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

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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

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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