Astronomy 223 Tuesday, Thursday 3:50 5:00 pm Tom Burbine tburbinemtholyoke.edu Darby Dyar mdyarMtHol

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Astronomy 223Tuesday, Thursday350 500
pmTom Burbinetburbine_at_mtholyoke.eduDarby
Dyarmdyar_at_MtHolyoke.edu
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I am talking at Astronomy Dept., Smith College

• Friday, Oct. 26, 1215 to 1 pm
• Clark Science Center
• McConnell Hall, Room 412
• http//www.smith.edu/map/ - Map of Campus
• If you go, I will replace your lowest HW score
  with a 100
• Email me if interested (they are buying pizzas)

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• Midterm average 82
• Grades ranged from a 48 to a 98
• I will give a retake of the exam next Tuesday
  (before or after class).
• Higher grade counts
• Email me to set up a time

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What percentage of the class didnt know the
correct order of the planets?

• A) 47
• B) 31
• C) 22
• D) 14

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What percentage of the class didnt know the
correct order of the planets?

• B) 31
• C) 22
• D) 14

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What percentage of the class didnt know the
correct order of the planets?

• B) 31
• C) 22

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What percentage of the class didnt know the
correct order of the planets?

• B) 31

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• For students who knew the order of the planets,
  average was 86
• For students who did not know the order of the
  planets, the average was 72

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Seasons
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Private Universe

• http//www.learner.org/resources/series28.html

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What causes seasons?

• The tilt of the Earths axis relative to the
  ecliptic

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Seasons
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Solstices

• Summer Solstice June 21 Northern Hemisphere
  receives its most direct sunlight
• Winter Solstice December 21 Northern
  Hemisphere receives its least direct sunlight

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Equinoxes

• Sun shines equally on both hemispheres
• Spring Equinox March 21 Northern Hemisphere
  goes from slightly tipped away from the Sun to
  slightly tipped towards
• Fall Equinox September 21 - Northern Hemisphere
  goes from slightly tipped toward from the Sun to
  slightly tipped away

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• Why does the orbital difference not matter?

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Reasons

• There is only a 3 difference in the distance
  from the Earth to the Sun at its farthest and
  closest point
• The Earth is actually closer to the Sun in the
  winter than in the summer

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Long Term Changes
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Precession

• Earth precesses like a top
• Precession - phenomenon by which the axis of a
  spinning object (e.g. a part of a gyroscope)
  "wobbles" when a torque is applied to it

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Forces

• For a top, the force is gravity, which is trying
  to pull the top down
• For the Earth, the forces are due to the pull of
  the Sun and Moon, which is trying to align the
  Earths axis with the ecliptic

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Because of precession

• The position of a star that corresponds to the
  North Celestial Pole changes

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Where does the light from the Moon originate?
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Answer

• It reflects light from the Sun

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Earth-Moon System

• Earths diameter is 12,742 km
• The diameter of the Moon is 27 of the Earth
• The average distance between the Earth and Moon
  is approximately 30 times Earth's diameter.
• Orbit of the Moon is inclined 5o to the orbital
  plane of the Earth

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Eclipses

• Lunar Eclipse Moon passes through Earths
  shadow
• Solar Eclipse Moons shadow falls on Earth

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• Umbra light totally blocked
• Penumbra light partially blocked

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Lunar Eclipse
Passing through Earths shadow
Why is the Moon red? Shouldnt it be totally dark?
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Why is the Earth Red?

• Even though Earth blocks the moon from direct
  sunlight during an eclipse, some sunlight is
  refracted, or bent, by the Earth's atmosphere and
  illuminates the moon.
• Most of this refracted light is orange or red

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• Should you look directly at a Lunar Eclipse?

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YES
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Should you look directly at a Solar Eclipse?
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No!!!!!!
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New Moon
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• http//www.almanac.com/astronomy/moon/index.php

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Eclipses
http//www.longwood.edu/staff/dunningrb/research/v
python/moon_orbit.html
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http//en.wikipedia.org/wiki/ImageSolar_eclips_19
99_4_NR.jpg

• Solar eclipses occur approximately every 18
  months
• However, they recur (on average) at any given
  place only once every 370 years
• Moon's umbra moves eastward at over 1700 km/h
• Every year, there are at least two lunar
  eclipses.
• Can be viewed anywhere on the night side of the
  Earth

http//home.cogeco.ca/astrosarnia/Photos/Lunar20
eclipse20binocular.jpg
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Planets

• There are 5 planets observable without a
  telescope

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Planets

• Planets is from a Greek word meaning wanderer

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What is the brightest planet in the skyand why?
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What is the brightest planet in the sky and why?

• Venus
• Because it is so close to the Earth and its
  clouds are very reflective (high albedo)

http//www.solarviews.com/browse/venus/venusmar.jp
g
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http//www.space.com/spacewatch/070914_ns_venus_mo
rning.html
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How do we know that the planets were considered
very important by the ancients?
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How do we know that the planets were considered
very important by the ancients?

• Named for Gods
• Days of the week are named after the planets
• Constellations (e.g., Pisces, Aries, Taurus) in
  the Zodiac are the ones that the planets pass
  through

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Why are there 7 days of the week instead of 5?
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Why are there 7 days of the week instead of 5?

• The ancients also included the Sun and the Moon
  as planetary bodies that they could see in the
  Sky

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Days of the Week
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Why Thor and not Jupiter?
http//en.wikipedia.org/wiki/Journey_into_Mystery
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• These names come to us originally from the Greeks
  and Romans, who named the days of the week after
  their gods.
• The Germanic languages substituted Germanic
  equivalents for the names of four of the Roman
  gods

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• Sunday Sun's Day. The Sun gave people light and
  warmth every day. They decided to name the first
  (or last) day of the week after the Sun.
• Monday Moon's Day. The Moon was thought to be
  very important in the lives of people and their
  crops.
• Tuesday Tiw's Day. Tiw, or Tyr, was a Norse god
  known for his sense of justice. He was the Norse
  god of War.
• Wednesday Woden's Day. Woden, or Odin, was a
  Norse god who was one of the most powerful of
  them all.
• Thursday Thor's Day. Thor was a Norse god who
  wielded a giant hammer.
• Friday Frigg's Day. Frigg was a Norse god equal
  in power to Odin and also his wife.
• Saturday Seater's Day or Saturn's Day. Saturn
  was a Roman god.

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Models

• When you have a model of how something works, you
  should be able to predict what will happen
• If observations do not fit the model, either the
  observations or the model is wrong
• The ancient astronomers wanted to predict the
  positions of planets in the sky

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Greek model
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Apparent Retrograde Motion backward motion
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Retrograde Motion
http//www.nmm.ac.uk/upload/img/retro.gif
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Stellar Parallax

• Stellar Parallax The apparent shift in the
  position of a nearby star (relative to distant
  objects) that occurs as we view the star from
  different positions in the Earths orbit of the
  Sun each year

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The distance the star moves is greatly
exaggerated in this figure. Stellar parallax can
only be seen by a telescope.
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Ancient astronomers could not detect stellar
parallax

• If Earth orbited the Sun, ancient astronomers
  believed that they would see differences in
  angular separation of stars as the Earth rotated
  around the Sun
• Since they saw no changes in angular separation
  of the stars, they assumed the Earth was the
  center of the universe
• They could not fathom that stars are so far away
  that stellar parallax is undetectable by the
  human eye

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Ptolemys (100-170 AD) Model of the Universe
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Nicholas Copernicus (1473-1543)

• Copernicus came up with a model that the Earth
  revolves around the Sun
• Similar to what Aristarchus (310 230 BC)
  thought 2000 years before
• However, Copernicus models did not match
  observations since he wanted everything to
  arouind in perfect circles

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Tycho Brahe (1546-1601)

• Tycho Brahe was the greatest naked eye observer
  of all time
• He lived before the invention of the telescope
• His observations of the alignment of Jupiter and
  Saturn occurred two days later than when
  predicted by Copernicus
• Tycho came up with a model where the planets
  orbit the Sun but the Sun orbits Earth

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Johannes Kepler (1571-1630)

• Tried to match circular orbits to Tychos data
• Couldnt do it
• Because Tychos observations were so good, Kepler
  had to come up with a new model

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Kepler was trying to match an orbit to Tychos
observations of Mars

• If I believed that we could ignore these eight
  minutes of arc, I would have patched up my
  hypothesis accordingly. But, since it was not
  permissible to ignore, those 8 minutes pointed to
  the road to a complete reformation in astronomy.
• Kepler came up with his 3 laws of planetary motion

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Keplers 1st Law

• The orbit of each planet about the Sun is an
  ellipse with the Sun at one focus (there is
  nothing at the other focus)

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Differences between ellipses and circles
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Definitions

• Perihelion planet closest to the Sun
• Aphelion planet farthest from the sun
• Semi-major axis the average of a planets
  perihelion and aphelion distances

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Keplers 2nd law

• As a planet moves around its orbit, it sweeps out
  equal areas in equal times.
• This means that the planet travels faster when it
  is nearer the Sun and slower when it is farther
  from the Sun

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• http//galileoandeinstein.physics.virginia.edu/mor
  e_stuff/flashlets/kepler6.htm

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Keplers 3rd Law

• More distant planets orbit the Sun at slower
  average speeds, obeying the precise mathematical
  relationship
• p2 a3
• where p is a planets orbital period in years
  and a is the average distance from the Sun in
  astronomical units.

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Calculations

• The period for the Earth to go around the Sun is
  1 year
• The distance of the Earth to the Sun is
  1 Astronomical Unit

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How long does it take Jupiter to go around the Sun

• If Jupiter is 5.2 Astronomical Units from the
  Sun, how long does it take Jupiter to go orbit
  the Sun once
• p2 a3 5.23 140.6
• p v140.6 11.9 years

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Another example

• Mercury is 0.4 Astronomical Units from the Sun.
• How long does it take Mercury to orbit the sun
  once?
• A) 1 year
• B) 3 months
• C) 9 months
• D) 5 years

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The calculation

• p2 a3 0.43 0.064
• p v0.064 0.25 years

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You can calculate a planets orbital speed

• Since you know a planets orbital distance
• And you know its orbital time
• You can calculate a planets average orbital speed

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• Planets orbit the Sun counterclockwise (if you
  are looking down toward the Earths Northern
  Hemisphere)

http//csep10.phys.utk.edu/astr161/lect/solarsys/r
evolution.html
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Arguments against the Sun being the center of the
solar system

• 1) If the Earth was moving, objects such as birds
  and clouds would be left behind as the Earth
  moved
• 2) The heavens must be perfect and unchanging.
  Noncircular orbits do not fit this model
• 3) Stellar parallax would be observable

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Galileo Galilei (1564-1642)

• He was able to figure out answers to these
  arguments
• 1) Things in motion tend to remain in motion.
• 2) He used a telescope to see sunspots on the Sun
  and features on the Moon.
• 3) Galileo found that stars were more numerous
  and more distant than imagined

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He also

• He discovered the moons of Jupiter and saw that
  they were orbiting Jupiter
• Proving that bodies could orbit other bodies
  besides the Earth

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Galileo also found that Venus orbited the Sun
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Acceleration

• Acceleration is when your velocity is changing
• Velocity not changing, no acceleration

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Difference between mass and weight

• Mass is the amount of matter in your body
• Weight is the amount of force acting on your body
• So on the Moon, you would have the same mass as
  on Earth but weigh less on the Moon since the
  Moon is less massive than Earth

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Who came up with the first understanding of how
gravity and forces really work?
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Isaac Newton (1642-1727)
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Isaac Newton (1642-1727)

• Supposedly saw an apple fall to the ground
• He then understood that gravity was universal,
  meaning it affected both the planets and us on
  Earth
• Came up with 3 Laws of Motion

http//homepages.wmich.edu/korista/newton-apple.j
pg
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1st Law

• In the absence of a net (overall) force acting
  upon it, an object moves with a constant velocity
• An object at rest remains at rest
• An object in motion tends to remain in motion
  unless a force is acting upon it

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2nd Law

• Force mass x acceleration (Fma)
• Units of Force kg?m/s2 newton
• So much do you weigh
• Say your mass is 100 kg
• F 100 kg x 9.8 m/s2
• F 980 Newtons

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3rd Law

• For any force, there is an equal and opposite
  reaction force
• Gravity is holding you on the ground
• The ground is also pushing back up on you with
  the same amount of force

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Universal Law of Gravitation

• Every mass attracts every other mass through the
  force called gravity
• Newton came up with this formula
• F G M1 M2
• d2
• M1, M2 are the masses of the two objects
• d is the distance between the objects
• G constant 6.67 x 10-11 m3/(kg?s2)

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So what should you know about this formula

• F G M1 M2
• d2
• The force of attraction between any two objects
  is directly proportional to the product of their
  masses
• The force of attraction between two objects
  decreases with the square of the distance (d)
  between their centers
• G is a very small number

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What is the attraction of two people in this room?

• F G M1 M2
• d2
• Say their masses are both 100 kg
• Their distances are 10 meters apart
• F 6.67 x 10-11 m3/(kg?s2) 100100 kg2/(1010
  m2)
• F 6.67 x 10-9 N 0.0000000067 N
• Remember the person weighs 980 N

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• F G M1 M2
• d2
• How would the force between the two people change
  if they were only 5 meters apart instead of 10
  meters?
• A) Stay the same
• B) Double (Increase by a Factor of 2)
• C) Quadrupul (Increase by a Factor of 4)
• D) halve (decrease by a factor of 2)

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• F G M1 M2 G M1 M2 4 G M1 M2
• (d/2)2 d2/4
  d2
• How would the force between the two people change
  if they were only 5 meters apart instead of 10
  meters?
• A) Stay the same
• B) Double (Increase by a Factor of 2)
• C) Quadrupul (Increase by a Factor of 4)
• D) halve (decrease by a factor of 2)

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Can you use this formula to calculate
acceleration of gravity?

• F M2a G M1 M2 you are M2
• r2
  M1 is the Earths radius
• a G M1
  r is the Earths radius
• r2
• a 6.67 x 10-11 m3/(kg?s2) (6.0 x 1024 kg)
• (6.4 x 106 m) (6.4 x 106 m)
• a 9.8 m/s2

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Escape velocity

• Velocity above this will allow an object to
  escape Earths gravity
• v square root(2 x G x M)/R
• v square root(2 x 6.67 x 10-11 m3/(kg?s2) x
  (6.0 x 1024 kg)
• (6.4 x 106 m)
• v square root 1.25 x 108 m2/s2
• v 11.2 x 103 m/s 11.2 km/s

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Any Questions?