellation and gives clue to the
relative brightness of the star!
The Brightness of Stars
 Astronomers measure the brightness of stars using the magnitude
scale, a system that first appeared in the writing of ancient
astronomer Cladius Ptolemy about 140 AD
o Most astronomers attribute system to Greek astronomer
Hipparchus (160-127 BC)
 Ancient astronomers divided stars into 6 classes
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The Sky
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o Brightest=first magnitude and fainter=second magnitude
scale continued downward, faintest visible to human eye
Larger magnitude, the fainter the star
Hipparchus complied first star catalog and used magnitude system
in it
300 years later, Ptolemy used magnitude system in his own catalog
Modern Astronomers have quantified the magnitude system
o Difference of 5 magnitude means a factor of 100 in flux
and Its Motion
Earth’s rotations causes the stars to move in a predictable manner
o Easterly rotation makes us perceive the stars as moving
westward
o Stars rise in the east move westward and set in the west
o Intersection of rotation axis
Earth’s rotation defines the rotation axis
o Intersection of rotation
The Celestial Equator
o The intersection of the plane defined by Earth’s equator and
the celestial sphere
o Midpoint between the NCP and SCP
The Earthbound Observer
 Horizon
o Plane of the ground meets the celestial sphere
o Is observer dependent
 Zenith
o The point on the celestial sphere directly above the observer
o Is observer dependent
 Nadir
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o The point on the celestial sphere directly beneath the
observer
o Is observer dependent
Cardinal Points
o North point is on the horizon directly (above/beneath) the
NCP
o South point is on the horizon directly (beneath/above) the
SCP
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o East and west points are defined by intersection of horizon
and celestial equator
Meridian
o Line from north point through the NCP, Zenith and South
Point
o Observer dependent
Latitude dependency of the Bowl Diagram
o Angle between North point, the observer and the NCP equals
your latitude
o (Positive/negative) values means (above/below) horizon
o (North/South) latitudes are represented by
(positive/negative) latitudes
It is important to realize that what an observer sees is dependent
on his location
Diurnal Motion
o Everyday rising and setting of the sun, moon, planets, and
stars
o Motion observer dependent
o Sun, moon, and planets is just like a star and is fixed on the
celestial sphere for a given day
Lets go back to an observer at 30 North latitude
Motions of the stars looking North
o Polaris
Motions of the stars looking East
o Stars appear to rise from the east
o Motion is not vertical but at an angle
o Angle between motion of the stars and the horizon is (90latitude
Astronomy 100
3/4/2009 8:31:00 PM
Precession
 In addition to the daily motion of the sky, Earth’s rotation adds a
second motion to the sky that can be detected only over centuries.
o Over 2,000 years ago, Hipparchus compared a few of his star
positions with those recorded nearly two centuries before and
realized that the celestial poles and equator were slowly
moving across the sky.
o Later astronomers understood that this motion is caused by
the top-like motion of Earth.
o If you have ever played with a gyroscope or top, you have
seen how the spinning mass resists any change in the
direction of its axis of rotation.
o The more massive the top and the more rapidly it spins, the
more difficult it is to change the direction of its axis of
rotation.
o However, you probably recall that the axis of even the most
rapidly spinning top moves as it spins, describing the surface
of a cone.
o The weight of the top tends to make it tip, and this combines
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with its rapid rotation to make its axis sweep around in a
conical motion called precession
Earth spins like a giant top and is tipped 23.5 degrees from vertical.
o Earth’s large mass and rapid rotation keep its axis of rotation
pointed toward a spot near the star Polaris, and the axis
would not wander if Earth were a perfect sphere.
o However, Earth, because of its rotation, has a slight bulge
around its middle, and the gravity of the sun and moon pulls
on this bulge. That tends to twist Earth upright in its orbit.
o The combination of these forces and Earth’s rotation causes
the Earth’s axis to precess conical motion, taking about
26,000 years for one cycle.
o Because the celestial poles and equator are defined by Earth’s
rotational axis precession moves these reference marks.
o We notice no change at all from night to night or year to year,
but precise measurements reveal the precessional motion of
the celestial poles and equator.
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Over centuries, precession has dramatic effects.
o Egyptian records show that 4,800 years ago the north
celestial pole was near the star Thuban (alpha Draconis)
o The pole is now approaching Polaris and will be closest to it in
about 2100.
o In around 12,000 years, the pole will have moved to within 5
degrees of Vega (alpha Lyrae)
o The figure shows the path followed by the north celestial pole.
Greek Astronomers
 Initially tired to measure the size of the known universe.
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Were the first to employ models in an attempt to make predictions.
Driven mostly by philosophical arguments, not by scientific
arguments.
 Developed the scientific method.
Eratosthenes of Cyrene
 Born: 276 BC, Cyrene, North Africa (modern Libya)
 Died: 194 BC, Alexandria, Egypt
 Calculated the diameter of the Earth
o Noticed the sun shone to the bottom of a well.
o On the same day, an obelisk in Alexandria.
 Gave angle from straight above at 7 degrees
 Therefore distance between Syene and Alexandria is
~1/50 of the circumference of the Earth.
 Result: 46,620 km
Aristarchus of Samos
 Measured the relative sizes of the Earth and the Moon.
o Used the shadow of the Earth on the Moon.
o Found the Moon to be 0.35 times the Earth’s radius.
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o Correct ratio is 0.27.
Lived between 310-230 BC
Explained phases of the Moon
Actually believed in a Heliocentric model
o Heliocentric means Sun centered.
o Meant that the Earth moved around the Sun.
Measured distance to the Sun
o Used first quarter moon.
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o Measured the angle between the Moon and the sun to be 87
degrees.
o Concluded the Sun is 19 times as distant as the Moon.
(rs/rm=19)
Deduced that the Sun is ~19 times the radius of the Moon.
Therefore the Sun is about 7 times the radius of the Earth.
o Important because the Sun is larger than the Earth.
o However we know this ratio to be more like 100.
Established that the Sun was not only very far away, but also larger
than the Earth.
Aristotle
 Lived 384-322 BC
 Geocentric model
o Earth centered model
o Saw no parallax—objects must be at a great distance
o Could detect no motion—Falling objects should be swept
westward
o Therefore, Earth at center and immobile
 Assigned intrinsic properties to objects
o Earth was corrupt and changing
o Sun and Heavens—perfect and unchanging
Greek Astronomers
 Made careful observations of the Sun, Stars, and Planets
o Yearly path of the Sun
 Easterly trend
 Defines Earth’s orbital plane
o Sun completes one cycle every 365.25 days
 Traces out Ecliptic
 Sun moves easterly ~1 degree a day
o Motion complicated by 23.5 degree tilt
 Angle between Celestial equator and Ecliptic
 Due to tilt of Earth’s axis
Orientation of the Celestial Sphere
 Earth revolves around the Sun once a year.
o Orbit defines a plane—the Ecliptic Plane.
o Earth’s North Pole points at the NCP.
o Earth’s axis is titled relative to the orbital plane of the Earth.
 Tilt between the Earth’s rotation axis and the ecliptic plane is 23.5
degrees.
 Earth’s rotations makes the Earth act like a gyroscope
o Orientation of the Earth’s rotation axis is fixed.
o NCP is always near Polaris (on the time scale of our lifetime)
Map Projections
 Projection of the Celestial Sphere onto a 2D flat plane.
o Similar to map of Earth—Mercator projection
 Can do several projections
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Cardinal
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Two required to represent the entire sky
Do the same to the Celestial Sphere.
Celestial Equator is straight line across a diagram.
Ecliptic is tilted by 23.5 degrees.
Most northern and southern point of the Sun is 23.5 degrees.
Directions on Sky Chart
On map of Earth north orientated up and East to the right
On a Sky Chart north is up and East is to the left
o Due to vantage point.
o For map of Earth you are looking down on the Earth.
o For map of Sky you are looking up at the Sky.
Intersection of the CE and Ecliptic
 Equinox
o Sun is found on the Celestial Equator
o Defines Vernal Equinox
 Defined to be March 21
o Defines Autumnal Equinox
 September 22-23
Zodiac
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Defined by the Ecliptic
o Astrological Sign
 Constellation the Sun is in when you are born.
 Defined according to the Ecliptic of ~2000 BC
(Babylonians)
o 12 main zodiac constellations
 Aquarius
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Aries
Cancer
Capricornus
Gemini
Leo
Libra
Pisces
Sagittarius
Scorpios
Taurus
 Virgo
 Precession has rotated the Ecliptic
Orientation of the Celestial Sphere
 In reality the Earth is orbiting the Sun, and the background stars
are changing because of the changing vantage point
Solstice
 Point where Sun is furthest North or South
 Northern hemisphere
o Summer—furthest North (June 21)
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o Winter—furthest South (December 21)
Southern hemisphere
o December 21
o June 21
Seasons
 The Earth’s orbit is very nearly circular
o The seasons we experience are due to the tilt of the Earth’s
axis, not the different in distance from Sun
o Aphelion (July 6), Perihelion (Jan. 3)
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Tilt of earth’s axis has two effects
o The tilt causes incoming sunlight to be more/less direct
 Changes heating efficiency of the Sun
o Changes the length of the day
 Changes the duration a location is heated by sunlight
When sunlight is more direct there is a greater amount of energy
per unit area.
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Notice the faction of the circle about the horizon versus the faction
below the horizon as a function of position on the Celestial Sphere
END QUIZ #3
Definition
 Rotation is used to reference a body rotating on an axis
o The Earth rotates on its axis once a day
 Revolution refers to a body orbiting about another body
o The Earth revolves about the Sun once a year.
Cycles of the Moon
 Period of the Moon
o Period is the time it takes the moon to revolve around
another body
 Sidereal Period
 Orbital period defined relative to the stars
 Time it takes the moon to orbit the Earth
 27.3 days
 Synodic Period
 Orbital period defined relative to the Sun
 Time between successive New Moons
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29.5 days
Cycles of the Moon
 Difference due to motion of the Sun on the sky
o Takes moon about 1 month to orbit Earth
o But in 1 month sun gas moved on the sky
o Takes 2.2 days for moon to catch up
 Motion in the sky
o In 24 hours
 Moon moves eastwardly 13 degrees on sky
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Rises about 50 minutes later each day
Lunar phases
 Moon orbits the Earth
o In a counterclockwise fashion when viewed about the NP.
o Earth rotates counterclockwise
 Moon moves Eastwardly on sky.
 Only half of the Moon that faces the Sun is illuminated.
END QUIZ #4
Ptolemaic Model
 Ptolemy’s Almagest
o Presents model in great detail
o Adheres to the circular geometry of the Greeks.
o Success is based upon experimental verification of
predictions.
Dante’s Universe
 From The Devine Comedy
o Geocentric model
o Established the location of divine spheres.
Copernicus
 Born: 1473 in Torun, Poland
 Died: 1543
 Published the De Revolutionibus Orbium Coelsetium
o Finished around 1530.
o Published in the year of his death
o Did not need epicycles to explain retrograde motion
o Still adhered to perfect circular motion
The Copernican Universe
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Heliocentric model where the sun is at the center of the Universe
o All planets revolved around the sun
o Moon is recognized to revolve around the earth
o Order of the planets is correct out to Saturn
Why is this model important?
o Religious consequences?
o Philosophical consequences?
Explained retrograde motion in a simple, straight-forward manner
o As Earth passes a Superior planet, it appears to move
temporarily westward.
o Inferior planets also show retrograde motion as they pass the
Earth in their orbits.
The Copernican Revolution
 Most important concept to come out of De Revolutionibus Orbium
Coelestium
o Earth is the 3rd planet from the sun.
 Earth is not at the center of the Universe.
 Meant that the Earth is not in a special place.
o Significant consequences regarding philosophical and religious
beliefs.
o Scientists adhere to this principle today.
 The Laws of Physics that apply here apply everywhere.
 We are in an ordinary location just like every other
position in the Universe.
Tycho Brahe
 Provided extremely accurate astronomical observations.
o Uraniborg
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Home in Hveen, Denmark
Observatory
Used quadrants to measure the positions of the planets
Provided a long baseline of observations for others to
study.
Tycho’s Universe
 Geocentric model
o Moon orbited the Earth
o Allowed Mercury, Venus, and the other planets to orbit the
Sun.
o Sun orbited the Earth.
Tycho’s Nova
 Nova means “new”
o A bright star that appears on the sky that was not there
before
o Observed Nova in 1572
 Made several observations was not able to detect any
parallax
Placed on celestial sphere
Directly contradict the previous belief that the celestial
sphere did not change
o Published De Stella Nova in 1573
 Obtained funding for Uranibrog in Hveen, Denmark
Galileo Galilei
 Born: February 15, 1564 in Pisa, Italy
 Died: January 8, 1642 in Arcetri
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First to utilize the telescope for Astronomical observations
o Invented by Hans Lippersay in 1608
Persecuted by the Catholic Church
o Died under house arrest
Published Sidereus Nuncius
Provided early efforts toward a theory of motion.
o Recognized uniform acceleration of objects due to Earth’s
gravity.
Pardoned by the Catholic Church in 1992!
Galileo’s middle finger mounted in a museum in Florence, Italy
o Faces Rome
Galileo’s Telescopic Observations
 Moons of Jupiter
o Galilean Satellites
 Lo, Europa, Ganymede, Castillo
o Provided evidence that other centers of revolution exist
 Jupiter kept moons with it
 Proved the Earth could do that with the Moon.
 Contradicted that the Earth was the center of the Universe/center of
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revolution
Craters on the Moon
o Mountains and valleys on the surface of the Moon.
o Showed that other planetary surfaces were not perfect.
Sunspots
o Marred surface sun
o Not a perfect surface. Showed rotation of the sun.
o Heavens were not perfect
Saturn’s Rings
o Called the Ears of Saturn
 Interpreted as 2 bodies orbiting Saturn
 Observations showed the bodies vanished
Milky Way Galaxy
o Appeared to the human eye as a milky band of light across
the sky
o A telescope revealed that in fact the Milky Way was
thousands of stars.
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The nail in the coffin
o Phases of Venus
 In Geocentric model the only allowable phases were
crescent phases (< ½ illumination)
 Observed gibbous phases (> ½ illumination)
 Strongly supported the Heliocentric model.
How did they know the Earth rotated?
 Foucault’s Pendulum
o Plane of pendulum wants to maintain the same orientation.
o Earth’s rotation causes plane of pendulum to rotate
o For a pendulum at the north pole the plane will rotate once
every 24 hours.
o First demonstration took place in February 1851
Johannes Kepler
 1571-1630 AD, Germany
 studied Music and Theology
o Learned of the Copernican hypothesis while in a university
o Went to Denmark to work with Tycho
o Inherited Tycho’s detailed observations
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Set out to model the motions of the planets using mathematics and
the Copernican model
 Resulted in the published work The New Astronomy in 1609
o Contains first 2 (of 3) laws of planetary motion
Kepler’s Laws of Planetary Motion
 1st Law of Planetary Motion
o The planets follow elliptical orbits
 Ellipses are a family of curves known as a conic section
which includes circles
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2nd
 Satisfy the equation x^2/a^2 + y^2/b^2=1
Law of Planetary Motion
o The planets sweep out equal areas of their orbits in equal
time
 Planets move faster when closer to the Sun
 Longer skinny triangles when planet is distant compare
in area to short wide triangles when planet is close to
the Sun.
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3rd Law of Planetary Motion
o The square of a planets period is proportional to its semimajor axis cubed.
 P^2 squiggly a^3
 If units of the semi-major axis (a) is in AUs then period
(P) is in years, and the above becomes”
 P^2 yr=a^3 AU
rd
Example of 3 Law
o What is the semi-major axis of a planet whose orbital period
(P) is 8 years?
 P^2=(8 years)^2=64=a^3
 a=3^square root of 64=4AU
o What is the orbital period of Jupiter if the semi-major axis of
its orbit is 5.2 AU?
 a3=(5.2 AU)3=140.608=P2
 square root of P ~ 12 yrs
o Note: the period is dependent only on the semi-major axis
Ellipse
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Ellipses are the set of points whose distance to two foci is a
constant
The Sun is at one of the two foci, but nothing as at the second
focus
Semi-Major axis
o Half of the Major-axis
o For a circle it becomes the radius
Astronomy 100
3/4/2009
8:31:00 PM
Sir Isaac Newton
 1643-1727 AD, England
 Professor of Mathematics at Cambridge University
o Lucasian Chair of Mathematics
o Currently held by Steven Hawking
 Published Principia in 1687
o Established laws of motion
o Universal Law of Gravity
 Also established modern optics and the branch of mathematics
known as Calculus
o Done at home while hiding from Bubonic plague (1665-66)
Newton’s Laws of Motion
 1st Law of Motion
o Known as The Law of Inertia
o An object in uniform motion will continue along in its motion
(or lack of motion) until acted upon by external force
o Example: For a spacecraft traveling in empty space,
unaffected by outside forces (like gravity), the spacecraft will
continue along a straight line, at constant speed, until a force

2nd

3rd
outside of it acts to change its trajectory.
Law of Motion
o The rate of change of momentum of an object is equal to the
external force applied to it.
o For constant mass objects, this says that the acceleration of
an object is proportional to the amount of force it receives.
F=ma
Law of Motion
o Known as The action-reaction Law
o Every action has an equal and opposite reaction.
o For every force applied by one body on another an equal and
opposite force is applied on the first body by the second.
F1=-F2
Newton’s Universal Law of Gravitation
 Inverse square law of gravity
 Curved orbits imply a force which we know to be gravitational
Fg=-GMm/r2

Using calculus proved that the orbits of planets are ellipses
o Actually able to calculate planetary orbits using mathematics.
o Now had a physical reason for planetary orbits.
Acceleration due to Earth’s Gravity
 Universal Law of Gravity Fg=GMmb/r2
 Newton’s 2nd Law of Motion: F=Fg=mba
 If we equate the two, we get mba=GMmb/r2 or, solving for a, we get
a=GM/r2
Planetary Orbits
 Planetary orbits can be any of the conic sections.

o Bound Orbits
 Circular orbits
 Elliptical orbits
o Unbound Orbits—orbits that escape from Earth due to velocity
 Parabolic
 Hyperbolic
Conservation of Angular Momentum
o Angular momentum is that quantity of motion which is stored
in the rotation or revolution of an object about an axis: e.g.
A planet in orbit about the Sun has angular
momentum= m v r
 An ice skater can use angular momentum conservation
to speed up when she brings in her arms
Conservation of Angular Momentum can explain Kepler’s 2nd Law
o For a given planetary orbit, the mass of a planet is a
constant, and so is its angular momentum
o . ‘ . if radius (r) decreases, then the velocity (v) must
increase


o Conversely, if radius (r) increases, then the velocity (v) must
decrease.
Albert Einstein
 Reformulated laws of gravity
o General Relativity
 Helped to lay the foundations for Quantum Mechanics
o Energy is quantized—discreet energy values
o Light is made up of packets of energy called photons


Received Nobel Prize for Photoelectric effect in 1922
Consequence of Relativity
o Energy & Matter are 2 states of the same thing
 Much like water and ice.
 E=mc2
 Matter can be converted to Energy, and back.
 Led to General Relativity
o Special relativity is a special case of General Relativity
Special Relativity
 First Postulate



o Law of physics are the same for all observers.
Second Postulate
o Speed of light is a constant.
o No matter velocity relative to the light source, observed
speed of light is c~3x108 m/s
Traditional velocity addition laws
o Still work at every day velocities.
o Fails at relativistic velocities
Both observers see light traveling at velocity c.

Velocity addition law:
o V= v1+v2/1+(v1v2/c2)
General Relativity
 Assumptions from Special Relativity
 First postulate
o Principle of Equivalence
 Observer cannot distinguish locally between inertial
force due to acceleration and uniform gravitational
forces due to the presence of a massive body

Second Postulate
o Mass determines the curvature of space-time, and the
curvature of space-time tells mass how to accelerate
 Mass’s effect on space time determines the motion of objects
 The presence of Mass warps space-time
o Deflects lights
o Causes planets to travel in orbits
Consequences

Time dilation
o Time is not a constant
o Observer sees the clock of another observer slow down
 Gravitational dilation
o As curvature of space-time increases due to the presence of a
mass, time slows
 Deflection of light
o Light falls toward a gravitational body the same as a mass
o Light is deflected whenever it passes near a mass
Principle of Equivalence

Observer in elevator feels downward force because of acceleration
of elevator
o Cannot distinguish between the two
The Nature of Light
 Isaac Newton discovered that white light is composed of different
colors
o Composed of many different colors.
o Emitted
o Reflected

Waves


o Absorbed
Properties of Light—Duality of Light
o Light as a particle
 Light meter reading
 Count of number of “baseballs” that strike detector
o Light as a wave
 Iridescence of a soap bubble
 Constructive and deconstructive interference of light
causes color
Longitudinal Waves
o Compression wave
 Sound
 Alternating regions of high and low densities
 Displacement of air molecules in direction of
travel
Transverse Waves
o Sea waves
 Water displaced perpendicular to motion of travel
o Light waves
 Transverse waves of electric and magnetic fields.
Structure of Waves
 Wavelength ()

o Distance over which wave repeats itself
o Distance between 2 crests
Frequency ()
o Number of crests that passes a point in one second
o Period of wave=1/

Relationship between frequency and wavelength
o =(speed of wave)for light this becomes =c

Units
o Visible light  is often given in nanometers (nm)

o 1 nm=1x10-9 meters
Example
o Calculate the frequency of yellow light
 Yellow light has =500 nm=5x10-7 meters

=c/, or =3 x 108 (m/s)/ 5x 10-7 m= 6x1014/s


Notice units
Units in cycles/s
Spectrum
 Intensity of Light verses Wavelength/Frequency
o Optical light goes from Violet (short /high ) to Red (long /
low )
o ROY G BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet)
 Long   short 

High   low 
The Electromagnetic Spectrum
 Optical Spectrum is only a small part of the Electromagnetic (EM)
Spectrum
 Radio at the low /long  end.
 Gamma () Rays at the high / short 
 Order from low  to high : radio, microwaves, infrared, optical,
ultraviolet, X rays,  rays


Not all of the EM spectrum makes it through the atmosphere
The EM spectrum is also and energy Spectrum
o  rays are highest energy
o Violet light is high energy
o Red light is low energy.
o Radio is lowest energy.
Light as a Particle
 Packets of energy
o Energy is related to frequency E=h= hc/
o Higher frequency photons have greater energy
 X-rays penetrate skin and bone
 Ultraviolet light causes sunburns.
 Infrared is felt as heat.
Astronomical Instruments
 Optical Telescopes
o Astronomer use light to study the Heavens.
o Objectives
 Collect light
 Telescope is a light bucket
Collects as much light as possible and bring to a
focus
 Form and image
 Correlates position and intensity
 Astronomers then study the image
Methods to Form Image
o Refract light
 Bend light to a focus.
 Uses lenses.


Refracting Telescopes
 First telescope discovered
o Invented by Hans Lippersay in 1608.
o Type used by Galileo
 Objective Lens
o Collects light
o Bends light to a focus.
 Eyepiece

o Forms image for eye to view.
o Magnifies image
Galilean Telescope
o Refracting telescope
 Refracting telescope
 Surfaces were spherical in nature
 To form image need parabolic surfaces
 Used to Convex objective lens
 Eyepiece was concave
 Placed before objective lens focus



Images not inverted
Pros
o no central obstruction
 excellent for high resolution work
 unbeatable contrast
Cons
o Extremely expensive to construct
 High quality glass required
 Many surfaces to shape
o Limit on size of telescope
 Lens is supported only by edges
 Lens can sag under own weight
 Largest possible size is about 1 meter—Yerkes 40
in refractor.
Chromatic Aberration
 Chromatic Aberration
o Focus depends on wavelength of light.
o Stars appear with a red halo.
o Can use Achromatic lens to help.
 Can partially correct with multiple lenses
 Achromatic lenses
o Two lenses of different glass to counter act dependency of
focus (never got rest of notes)
Reflecting Telescopes
 Invented by Isaac Newton
 Primary Mirror


o
o
Cage
o
o
o
Pros
o
Collects light
Reflects to a focus
Located at the Primary Focus
Location of Astronomer
Location of instruments
No Chromatic Aberration
 But can suffer from other aberrations
 Spherical aberration
 Spheres do not bring light to a single focus.
 Only parabolas do.
 Higher order aberrations
 Off axis parabola no longer looks like a
parabola.
 The further off axis you go the worse the
aberration gets.
o Cheap to construct
 Poor quality glass

Only one surface to form
QUIZ #1 END
Reflecting Telescopes
 Invented by Isaac Newton
 Primary mirror
o Collects light
o Reflects to a focus
 Cage
o Location at the primary focus location of astronomer

o Location of instruments
Pros
o No Chromatic Aberration
 But can suffer form other aberrations
 Spherical Aberration
 >>Spheres do not bring light to a single focus.
 >>Only parabolas do.
 Higher order aberrations




>>off axis parabola no longer looks like a
parabola.
>>the further off the axis
Pros
o –No limit on size of mirror
 Mirror supported by entire backside.
 Can reform mirror by pressing at different points
 Can use segmented mirrors to form a larger mirror.
Cons
o Central Obstruction
 Lowers resolution
 Poor Contrast
Properties of a telescope
 Light Gathering Power (LGP) of a telescope
o Proportional to the collection area.
See Bri’s notebook for equation
 Given by ratios of the squares of the radius.
 Also given by the ratios of the squares of the diameters.
See Bri’s notes for this equation

Example
o How much LGP does an 8 inch telescope have over the human
eye?
 Human eye D1=7mm=0.7 cm
 8 inch telescope d2=8in=20cm
 LGP=(20cm)^2/(0.7cm)

o Resolving Power
 Telescopes allow us to see finer detail

Given by
See Bri’s notes

Where
o Dcm=diameter of telescope in centimeters
o Alpha =angular resolution of telescope in ”.
-If two objects are separated by an angle less than 20”, then the human eye
will see them as one object.

Magnification
o Number of times an image is enlarged
o Focal Length
 Distance between Lens/mirror and focus.
o Both Objective lens/Primary Mirror and Eyepiece have focal
lengths
o Magnification is equation in bri’s notes
Other design exist
 Newtonian style
o Style invented by Newton
o Uses flat secondary mirror to divert light to side.
 Cassegrain Style
o Focus of Light behind primary mirror
o Uses curved secondary mirror
 Still others
o Often require a tertiary mirror.
o WIYN
Cassegrain Style Reflecting Telescope
 Classical Cassegrain
o Parabolic primary mirror
o Hyperbolic secondary mirror
 Gregorian Telescope
o Parabolic primary mirror
o Elliptical secondary mirror
 Ritchey-chretidn
o Hyperbolic Primary mirror
o Hyperbolic secondary mirror
Catadioptric telescopes
 Involves both refraction and reflection.
 Usually involve spherical mirrors
o Spherical aberration
 Sphere does not bring light to a focus.
 Conic sections do—parabola
 Often only involve corrector plates so minimal chromatic aberration
o Used to make spherical mirrors to look parabolic
o Spherical mirrors are cheap/easy to make
 Schmidt Cassegrain
o Focus behind the mirror.
o Spherical primary
Radio Telescopes

Telescopes are used in other regions of the electromagnetic
spectrum
 They may look different, but principle is the same
 Largest Radio telescope
o Arecibo, Puerto Rico
o 350m in diameter
o Cannot be supported in the usual manner
o Mirror is built into valley between hills
X-ray Telescopes

Grazing incidence mirror
o Still parabolic surface that brings light to a focus.
o Light hits surface at a grazing angle.
o Cylindrical mirrors are parabola with missing center.
Telescope Mounts
 German Equatorial Mount
o Designed to align rotation of telescope with Earth’s rotation
axis
o Can attack a “clock” that moves telescope to counter act
Earth’s rotation
 Equatorial mounts can be heavy and expensive.
 Alt-Az mounts are cheaper
o But do not align with rotation axis
o Requires computer control on both axes to follow stars
o Most large telescopes use these mounts
Right Ascension-Declination
 Right Ascension (RA)
o Analogous to Longitude on Earth
o 0 RA is marked by the Vernal Equinox
o increases Eastward
o Unites in degrees (0-360) or time (0-24 hours)

Declination (Dec)
o Analogous to Latitude on the Earth
o Celestial Poles have N/S Dec (-=South)
o Equator is 0 Dec circle
o Units are given in degrees
Altitude-Azimuth

Altitude
o Angle above the Horizon
o Zenith is defined to be at an altitude of 90

Azimuth
o Angle measured from North cardinal point toward/through
East cardinal point
o East Point=90
o South Point=180
o West Point=270
 Time Dependent
The Image
 Looking through a telescope does little for science.
 Astronomers attach detectors for measurements
o Photographic plates
 Inefficient, but can cover large areas of the sky.
 Development imprecise, emulsions differ
o Charge-Coupled Device (CCD)
 Used by modern instruments

Getting better at making devices
Angstroms (A)
 1 Angstrom = 10-10 m
o unites often used to express wavelength of optical light,
o 1 nm = 10 A
o typical size of an atom
o optical light is from 4000A---7000 A
o older unit that is losing popularity, but is still often used
Mass Volume and Density
 Objects have mass consistent with their weight. F=mg
o “g” is the acceleration due to gravity
o the pound (lb) is actually a unit of force
o metric unit of mass is the kilogram (kg)
 Volume is the 3-dimensional size of an object
o Metric unit of volume is meter3 (m3)
 Mass density of an object is equal to its mass divided by it volume:
o Density=mass/volume
o Unites are in kg/m3
Energy
 Energy is a quantity that scientists use to describe an object
o Motional behavior of an object (kinetic energy)
o Stored or the potential to release energy (potential energy)
o Energy emitted as light (radiative energy)
o Energy stored in internal particle motion (thermal energy)
o Energy stored in or released by the nuclei of atoms (nuclear
energy)
o And many other examples…
Temperature and Thermal Energy
 Temperature is the average energy of motion of a particle
composing a substance
o Absolute temperature is measured in Kelvin (K) where 0K
corresponds to zero velocity of the particles within
 Thermal Energy is that energy of particle motion for an entire
object:
o i.e. more atoms=more energy
Atomic Structure

Atoms are made of protons, electrons, and neutrons,
o Protons and neutrons are found in the nucleus
o Electrons swarm the nucleus in orbits about it
o The negative charge of the electrons are attracted to the
positive charge of the protons
 Opposite charges attract
 Like charges repel
o The nucleus is about 100,000 times smaller than the atom

Electrons are bound to the nucleus
o Similar to planets around the Sun.
o It takes energy to remove and electron or increase its energy
 Provided by photons
 Energy is conserved
 Quantum Mechanic allows only specific energies for an electron
o Only specific energies can be emitted or absorbed by an
electron bound to an atom.
o This give rise to atomic spectra.
Nuclear Energy


Protons and neutrons are bound to each other in the nucleus
o Heavy atoms give up energy when they break up into
constituent parts.
 The mass of the parts is less than the mass of the initial
nucleus
 This is called nuclear fission
 Einstein’s E=mc2 applies
 Atomic bombs are powered by nuclear fission
The Sun is powered by nuclear energy
o Energy is releases as a photon when a light is formed by
combining two lighter atoms.
 The mass of the constituents is greater than the final
nucleus
 Einstein’s E=mc2 applies.
 This is known as nuclear fusion (atoms fuse together)
 Covert 4 Hydrogen into 1 Helium
Energy Units
 MKS system
o Joules (J)= Nm = kg m^2/ s^2
 CGS system
o Ergs=dynes cm=g cm^2/ s^2
 Atomic scales are much smaller. We use electron volts (eV)
o 1 eV = 1.602 x 10^-12 erg = 1.602 x 10^-19 J
o 1 J = 1 x 10^7 ergs
QUIZ #2 END
Atomic Spectra



Atom can absorb only photons of a specific energy.
o Gives rise to atomic spectra
o Also only photons of specific energy can be emitted.
o Each element is unique
Electron orbits and energies is unique to the element
o Several known elements given by the Periodic Table
o Each has unique energy levels of the atom
Each spectra of each element is unique
o Each element has “fingerprint” emission/absorption
o We can figure out the composition of something by looking at
o

Most
o
o
o

its spectra
Spectra of Orion nebula shows superposition of Hydrogen,
Helium, Oxygen, Neon, etc.
of the Universe consists of Hydrogen
Simplest spectrum
Lymann Series
 When electron jumps to level 1
 Found in UV and higher energy photons
Balmer Series
 When electron jumps to level 2.
 Found in visible-UV
o Paschen Series
 When electron jumps to level 3.
 Found in the Radio
 Calculation of Atomic Spectra
Calculation of Atomic Spectra
o Energy of photon equals difference of energy levels for
electron
 hv =  = E2 – E1


h is known as the Planck constant.
 H = 6.626 x 10^-27 erg s
 H = 4.136 x 10^-15 eV s
Calculate energy of photon emitted for an electron
jumping from level 3level 2

Calculate energy difference E3 – E2 = 12.1 eV –
10.2 eV



Energy of equals energy difference h = 1.9 eV
 = 1.9 eV/4.136 x 10 -15 eVs = 4.59 x 10 14 Hz
And  = c/ = 3.0 x 10 8 m/s / 4.59 x 10-14 m/s =
6.53
Electrons and Light
 Correspond to the difference of possible energy levels the electron
can orbit in.
 If an electron is knocked out of an atom it is said to be ionized.
o Any photon with energy > than the energy required to ionize
an atom will be absorbed.
Atomic Designations
 Designate element 1 or 2 letter code
o H, He, Li, Be, Na, Au, and Fe are all examples.
o Following superscript gives atomic weight (A)
 Number of protons and neutrons in nucleus.
 H1, H2 (deuterium), He4, Fe56 are examples.
o Atomic Number (Z)
 Number of protons in the nucleus
 Can precede the 1,2-letter designation.
Subscript gives atomic number
 Example 26Fe56 or 5626Fe
 Number of neutrons (N) becomes 56-26=30
Thermal “Blackbody” Spectra
 Opaque objects that absorb all light and emit none are blackbodies
o The mixture of photons found within a blackbody has a
thermal blackbody spectrum.
o Things that act like blackbodies
 Stove burners, fire pokers, iron pans, light bulbs.

 Can tell the temperature of an object by the spectrum.
o Temperature determines overall emission of object.
Blackbody Spectra
 Very characteristic spectrum.
o As you increase the temperature you increase the emission at
all wavelengths
 Total energy/luminosity of a Blackbody is related to
temperature.

Stefan-Boltzman Law:
 E = T4 (J/ s  m2)
 Energy per unit area per second
o Temperature determines wavelength of light with maximum
intensity (max).
 Wein’s Law
 max= 3 x 106 K nm/T
 increase the temperature and you decrease max
 decrease temperature and you increase max
Kirchhoff’s Laws of Radiation





Lived 1824-1887
Born in what would be modern day Germany
Three Laws of Radiation
o Tell us what kind of spectrum we observe
Law 1—Continuous Spectrum
o A solid, liquid, or dense gas excited to emit light will radiate
at all wavelengths and thus produce a continuous spectrum
Law 2—Emission Spectrum
o A low-density gas excited to emit light will do so at specific
wavelengths and this produce an emission spectrum.
 Law 3—Absorption Spectrum
o If light comprising a continuous spectrum passes through a
cool, low-density gas, the result will be an absorption
spectrum.
 Stars follow this law
Stellar Spectra
 Absorption spectra
o Continuous spectra
Blackbody Spectra
 Hot stars are blue
 Cold stars are red
 Absorption Lines
o Comes from atmosphere surrounding star
o Lines dependent on temperature of star
Nebular Spectra
 Emission spectra

o
o
o
o
Spectra in discreet colors.
Seen in low-density clouds of gas at high temps.
Consist mostly of hydrogen
Example
 Orion nebula
 Lagoon nebula
Doppler shift
 Motion of an object causes the wavelength to change.
o Doppler shift
o Happens for sound waves.

 Sound of a fire truck passing you on a road.
 Sound of a Indy car passing you on the track.
Motion of an object will Doppler shift light
o Affected by velocity along line of sight.
o Motion towards an observer shifts the color blue--shorter
upside down y
 Blue shift
o Motion away from an observer shifts the color red--longer
upside down y
 Red shift
o We see Doppler shifts in stellar spectra
 Motion of the earth will cause a Doppler shift.
 Doppler shift formula
 Vr/c=triangle upside down y/upside down y 0
 Change in velocity of object.
Magnitude scale
 Apparent magnitude(m)
o Magnitude of a star as measured from the earth

o This is despite its distance.
Absolute magnitude (M)
o Brightness of a star located 10 pc from the earth
o Compares the intrinsic brightness of a star by comparing stars
at a common distance
o m-M is known as the distance modulus.
o Is a measure of distance
o Represents the inverse square law in magnitudes.
Surveyor’s method
 Used to measure the distance to an object
o Measure the change in position angle as a change of vantage
point.
o Also known as triangulation.
o Angles ( a & b) and the baseline give distance (d) to object.
o Approximate distance is given by d=b/t tan
Astronomer’s triangulation method
 Search for a star that moves when viewed 6 months apart.
o Baseline is given by earth’s orbit
 Baseline=2 AUs
o shift in position is the parallax
Stellar Parallax
 Used to measure the distance to stars.
o First technique in a chain of techniques to measure distance.
o Can only be used on nearby stars.
o Baseline is earth’s orbit.
o 1 parsec =3.26 light years
o 1 parsec is defined to be the distance to a star whose parallax
is 1 “.
 If baseline is 2 AUs and parallax is given in arcsec (“) then
o D=1/p
o Where d=distance to the object in parsecs
o P= parallax in arcsec.
Example find the distance to alpha Centauri if its parallax is 0.75”
 D= 1/.75”=1.33 parsecs(pc)
 Now convert to light years
 1 parsec =3.26 light years
 1.33 x 3.26 light years = 4.34 light years
 Even the nearest star has a parallax less than 1”
 This tech can only be used for star about 100 parsecs away…
Hertzsprung-Russell Diagram
 Plot of a star’s Luminosity versus Temperature/spectral type
o Stars found in specific regions of the H-R diagram
o Main sequence
 About 90% of stars
 Diagonal across H-R diagram
 Giants and supergiants
o Cool T/high L
 Cool T means low surface
 White dwarfs
o Hi
Line Strengths
 Temperature measures the average kinetic energy per atom
o Collisions between atoms can excite electrons in atoms.
o These excited electrons will emit photons.
o Temperature determines the typical energy an electron has in
an atom.
o Hotter stars have elections with greater energy
  higher states in atoms

Balmer Thermometer
o Transition from n>2 to n=2 state
o Need eno0ugh energy to excite electrons into n=2 and
greater states
o Difficult to do for cool stars








To excite and electron from n=1 to n=2 takes 10.2 eV.
Few collisions/photons have this energy
Few electrons make it to the n=2 state
Metals
o Everything but Hydrogen or Helium
o Calcium is an example
o Outer atoms are weakly bound
 First they are far from the nucleus
 Second shielded by several electrons interior
o Strong for cooler T stars
 Don’t require the energy to excite like H
Other metals are similar to Calcium
Coolest starts allow molecules to form
Helium extremely difficult to excite
o Seen only in the hottest stars
Ionized Helium
o Helium with one electron stripped
o Like H but 1 (-) electron held in orbit by 2 (+) protons.
o VERY tightly bound
o Seen only in the hottest (O) stars
Masses of Stars
 How do we measure the mass of a star?
o Look to the gravitational influence.
o Binary Stars
 2 starts in orbit about each other
 Use gravity to determine the mass
 Newton’s (modified) Kelpler’s 3rd Law



(M1+M2) P2yrs=a3AU
M1 is the mass of object 1 in M [Solar Units]
M2 is the mass of object 2 in M [Solar Units]

Both “P” and “a” are same units as before. (years
and Aus)
1M=1.9891 x 1033 g (see Appendix A-5)

Types of Binaries
 Visual Binaries
o Both starts seen in a telescope

 Able to follow orbit visually
 Usually takes many years for an orbit to complete
 Can get mass of both stars.
o Example is the star Sirius (the brightest star in the night sky)
o Orbit Center of Mass
 Position in space where the system’s mass behaves as if
it were concentrated at a point.
 Can also be called the center of gravity
Spectroscopic Binary
o Uses Doppler shift
o Only one star visible
o Lines shift as a function of time
 Gives line of sigh velocity
 Can see 1 set of shifting lines
 SB1
 Can see 2 sets of shifting lines
 SB2

Eclipsing Binary
o See only one star
o One star eclipses the other (Earth nearly in orbital plane.)
o Measure period from light curve
 Brightness of star as a function of time
 During eclipse see only 1 of two stars.

Distance from parallax
o P=0” .38
o 2.64 pc

has companion names Sirius B
o white dwarf with radius of about that of the Earth.
o 0.0084 R (0.92 R)


One orbit completed every ~50 years
Masses
o Sirius A has mass 2.02 M
o Sirius B has mass 0.98 M
Sirius
Eclipsing Variable Star
  Persei
o The demon or winking star.
Astronomy 100
3/4/2009 8:31:00 PM
ISM

Dark clouds
o Regions where no stars appear on the sky
o Cloud is non-luminous
 Opaque
 Made of dust particles
 Very cold gas with typical T = 10-30 K
 Presence of molecular Hydrogen (H2)
o Most likely regions where star formation occurs
o Often called molecular clouds
o Contains dust grains and complex molecules
o Examples: Horsehead Nebula, Barnard’s Dark Nebula (B68)
Interstellar Reddening
 Same phenomenon causes the sunsets to have a red color
o Blue light is preferentially scattered by the dust in the cloud
o Removes blue light from line of sight
o Red light makes it through
o Color is therefore red
Why is the sky blue?


Sun light enters Earth’s atmosphere
Blue photons are scattered more easily than longer wavelengths
and blue photons enter your eyes from all directions, making the
sky look blue.
 Dust in atmosphere scatters the blue light but lets the red light go
through.
Dark Clouds
 Gravitationally stable
o Outward gas pressure=inward gravitational force
o Need something to initiate cloud collapse
 Shock wave
 High velocity gas meets low velocity gas
 Causes gas compression
 Examples
 Supernova explosions
 Spiral arms in galaxies
 Collisions between clouds

 Collisions between galaxies
Shock wave initiated cloud collapse
Formation of Protostars
 Internal pressure of cloud not able to halt gravitational collapse.
o Gravitational collapse happens very quickly
 Few million years
 0.1% lifetime of star
 depends on mass of star generated
 more massive stars collapse faster
 O stars collapse fastest—most massive

M stars collapse slowest—least massive
Bok Globules
 Small dark clouds seen in emission of nebulae
 Possible sites of collapsing clouds
Ideal Gas Law
 Described the behavior of a gas
o PV=nkT
 Where P=pressure
 V=volume
 n=number of particles
 k=Boltzmann constant=1.381 x 10-16 erg K-1
 T=temperature
 Describes relation between Pressure, Temperature, and Volume.
Cloud Collapse
 Large Molecular Hydrogen cloud collapses
o Angular momentum problem—Ice skater effect
o Majority of matter falls into core where star forms
o Angular momentum causes some matter to fall into a disk

around central core
Clouds heats up converting a gravitational potential energy in to
kinetic energy of atoms
o Ideal gas law says that if V and T then P must 
o Presence of dust and molecules critical to cloud collapse
 Allows cloud to cool and allows collapse
 Emission from dust and molecules in light transparent
to cloud.

Core of cloud heats up
o Reaches a few million K

Nuclear fusion begins
 Begins conversion of Hydrogen into Helium
 Proton-Proton Chain
 Source of power for majority of stars lifetime
Solar Nebula Theory
 Angular momentum of cloud around center of the Galaxy causes
cloud to flatten as it collapses
o Central region attracts most of matter—location of Sun





o Disk forms planets
 Inner regions heated by Sun
 Outer regions remain cool
Inner regions of disk by the Sun
o Only materials with high condensation T form planetesimals
 Silicates, Iron, Nickel, etc.
 Build in size like rain drops in a cloud
o Terrestrial Planets
 Typical composition like Sun without H and He
 Formed in High T region of Solar nebula
Outer planets formed in cooler outer regions of Solar nebula
o Consist mostly of Hydrogen and Helium
 Composition similar to Sun
 Jovian Planets
 Low density, large in size
 Many moons and often ring systems
Terrestrial Planets
o Differentiation
 Heavier elements fall to core
 Lighter materials found in outer regions
Jovian Planets
o Large atmospheres
o Heavier elements form core
Terrestrial planets have thin atmospheres
o Earth cannot hold on to Hydrogen
 Interiors liquid and help replenish atmosphere
 Solid interiors do not replenish atmospheres
o Jovian planets keep gasses.
Protostellar Disks
 Star forms in central core
 Disk forms because angular momentum prevents core matter from
collapsing into core
 Nuclear fusion begins
o Jets and stellar winds help to clear out protostellar disk
o Much like the formation of rain droplets,
 Numerous examples of protostellar disks
o Protostellar disk collimates stellar winds and jets
Stellar Structure
 Hydrostatic Equilibrium
o Sun’s radius and structure is constant
 Energy generation in equilibrium with inward
gravitational force
o Inward gravitational force=outward gas pressure
o High pressure seen in core
 Requires high temperature to produce high pressure
 Determines energy generation
o Outer regions lower pressure
 Lower temperatures
 No energy generation
Hydrostatic Equilibrium
 Determines structure of star
o Determines surface temperature
o Determines amount and rate of energy generated
o Determines what zones are radiative and which are


convective
The more mass the greater the gas temperature has to be to
balance the gravitational force
o More massive stars are hotter
o Less massive stars are cooler
Greater mass means higher energy output
o L=4piR*F and the flux F=T4
o Burn more hydrogen to keep up energy output


o Estimate lifetime of a star
 If 10% of total mass is available to fusion, and .07% of
that mass is converted to energy then,
 Etotal=0.0007 M*c2
 Etotal/L* gives lifetime.
High mass stars have high luminosity, short lifetimes
o High surface flux (F=T4), large surface areas.
o Thus short lifetimes
Low mass stars have low luminosities, long lifetimes
o Low surface flux, small surface areas
o Thus long lifetimes
Main sequence
 Marked by the ignition of hydrogen burning in the core of a star
o Either by p-p chain or CNO cycle
o Expected lifetimes
 If we assume .07% of 4H He is converted to energy
and 10% of mass of star undergoes conversion in core
 Etotal=0.1*0.07 M*c2=.0007 M*c
Star evolution

Main sequence stars
o Stars that are burning He in their cores:
 P-P Chain in cooler stars
 CNO cycle in hotter stars
 Carbon acts as a catalyst to convert 4HHe
 More complicated than P-P Chain
Main Sequence Lifetimes
 Age of the Universe is = 1.4 x 10^10 years (14 billion years)
o M Stars live longer than the age of the Universe
o O Stars have a lifetime much shorter than the Universe
o As one moves from O type stars to M type stars
Post-Main Sequence Evolution
 Depends on the Mass of the star
o Mass determines the gravitational force present
o Determines the interior structure of star
o Lifetime of a star is a constant struggle between gas pressure
and gravity

End of the Main Sequence
o When the hydrogen is exhausted in the core
 No energy generation
 Nothing to halt gravitational collapse
o Star evolves off the main sequence
Low-Mass Stellar Evolution
 For stars with M0.5 M
o Main sequence lifetime is longer than the age of the Universe
o Never get to Helium burning
o Evolve off main sequence to form helium white dwarf stars

White Dwarfs
o Cooling star with no energy generation
o Gravity forces all electrons into lowest energy states
 Star supported by degeneracy pressure
 Different from thermal/gas pressure—temperature
insensitive
Intermediate Mass Post-Main Sequence Evolution
 For stars with M=1-5 M
o Core of star collapses
o Nothing to support the star under the gravitational force
o core heats up as core contracts
 consists entirely of He
 He requires high Temperature to burn
o Material immediately outside core is rich in H
 Also collapses and heats up
 Eventually temperature is reached when H begins
to fuse into He
 Hydrogen shell burning


Outer portions of star swell and cool
o Evolves to upper right of H-R Diagram
o Will be found in Giant and Supergiant regions
o Will reach a point when He ignites in the core
Eventually Core reaches temperature Tcore = 100 million K
o Hydrogen ignites in helium flash
 Star shrinks during Helium burning
Establishes “Helium main sequence” called horizontal
branch
o Triple Alpha Helium burning
 3 He  1 C.

 Ignites at 100 million K
Open (Galactic) Clusters
 Groupings of ~102-104
o Born together of the same cloud at the same time
o Stars of the disk of The Milky Way Galaxy
o Often associated with nebula emission
The Pleiades (M45)
 Young star cluster of ~100 million years olds
o Most of the Stars are still on the Main Sequence
o Under the assumption that the stars formed at the same time
 Turn off determines cluster age
 Turn off says Pleiades is ~100 million years old
Mass Sequence (MS) Lifetime
 Main Sequence turn off
o A star of a given mass spends a certain amount of time on
the MS
o Then they evolve to the upper right after H is spent in core
(end of MS)
o The point where stars are running out of H in their cores
forms the “turn off” point
Estimating the Ages of Clusters
 Location of turn off gives age of the cluster
o Range of ages
Global Star Clusters

Oldest object known
o Contain 105-106 stars
o Consists of Stars not from the disk of The Milky Way Galaxy
 Metal poor stars
 Oldest stars
 Typical diameters ~25pc
o Main Sequence turn off gives ~12-14 billion years old
o Universe is ~12-14 billion years old
Post-Main Sequence Evolution
 Star evolves to the upper right a second time.
o He in core is exhausted
 Carbon core contracts
 He and H shell burning around contracting carbon core.
 Second time is Asymptotic Red Giant (AGB) branch.
o Double shell burning giant ( He and H shells)
o Begins to blow off outer atmosphere.
Planetary Nebula (PN)
 Called Planetary nebula because looked like outer planets of the

solar
o
o
o
o
After
o
o
system
Large and often green in color.
Often round shape
Green color from oxygen transition
Numerous examples
AGB
Outer atmosphere blown off at speeds of 10-30 km/s.
Stellar remnant is white dwarf
 Slowly exposed


Degeneracy pressure
 Gravity all electrons into ground state.
Very hot with lots of UV radiation
 Can have temperatures of ~150000 K.
 Illuminates expanding atmosphere
 See strong transitions of Oxygen , and heavier
elements.
White Dwarf
 Eventually PN expands and disappears
o Usually takes ~10,000 years.
o Cooling He or C White Dwarf (WD) left behind
o Cooling track for WD is a constant radius line on H
High Mass Stellar Evolution
 Extremely Hot cores (M*>5 M circle with dot)
o Hydrogen burning dominated by cno cycle.
o Burn more rapidly
Helium Capture in Supernovae

After burning He core
o Core Shrinks
o Rapid helium capture begins
o Produces heavier elements like O, si, Fe.
 Elements heavier than Fe cannot be produced.
o No more energy source
o Supernova (SN)
Iron—The Final product
 56Fe is the most tightly bound nucleus
o Fusion reactions producing products lighter than Fe are
exothermic (releases energy)
o Fission reactions from nuclei heaver than Fe are exothermic
o To produce elements heavier than Fe through fusion is
endothermic
Chandrasekhar Mass Limit
Mass of neutron star cannot exceed 1.4 M

o Mass limit of degenerate matter
o Limit where e- are forced into nucleus and neutralize protons
o White Dwarfs cannot exceed or electrons are forced into
protons to form neutrons
o Typical for stars whose initial masses are 5M<M*<8M
Neutron Stars
 Not even degeneracy pressure is able to hold the star against
gravity
o P+en+
o Result in generation is a Supernova (SN)
 Totally energy releases ~1050 ergs
 Most luminous event in the Universe

SN can be as luminous even more luminous than
the entire galaxy in which it resides
 Total luminosity on the order of 1011-12L
Masses are on the order of 1.4M to 3M

o Radius ~10 miles
 Incredibly high densities
 Rapidly rotating—ice skater effect
Magnetic fields are incredibly high

o Entrained in collapses material
o Allow light to escape thought magnetic poles
o If points at us we see a flash
Supernova
 Matter collapses on Fe stellar core
o Electrons are forced into nucleus
o Falling matter is incredibly dense.
 Even opaque to neutrinos
 Neutrino pulse from p + e  n +  pushes falling
matter
o Result is a violent explosion
 About as luminous as the host galaxy for ~1 week
 Totally energy released ~1050 ergs
 Almost equivalent to the total energy released in the
stars entire lifetime
Pulsars
 A neutron stars whose magnetic pole points toward Earth
 Light produced by electrons accelerated by magnetic field
o Synchrotron Radiation
o Beamed along magnetic field poles
Synchrotron Radiation
 Electrons circle magnetic fields
o Highly relativistic (v=0.9c)
o Velocities accelerated
o Accelerated particles radiate
o Typical emission in Radio
o Can be in optical and even high energy emission
High Mass Stellar Evolution
 If M*>8M then Fe core is >3M
o Neutron degeneracy cannot stop gravity
o Still produced neutrino pulse from neutron production
 However, matter collapses to a singularity
 Result is a Black Hole
o Matter so dense not even light can escape
Black Hole (BH)
 Gravity’s ultimate victory over mater

Structure
o Singularity
 Point where all the mass is concentrated
 No finite size
Black hole Structure
 Event horizon
o Point of no return
o Distance from singularity where escape velocity is the speed
of light [c]
 For each M in the black hole Event horizon has a radius



of 3 km
 3M black hole has an event horizon radius of 9 km
o radius known as the Schwarzschild Radius (Rs)
o Interior Laws of physics are unknown!
Photon sphere
o Radius where the circular orbit velocity is the speed of light
Rotation
o Drag space time with it and causes ergosphere
o Objects within the ergosphere cannot stand still
 So if no light can escape a black hole, how do we see one?
Black hole Candidates
 Cannot see black hole itself
o BH is part of a binary system
o Matter accreted onto BH
o Matter is
Astronomy 100
3/4/2009 8:31:00 PM
15 Q’s From each test

Hit the most missed Q’s 50% on final
What did tyco do? Why was it important? Hired Kepler, gave Keplor is great
observations of Planets. Disproved Copernican model, belief before was of
perfect circles, Kepler believed in elliptical orbit proved mathematically by
Newton.
Kepler law 2nd-equal area as long as time is same areas will be the same.
Planets do not move around orbit at uniform rates….Faster when closest
slowest when farthest.
Kepler law 3- P^2 = a^3 - Period in years = AU
Semi-major axis=longest line that can be drawn in an ellipse, always
includes the floci
Earth’s semi-major axis = 1 AU
NEWTON
Newton proved all of Kepler’s laws using=
Newton =universal law of gravity always 2 objects
Laws of Motion
1=law of inertia still or moving an object will stay in that state unless
another force acts upon it.
2-E =ma
3- every action has an equal and opposite action
Invented calculus
Discovered the light spectrum.
Basically invented reflecting telescope.
-What are to types of telescopes, reflecting and refracting
Mirrors versus glass
Refract bend light to focus-suffer from chromatic aberration.
Reflect light to focus.
Modern day all reflecting telescopes.
Arc min/seconds
Has to do with angles 360deg=1rot 1 deg=60 arc min 1arcmin=60 arc sec
1deg=3600arc sec angular measurement.
Parsec= a unit of astronomical length based on the distance from Earth at which
stellar parallax is 1 second of arc. The distance you must have to have a parallax
of 1 arc sec.
GALELIAO
-moon not perfect
-discovered Saturn’s rings-thought they were satellites
-discovered Venus’ phases supported the heliocentric model
-discovered moons that orbited Jupiter. 4 Galilean moons
Copernicus
 Introduced the Heliocentric model
 Copernican revolution= all observers must observe the same thing
no matter what planet you are on. Physics are the same
everywhere.
Ptolammic = geocentric 1500 yrs turned over and revolutionized astronomy.
Mass of star determines everything about a star.
Determines-temp, luminosity, evolution, magnitude,ect
Determines all of this because it determines the gravitational force when the
star is in the gas pressure pushes out and the gav force inward Hydrostatic
equilibrium.
*Ideal Gas Law
star on main sequence is burning hydrogen converting 4 H to 2 He when it
has converting H it goes off to upper right gets cooler and brighter becomes
helium white dwarf when less than 1 solar mass.
1- 5 solar mass reaches hot enough to ignite He becoming a carbon core in
shell around burning He it is Burning H basically becomes White Dwarf of
Carbon
opposite of making a snowball.
Above 5 does not go to horizontal branch burns through heavier elements till
it produces an iron core creating a super nova. 5-8 neutron star.
Above 8 equals a black hole.