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Saturday Day 2 1-5 PM

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Saturday Day 2 1-5 PM. Math Review, Computers and the Internet, and ... Geocentric universe. Uniform circular motion (assumption) BUT planetary speeds varied! ... – PowerPoint PPT presentation

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Title: Saturday Day 2 1-5 PM


1
Saturday Day 2 1-5 PM
  • Math Review, Computers and the Internet, and the
    History of Astronomy

2
Math Review
  • Solving for a given variable (and why)
  • ymxb
  • Subtract/Add the stuff you dont want on this
    side
  • Divide what you want moved to the other side
  • EMC2
  • IF you wanted to solve for C
  • Divide by M
  • Take Square Root (to move square to the other
    side)

3
Math stuff
  • Cartesian Graphing (linear scales)
  • A clear way to visualize data
  • 2-D graph X horizontal, Y vertical
  • Equal spacing on X and Y axis
  • Units can be different between X and Y
  • Example and Exercise

4
Math and more Math
  • Significant Digits
  • Allows us to communicate confidence
  • Can carry through arithmetic
  • Keeps you from writing down all the junk in the
    calculator screen!
  • Three-four decimal places usually enough unless
    precision is really needed
  • Pi 3.1416
  • Addition 2.1400 1.1 3.24? Really 3.2
    accurately since 1.1 might be 1.11 or 1.16 (its
    unknown)
  • Multiplication add up all the significant
    digits
  • 2.1401.00 2.14000 (pretty confident!)
  • Round the calculator screen (four places)
  • 5.684939033942 5.6849 (if fifth decimal is lt5
    round down, if it is gt or 5 then round up
  • 5.684979033942 5.6850

5
Math continued
  • Ellipses
  • FFoci, asemi-major axis, ccenter

6
Math continued
  • Scientific Notation (and why)
  • Shorthand for VERY large or small numbers
    (essential)
  • Count the zeros and express the zeros as a power
    of 10 but REALLY you are moving the decimal point
  • 1,000,000,000,000 1012 1.0E12
  • 3,150,000 3.15X106 3.15E6
  • .0000001 10-7 1.0E-7
  • .000000000056 5.6X10-11 5.6E-11

7
Units for everyone
  • Often units are not what you need to do a
    calculation (the distances must all be the same
    unit, the times must all be the same unit, the
    energy must all be in the same units etc.)
  • The conversions in the () are all 1 (but just
    different units
  • Page A-3
  • Set up a ratio to change the units
  • Original number (conversion ratio)
  • Ex. 3 inches (2.54cm/1 inch) -- set it up so
    the unit you want to kill is on the opposite side
    (top or bottom) so it cancels
  • Ex. 4 m/s (1 foot/.3048m)(1 mile/5280
    foot)(3600 seconds/1 hour) 8.96 mph
  • Temperature must be converted using the equations
    in Table A-4

8
mAtH
  • Using a scientific calculator
  • In Class EXERCISE
  • The SOFTWARE in the textbook
  • Quiz 2 (Planetarium and Math)

9
The History of Astronomy Saturday PM
  • Pre-Copernican Astronomy
  • Astrology/Astronomical Observations
  • Babylonians, Chinese, Arabia Region
  • Aristotle 384 to 322 B.C. in Greece
  • His work persisted for almost 2000 years
  • Created a Philosophy not science
  • Assumptions
  • The Earth was changeable and imperfect, the
    heavens were perfect and unchangeable
  • Crystalline spheres pg 44 Fig top right
  • No parallax
  • Bowl shaped sky

10
History Continued
  • Eratosthenes (?273-192B.C.) f Project Idea f
  • Determined the size of the earth using sticks at
    the Summer Solstice
  • Was accurate to within 1
  • Ptolemy 140 A.D.
  • Mathematical model of the universe
  • Geocentric universe
  • Uniform circular motion (assumption)
  • BUT planetary speeds varied! RETROGRADE MOTION
    pg44 figure at bottom
  • Solution Epicycles. Pp45 figure at bottom
  • This model lasted for 1500 years

11
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12
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13
History Continued See Fig4-16 Page 60
  • Copernicus 1473-1593
  • Long church affiliation
  • Uncle was an important bishop in Poland
  • Lived in quarters adjoining the cathedral in
    Frauenburg
  • Heliocentric model (sun central model)
  • De Revolutionibus Finished in 1530
  • Explained planetary motions without epicycles
  • BUT didnt predict the motions well still
  • Perfection still expected
  • Circular orbits modeled, real orbits ellipses
  • He had to add small epicycles to fix it

14
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15
History continued
  • Post-Copernican Astronomy
  • Tycho Brahe 1543-1601
  • Measured positions of planets in the sky
  • 1572 a new star appeared (Tychos supernova)
  • Measured the parallax of the nova- no parallax!
  • Broke the perfect universe assumption
  • He saw no parallax in the stars concluded
    Copernican model poor
  • Without telescope measured 777 star positions
  • Planetary positions daily for 20 years
  • Hired Mathematicians to work out the orbit
    Kepler

16
History continued
  • Johannes Kepler (1571-1630)
  • Poor beginning
  • Mystical Almanac (five solids six planets)
  • Illegally kept Keplers books
  • 1609 the book Astronomia Nova (New Astronomy)
  • Planets move faster when nearer the sun
  • Laws of planetary motion
  • Very close to stating the law of mutual
    gravitation (Newton later)

17
History continued
  • Keplers Three Laws
  • Ellipse solved the motion problems LAW 1
  • Foci
  • Semimajor axis, a
  • Eccentricity, e (foci dist/longest diameter)
  • Equal Area in Equal Time LAW 2
  • P2(years)a3(AU) LAW 3
  • BUT he didnt know why the planets moved

18
History Continued
  • Galileo Galilei (1564-1642)
  • False Facts
  • He did not invent the telescope
  • He was not condemned by the Inquisition for
    believing the Earth went around the sun
  • He did solidify the scientific method
  • The telescope was invented by lens makers in
    Holland around 1608
  • He was not the first person to look up into the
    sky either, but he was first for systematic
    observations.
  • First 3 major discoveries
  • The moon is not perfect (philosophy crumbles)
  • Calculated sizes for mountains
  • The moon was another world like ours
  • The Milky Way was made up of more tiny dim stars
  • Jupiter had 4 new planets circling

19
History continued
  • Galileo
  • The Moons of Jupiter
  • Small things go around larger things
  • Critics had said the Earth cant go around the
    Sun the moon would be left behind. But not at
    Jupiter
  • More discoveries
  • Sunspots on the sun (the sun was not perfect)
  • The sun rotated
  • Venus had phases
  • Galileo was embraced by church leaders in Rome
    but was outspoken, forceful and sometimes
    tactless.
  • Controversy flared- opponents fought and debated
    him
  • He was asked by Pope Paul V to cease debate and
    his books were banned or revised.
  • Later Pope (his friend) encouraged him to
    continue to work
  • Wrote the controversial Dialogue Concerning Two
    Chief World Systems
  • Put under house arrest for life for not following
    orders by the Inquisitors.

20
History marches on
  • Isaac Newton (1642-1727)
  • Discoveries
  • Studied optics
  • Developed the Three Laws of Motion
  • Expressed the Nature of Gravity
  • Invented Differential Calculus

21
History schmistory
  • Newtons Three Laws
  • A body (mass) continues at rest or in uniform
    motion unless acted upon by an outside force
  • A bodys change of motion is proportional to the
    force acting on it and is in the direction of the
    force Fma
  • When one body exerts a force on a second body,
    the second body exerts an equal and opposite
    force back on it.

22
History
  • Newtons Law of Gravity
  • Greater speed results in eventual orbit orbital
    speed speed needed to move sideways fast enough
    to fall around the body rather than into it.

23
Recent History
  • Albert Einstein (1879-1955)
  • Assumption from Newton Absolute rest in the
    universe
  • As a teenager wondered what light would look like
    if you tried to catch up with it
  • Michaelson-Morley Experiment (most important
    null-result in science
  • Mass-Energy Relationship
  • Only used simple geometry and algebra!
  • Special Relativity
  • General Relativity

24
Dont know much about
  • Edwin Hubble
  • Observed red shift of galaxies (more on that
    later) and showed the universe is expanding
  • Einstein had to revise General Relativity to put
    back the expansion term
  • Modern Names
  • Wheeler
  • Steven Hawking
  • QUIZ 3 History
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