Cosmic Distances from antiquity to present day

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Cosmic Distancesfrom antiquity to present day

• Manel Errando Trias
• IFAE Thursday Meeting - 13.01.2005

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Outline

• How to describe celestial motions
• Ptolemy and the Greek astronomy
• Copernican revolution
• Tycho and Kepler
• Venus transit of 1761 and the
• astronomical unit

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The simplest example...
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lets make it a bit more complicated
we require the radius from D to A to remain
parallel to BC
Not a perfect description...
How would the inhabitants of planet B describe
this universe?
A and C can collide!

• it allows AB to vary over the correct range
• it keeps distances CB and CA fixed
• it avoids collisions between C and A!

this is what the Greeks called an
Epicycle-Deferent system
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what did the greeks know?

• they knew the sun, the moon and the five
  classical planets mercury, venus, mars, jupiter
  and saturn.
• some planets present a bounded elongation respect
  to the sun.
• planets exhibit retrograde motion at certain
  times.
• they observed the phases of the moon, eclipses,
  conjunctions and oppositions, ...

Mercury is allways found within 28º on either
side of the sun and Venus within 46º
and of course they had powerful mathematical
tools to account for these phenomena...
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Aristarchus of Samos

• Aristarchus lived in the third century B.C.
• He was the first to put forth the thesis that the
  earth rotates and also revolves around the sun,
  being it taken as the center of the cosmos.
• His work On the Sizes and Distances of the Sun
  and Moon presents a method for determining the
  relative radii of the sun and the moon and also
  the relative distances of those objects from us.

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Aristarchus of Samos
The lunar dichotomy method

• He estimated the ratio ES/EM to be between 18 and
  20...
• The actual value is around 390.
• The MES angle is not 87º but 89º50.
• This method depends strongly on a good
  determination of the moment when the moon is in
  half phase.
• The results depend on an accuracy of measurement
  that was impossible to achieve.

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Ptolemy

• Claudius Ptolemy lived in the second century A.D.
  in Alexandria.
• His treatise Almagest presents the Ptolemaic
  Model, that kept its validity over thirteen
  centuries.
• His scheme of cosmic dimensions, derived from the
  mathematical models of the Almagest, are
  presented in his Planetary Hypotheses.

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The Ptolemaic System

• His model was based on the Epicycle-Deferent
  system, improved with the use of the eccentric
  circle and the equant
• He had to account for retrograde motions
• and bounded elongations

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The Ptolemaic System
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Nicholas Copernicus

• Copernicus was born in 1473 and published De
  revolutionibus orbium coelestium in 1543, weeks
  before his death.
• His work pointed out the need of changing from a
  geocentric and geostatic system to an
  heliocentric system.
• His heliocentric theory was one of the most
  important breakthroughs on the history of
  science, transcending astronomy to philosophy and
  theology.

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The Copernican System
Main Copernicus theses

• The Universe is spherical
• The Earth too is spherical
• The motion of the heavenly bodies is uniform,
  eternal, and circular or compounded of circular
  motions
• The Earth rotates and orbits around the Sun
• The heavens are immense compared to the size of
  the Earth
• The Sun is at rest in the middle of the universe

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The Copernican System

• It accounts for the movement of the sun trough
  the ecliptic
• It gives an explanation for the bounded
  elongation of mercury and venus
• It also explains the retrograde motions of the
  outer planets

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The Copernican System
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Implications of the Heliocentric Theory

• Copernicus showed that the annual orbit of the
  Earth around the Sun would explain the observed
  irregularities in the motions of planets.
• His cosmological model was by far simpler and
  more elegant than the Ptolemaic and all its
  improvements made on the last thousand years.
• Its philosophical implications transcended even
  its astronomical impact, moving away the earth,
  and humans, from their privileged position in the
  universe.

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Implications of the Heliocentric Theory
Book of Joshua 1012 ...Joshua said to the LORD
in the presence of Israel O sun, stand still
over Gibeon, O moon, over the Valley of
Aijalon. 1013 So the sun stood still, and
the moon stopped

• The absence of Parallax
• Effects of Earths motion
• Theological problems

On equator, a person moves at about 1.500
km/h Due to translation, the Earth travels at
5.000 km/h
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Tycho Brahe

• Tycho was born in 1546 and was the finest
  pre-telescopic observer of all time.
• He constructed the best astronomical observatory
  available at his time, where he attained
  unprecedented accuracy on measuring the position
  of an object in the heavens.
• Tycho favored neither the Ptolemaic nor the
  Copernican system, but created his own one.

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The Tychonic System

• All the planets orbit around the sun.
• The sun revolves around the earth carrying the
  orbits of the planets with it.
• The entire arrangement should rotate once a day
  to account for the daily motion of celestial
  bodies.

• Brahe criticized the Ptolemaic system
• Use of the equant
• Lack of elegance in accounting for retrogressions
  of the planets
• and also the heliocentric view of Copernicus
• It violates physical principles
• It necessitates a stellar parallax
• It contradicts Holy Writ

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Johannes Kepler

• Kepler was born in 1571 and published his
  Harmonices Mundi in 1619.
• He worked with Tycho Brahe and was one of the
  first supporters of heliocentric theory.
• He developed an heliocentric model compatible
  with the observations made by Tycho Brahe.

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The First Keplerian Model

• Kepler pondered three main questions
• Why are there six planets?
• Why are their orbits positioned as they are?
• Why do planets farther from the sun move more
  slowly?

• 5 Perfect Solids

tetrahedron
cube
octahedron
dodecahedron
icosahedron
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The First Keplerian Model
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Keplers Synthesis

• Perfect solids model had not enough predictive
  power, specially for Mars. After many attempts,
  Kepler proposed three conjectures that he could
  also extend to all the planets
• A planet orbits the sun in an ellipse, with the
  sun at one focus of the ellipse
• A line connecting a planet with the sun sweeps
  out equal areas in equal times
• The square of the orbital period divided by the
  cube of the orbital distance is a constant for
  any planet

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Keplers Synthesis
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Venus transit of 1761

• In 1716 Edmund Halley proposed a method to
  observe the parallax of Venus on the Sun during a
  Venus transit and infer the Sun-Earth distance
  from it.
• With the instruments available, mainly
  telescopes, a very good accuracy could be
  achieved.
• It was the first international scientific
  campaign, with almost 200 astronomers in more
  than 70 stations around the globe tried to
  observe the transit.

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Venus transit of 1761
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Up-to-date measurements

• Bouncing a radar signal off another planet, the
  time it takes the radar signal to go to the
  planet and return divided by the speed of light
  gives twice the distance to the planet.
• Nowadays the astronomical unit is calculated with
  great precision using the echo of radar signals
  sent to Venus and relating this distance to the
  earths orbital radius using Keplers the third
  law.
• The actual value is 149.597.870 km and comes from
  the averaging of years of measurements.

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Final conclusions

• The first astronomers did not failed describing
  the universe, they just tried to be coherent with
  the observations they made.
• These models could give estimations for the
  relative distances between heavenly bodies, but
  direct measurements of these distances needed
  instrumentation that was not available until the
  17th century.
• Maybe future scientists will think about some of
  the now accepted theories in the same way as we
  now see the first cosmological models.