The Heliocentric Universe

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The Heliocentric Universe

• Scientific reasoning began again in earnest in
  Europe in the 1400s.
• Francis Bacon and other philosophers embarked on
  experiments to test hypotheses and challenged
  Aristotles claims.
• The Renaissance in art, literature and
  engineering (e.g. Leonardo da Vinci) flowed from
  Italy northward.

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The Copernican Revolution

• Nicholas COPERNICUS (1473-1543), a Polish cleric,
  argued in favor of a
• HELIOCENTRIC COSMOLOGY THE EARTH IS NOT THE
  CENTER OF THE UNIVERSE.
• The center of the Earth is the center of gravity
  for objects near it and for the MOON.
• The other PLANETS REVOLVE around the SUN.
• The STARS are MUCH FARTHER from the EARTH than is
  the SUN.
• STELLAR (SOLAR) MOTIONS'' ARE APPARENT ALL ARE
  DUE TO MOTION OF THE EARTH.
• PLANETARY MOTIONS'' are also substantially DUE
  TO THE EARTH'S MOTIONS.

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Copernicus Model Explains Retrograde Motions of
Planets
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Copernicus vs. Ptolemy

• Copernicus' model still assumed circular orbits
  and still had epicycles --- but now the main
  orbits went around the Sun and the epicycles
  could be smaller.
• While this model fit the data available then, it
  was only slightly better and certainly not
  proven.
• SO WHY IS IT BETTER''?
• THE HELIOCENTRIC MODEL is BOTH SIMPLER and more
  BEAUTIFUL than the geocentric model.
• "Occam's razor if two hypotheses both describe
  the same data equally well, choose the simpler
  one.
• Back then each gave nearly equal explanations of
  the data Heliocentric model was a little
  simpler.
• Still, it gained few adherents it went against
  "common sense" and was written in Latin.

5
Better Observations Mean Better Models

• TYCHO Brahe (1546--1601), a Danish noble,
  designed and had built HUGE instruments at
  Uraniborg on Hveen, including
• sextants (for measuring angles)
• astrolabes (for locating positions on the sky)
• These allowed for PRECISION MEASUREMENTS,
  particularly of planetary positions.
• Accuracies of about 1 arc minute in planetary and
  stellar positions were achieved.
• Tycho was the first to quote errors along with
  his measurements.
• After the peasants protested that his taxes were
  too high, he lost favor with the new Danish king
  and moved to Prague in 1597.

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• Tycho in Uraniborg a naked eye observatory,
  with large instruments that worked like
  protractors to measure angles to high accuracy.
• He discovered and tracked the brightness of a
  supernova in 1572 and showed a comet in 1577 had
  to be outside the earths atmosphere
• But he still thought earth was at rest, w/ Sun
  orbiting it, while other planets went around the
  Sun.

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A Key Empirical Discovery

• Johannes KEPLER (1571-1630) an Austrian, a
  great amateur observer, worked under Tycho from
  1600 and inherited his data.
• He had already accepted the Copernican picture
  and tried to use this superior data to see if it
  could fit better than the Ptolemaic theory.
• Tycho assigned Kepler to examine the data on
  Mars first, since it required the biggest
  epicycles.
• Finally, he could understand the relative
  positions of Mars and Earth if
• MARS MOVED IN AN ELLIPSE, WITH THE SUN AT ONE
  FOCUS.
• This broke with the longstanding assumption that
  combinations of circles were the only way to
  explain things. But after all, a circle is just
  a special ellipse,
• with ECCENTRICITY 0.
• By 1609 he had also realized that Mars' orbit
  swept out equal areas in equal times.

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Keplers Laws of Planetary Motion

• Ten more years of work led to the THREE
  EMPIRICAL LAWS
• 1. All planets follow elliptical orbits, with the
  Sun located at one focus. (Nothing is at the
  other focus.)
• 2. Every planet sweeps out equal areas in equal
  times as it orbits the Sun.
• In other words, planets move fastest when closest
  to the Sun (near PERIHELION) and slowest when
  furthest away (APHELION).

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Keplers Second Law Equal
Areas Swept out in Equal Times
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Kepler and Ellipses
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Sidebar on Ellipses 1

• To draw one, loop a string around two tacks,
  holding it taught with a pencil point.
• Definition the locus of points the sum of whose
  distances from two other points (the foci) is
  constant.
• The longest axis through an ellipse is the MAJOR
  AXIS One half of that is the SEMI-MAJOR AXIS, a
• One half of the shortest axis ( perpendicular to
  the major axis) is the SEMI-MINOR AXIS, b
• Distance from the Center to each Focus is
  semi-major axis times the ECCENTRICITY or FC ae
  
• e 1 - (b/a)21/2 OR b2 a2(1 -
  e2)
• If e 0 we have a circle (ba foci and center
  coincide)
• if e 1 we have a line-segment

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Sidebar on Ellipses 2

• An ellipse is a conic section slice a cone with
  a plane not parallel to its base but not as steep
  as its side.
• The other conic sections are circle (slice
  parallel to base), parabola (as steep as side)
  hyperbola (steeper)

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Ellipses and Planetary Orbits
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Keplers Third Law of Planetary Motion

• 3. The cube of the semi-major axis of a planet's
  orbit is proportional to the square of its
  period.
• a3 P2
  
  
  if a is in units of AU and P is in
  years (in OUR solar system).
• Examples
• aMars 1.524 AU so PMars (1.524)3/2 1.881
  years aJupiter 5.20 AU so PJupiter
  (5.20)3/2 11.86 years.
• More generally, a ? P2/3 or P ? a3/2
• Later Newton showed that these general
  proportionalities (but not equality) was always
  true for systems with a single dominating mass,
  not just our solar system.

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New Technology New Evidence

• GALILEO Galilei (1564--1642) taught mathematics
  and astronomy at Padua.
• He performed EXPERIMENTS e.g., balls rolling
  down inclined planes and learned about INERTIA.
• Galileo Built a TELESCOPE in 1609. Instead of
  commercial or military use (since 1608)
• GALILEO POINTED IT AT THE SKY and DISCOVERED
• The LUNAR TERMINATOR WAS IRREGULAR it had
  MOUNTAINS and WASN'T A PERFECT SPHERE.
• PLANETS LOOKED LIKE DISKS, STARS STILL LOOKED
  LIKE POINTS.
• MILKY WAY IS COMPRISED OF MANY STARS --- many
  fainter stars could be seen between those visible
  to the naked eye.

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Galileo and the Moon
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More of Galileos Discoveries

• VENUS WENT THROUGH PHASES (including a Full
  phase, not possible in Ptolemaic model) ---
  reflecting light from the Sun. Phases of Venus
  applet
• THE SUN HAD SPOTS --- the most perfect of all
  heavenly bodies had blemishes.
• JUPITER HAD FOUR MOONS --- something other than
  Earth had things going around it.
• All of these discoveries, published in 1610
  Sidereus nuncius, challenged the Aristotlean /
  Catholic picture of the Universe --- perfect
  spheres shining by themselves, perfect circular
  orbits, only the Earth at the center of
  everything.
• While he had already thought Copernicus' model
  was best Galileo felt this DATA had PROVEN it.

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Galileo the Vatican

• While others in Germany, England, etc.,
  confirmed these discoveries and accepted the
  HELIOCENTRIC PICTURE, the response in Rome wasn't
  very good
• Although Vatican astronomers confirmed his
  observations, they didn't accept his logic and
  demanded that Copernicus' model not be taught.
• Galileo was ordered to stop supporting this view,
  and he became more circumspect, finally
  publishing a Dialog Concerning the Two Chief
  World Systems in Italian in 1632.
• After facing the Inquisition and nominally
  renouncing his ideas, he was placed under house
  arrest in 1633.
• Catholic church stopped banning heliocentric
  books in 1757 but formally vindicated Galileo
  only in 1992!

20
When was the Earth known to be circular and its
circumference measured?

1. From the earliest times
2. By the Greeks
3. At the start of the Renaissance
4. By Galileo, in the early 17th century
5. Around 1800

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When was the Earth known to be circular and its
circumference measured?

1. From the earliest times
2. By the Greeks
3. At the start of the Renaissance
4. By Galileo, in the early 17th century
5. Around 1800

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Whose suggestion that the Sun is the center of
the solar system was first taken seriously by
many people?

• Copernicus
• Tycho
• Kepler
• Galileo

23
Whose suggestion that the Sun is the center of
the solar system was first taken seriously by
many people?

• Copernicus
• Tycho
• Kepler
• Galileo