Astronomy and Space Science I

1
Astronomy and Space Science I

• Dr. Hoi-Fung Chau
• and
• Dr. Alex Tat-Sang Choy
• Jointly Organized by
• The Space Museum
• HKU Physics Department
• Co-organized by
• Science Education Section, EMB

2
Astronomy and Space Science

• Astronomy Basics
• Length, time, angles
• Celestial sphere, star maps
• Solar System
• Orbital Motion of the Earth around the Sun
• Geocentric models
• Heliocentric models
• Modern views
• QA

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Length Power of Ten
4
Units of Length

• 1 ls distance light travel in 1 second
  299792485 m 3x108 m
• 1 ly distance light travels in 1 year
  9.46x1015 m 1016 m
• 1 AU (astronomical unit) mean distance between
  the Sun and Earth 1.49x1011 m
• 1 pc (parsec) distance from which 1 AU extends
  1 arcsec 3.26 ly 3.24x1016 m

• 1 Mpc 106 pc 3.26x1022 m

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Examples
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Time Scales
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Angles

• Angles are measured in degree (), arcmin ('),
  arcsec(") radians (rad, or no unit).

• 1 60' 3600"
• 1 rad 180/p 57.3.
• Small angle approximation angle arc
  length/distance
• The apparent diameter of the Sun and the Moon are
  about 0.5.
• Resolution limit of a 4" telescope 1".
• Note Do not confuse arcsec with inch, both use
  the same symbol.

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Objects with Large Angular Sizes(roughly to
scale)
Sun, 30.
Andromeda Galaxy (M31) 180 x 63.
Orion Nebula (M42), 85 x 60.
M54, extragalatic globular star cluster, 12
Moon, 30.
Pleiades, open star cluster, 180.
M4, globular star cluster, 36
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More Examples
Ring nebula, planetary nebula, 1.4 x 1.
Crab Nebula Supernova remnant, 6x4.
Io, Jovian satellite, 1.
Polaris As apparent size 0.002. Polaris A to
Polaris Ab is 0.2 Polaris A to Polaris B is
20 Polaris A to Dubhe 30.
Hubble Deep Field, 1.5.
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Celestial Sphere

• The celestial sphere is a hypothetical sphere
  centered at the center of Earth.
• On the celestial sphere, stars are fixed, while
  the Sun and the planets moves slowly.
• The celestial sphere rotates, thus most stars
  rise and fall daily.
• The celestial poles and celestial equator are
  projections of the poles and equator on the Earth
  on to the celestial sphere.

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Useful Relations

• Altitude of north celestial pole latitude L
• Local zenith forms an angle 90-L with the north
  celestial pole
• Local zenith forms an angle L with celestial
  equator

zenith
____
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Star Maps

• Star maps show the sky East-side West, because it
  is intended for looking up. There are 88
  constellations.
• Brighter stars are shown with bigger dots. Many
  star maps also mark the location/type of deep sky
  objects, multiple stars, and the Milky Way.

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The Solar System
Source NASA
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Motion of the Sun on Celestial Sphere

• Axial tilt of Earth is 23.44 23 ½ .
• Different parts of the sky are in the glare of
  the Sun in different months.

Vernal equinox (??), autumnal equinox(??) are the
points at which the Sun passes the celestial
equator, while summer solstice(??) and winter
solstice(??) are the northern and southern
extreme points of the ecliptic (??).
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Ecliptic Plane
Figure of showing the Earth around the Sun in the
ecliptic plane.

• the ecliptic plane is the plane in which the
  Earth orbits.
• the ecliptic is the circle form by the ecliptic
  plane intercepting the celestial sphere

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Planetary Motion on Celestial Sphere
Planets usually moves on the celestial sphere
from east to west (prograde motion) near the
ecliptic while sometimes moves from west to east
(retrograde motion).
Motion of Mars in 2003 and 2005. Time step10
days.

Pictures from NASA.
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Geocentric Model of Planetary Motion(Apollonius,
260-190 BCE)

• Explains qualitatively the prograde and
  retrograde motions, and brightness variation.
• Motion planets around epicycle centers and
  epicycle centers around the Earth are uniform
  circular motions.
• Note the centers of epicycles for Mercury and
  Venus always align with the Sun, which explains
  their maximum elongations (29 and 48).
• Ptolemy (90-168 CE) modified this model to be
  quantitatively accurate compared to the
  observations of the time. His model was used for
  1400 years until the Renaissance.

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Heliocentric Model of Planetary
Motion(Copernicus, 1473-1543 CE)

• In the heliocentric model, the Earth and other
  planets orbit the Sun.
• The prograde and retrograde motions are apparent
  effects due to relative motions of the Earth and
  the planets.

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Advantages of the Heliocentric Model

• The heliocentric model of Copernicus is not
  intrinsically more accurate.
• Calculation is easier with the Copernicus model.
• Copernicus was able to determine the orbital
  radii (relative to Earth orbit) of all six
  planets, while in Ptolemy model the lengths are
  incorrect.
• Heliocentric models predict stellar parallax,
  while geocentric models predict otherwise.

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Further Developments

• A schematic heliocentric model is shown on the
  right. The heliocentric model would later be a
  great help to Kepler (1571-1630 CE) in finding
  his laws of planetary motions empirically.
• Later Newton (1643-1727 CE) gave the model a firm
  physical basis using law of gravity and motion
  would
• Stellar parallax, hence distance, was first
  measured in 1838 (Bessel).
• In Copernicuss theory, the Sun is at the center
  of the universe, while the Earth is merely a
  planet.

• We now know that Sun is just one of the stars in
  one of the galaxies (Milky Way Galaxy) in one of
  the group of galaxies (Local Group) in one of the
  superclusters (Virgo/Local Supercluster) in the
  universe.

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Modern View of the Solar System

• Sun
• Terrestrial planets
• Asteroids
• Gas Giants (outer planets)
• Trans-Neptunian Objects (TNO)
• Kuiper Belt
• Scattered Disc
• Oort Cloud (hypothetical)
• Comets
• Note Dots represent objects. Someone looking at
  the solar system at this scale shouldnt see
  asteroids and the Oort cloud with naked eyes.
  Much of the Solar System is empty space.

http//en.wikipedia.org/wiki/ImageOort_cloud_Sedn
a_orbit.jpg
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Beyond the Solar System (Hierarchy of
Objects)pictures from atlasoftheuniverse.com
http//atlasoftheuniverse.com/12lys.html
Solar Neighborhood
http//atlasoftheuniverse.com/5000lys.html
Orion Arm Note nebulae are usually in spiral
arms.
http//atlasoftheuniverse.com/galaxy.html
Milky Way Galaxy (2-4x109 stars) Note globular
clusters (105-106 stars) orbit the galactic core
as satellites.
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Beyond the Milky Way pictures from
atlasoftheuniverse.com
http//atlasoftheuniverse.com/localgr.html
http//atlasoftheuniverse.com/superc.html
Neighboring Superclusters (100 superclusters
shown)
Local Group (30 galaxies)
http//atlasoftheuniverse.com/universe.html
http//atlasoftheuniverse.com/virgo.html
Visible Universe (107 superclusters) visible
? whole but not visible has no physical relevance.
Virgo Supercluster (100 groups/clusters of
galaxies)
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In Depth Questions
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Q What is a constellation?
A The IAU divides the celestial sphere into 88
constellations (regions) with precise boundaries
(yellow dashed lines in the figure).
More Each star belongs to exactly one
constellation. The term constellation is also
less formally used to describe a group of star
visibly related to each other in a pattern, such
as those connected by green lines in the figure.
However, in such a scheme, some stars such as
Sirrah in Andromeda, may be considered as both
the head of Andromeda or part of the Square of
Pegasus. Also, stars not connected by patterns
still need to be assigned a constellation.
http//en.wikipedia.org/wiki/ ImagePegasus_conste
llation_map.png
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Q How does the coordinate systems on the
Celestial sphere look like?
A As shown on the graph the longitude and
latitudes of the Celestial sphere are called RA
(right ascension) and DEC (declination). DEC runs
from 90 to -90. RA runs from 0 to 24 hours.
Each hour has 60 minutes, and each minute has 60
seconds, just like the clock. The RA of zenith of
a fixed location increases by roughly 1 hour for
every hour in time.
(Note Do not confuse the minute with arc minute
which is 1/60, both measure angles.) Refer to
the previous figure, the light blue lines are RA
and DEC lines.
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Q Where exactly is the center of the celestial
sphere?
A The center of the celestial sphere is the
observer. In other words, each observer has a
celestial sphere.
More The celestial sphere is a device used to
represent the direction of celestial objects for
observation. For example, someone in Beijing
would see the Moons position a little
differently from someone in Hong Kong, due to
parallax of the observing locations. Therefore,
it only make sense to have a different celestial
sphere (and the objects on them) for each for
observer. Another example is the satellite or
space station, which, due to there close distance
from Earth, depends greatly on the location of
the observer. Also, if one were to observe from
Mars, it would not make sense if the celestial
sphere is centered on Earth! Note however that
in most situations, we are observing on the Earth
and most objects are far away so it is convenient
to set the center of the Earth as the center of
the celestial sphere.
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Q I heard that the definition of the ecliptic
plane has been changed, is it?
A Yes, but for all purpose in this course, the
change has no real effect.
More

• A very first definition is the ecliptic plane is
  the plane in which the Earth orbits.
• A few amendments have been made since then.
• In 2006, the IAU adopted a new definition
• the ecliptic pole is explicitly defined by the
  mean orbital angular momentum vector of the
  Earth-Moon barycenter in an inertial reference
  frame.
• This change is to better agree with dynamical
  theories, however, the actual change in value is
  extremely small.
• As a result the Earths orbital plane is very
  slightly different from the ecliptic plane.

29
Q Whats the relation between solar motion and
the calendar?
A The Suns position relative to Vernal Equinox
is important for determining the seasons and the
calendar. A major function of the calendar was
for agriculture.
More

• Solar motion on the ecliptic is not uniform (due
  to the Earths elliptical orbit), hence seasonal
  lengths are different.
• The mean tropical year, i.e. the mean duration
  for the Sun to pass though the same point on the
  ecliptic twice, is 365.242 190 419 days (epoch
  2000).
• A good approximation is 365 97/400 365.2425
  days. This leads to 97 leap years in every 400
  years (Gregorian calendar). The rule for
  assigning leap year is leap years are all years
  divisible by 4, except for those divisible by 100
  but not 400. E.g. 1900, 1999 are not leap years
  1996, 2000, 2004 are leap years.
• A less accurate approximation is 365 ¼ 365.25
  days. This leads to a leap year in every 4 years
  (Julian calendar). But in the order of hundreds
  of years, the calendar will become less accurate.
  This approximation, however, is convenient for
  many estimations.

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Q How was the Sun/Earth orbit modeled by Greek
astronomers?

• A Seasonal lengths are sensitive to the Suns
  motion, therefore the non-uniform motion of the
  Sun was discovered early. In Hipparchus model,
  the Earth is shifted off-center of the deferent.
  This point is called the eccentric. Effectively,
  this model approximates the Kepler ellipse and
  area laws.

• More
• Using the length of seasons (i.e., time taken for
  the Sun to pass between equinoxes and solstices),
  Hipparchus found parameters to his model, which
  agreed well with observations until
  Tycho/Keplers time.
• Note that the length of seasons changes over
  time, due to precession of the equinoxes.
  However, eccentricity does not change.

http//www.venusoptics.com/AstroNotes/ files/Hippa
rchus1.png
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Q What is the cause for precession of the
equinoxes?
A Precession is caused by the torque applied by
the Sun, the Moon, and the planets. The torque is
the result of the gravitational pull on Earths
equatorial bulge. More The lower left picture
explains the effect due to the Sun. The lower
right picture shows the 26000 year period
precession of the north celestial pole.
http//en.wikipedia.org/wiki/ImagePrecession_torq
ue.jpg
http//en.wikipedia.org/wiki/ImagePrecession_N.gi
f
Pictures from Wikipedia.
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Q What is a day anyway?
A A (solar) day is the duration for the Sun to
pass the meridian twice.
More

• The celestial sphere rotates about 360.9856
  daily, i.e. it takes about 23 hr 56 min for stars
  to go around in a circle. In other words, stars
  rises 4 minutes earlier each day. (360/365.25
  .9856, 24x60/365.25 3.94).
• As a result, the Sun passes the meridian
  (highest) at the approximately same time each
  day. For Greenwich, it is 1200pm for HK, it is
  1224pm.

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Q Can you give some example of planetary events?
A Some events are

• Conjunctions (?)
• Two objects closest from Earths point of view
• Stationary (?)
• When the ecliptic longitude (sometimes RA) do not
  change
• Greatest elongation (??)
• Approximately the best time for observing
  inferior planets

http//en.wikipedia.org/wiki/ ImagePositional_ast
ronomy.png

• Transit (??) of inferior planets across the Sun
• Mercury , 11/1999, 5/2003, 8/11/2006 (during
  sunrise in HK), 5/2016,
• Venus , 12/1882, 6/2004, 6/6/2012 (visible in
  HK), 12/2117,
• Eclipse (?) of Sun or Moon.
• Similar events in the Jupiter system.

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Continue

• Opposition (?)
• Best time for observing superior planets
• For Mars, opposition occurs approximately every
  2.14 year. Due to higher orbital eccentricity
  (0.093) and smaller semi-major axis (1.52 AU),
  the Earth-Mars distance varies between 0.66 and
  0.38 AU (1.52(1 0.093)1), giving large size
  and brightness variation at opposition.

Great opposition of Mars (near perihelion)
(????) occurs every 15-16 years. The one in 2003
was the closest in 60,000 years, which the media
made a big deal of. However, as shown on the
graph, the other great oppositions such as the
1988 one are not much further away. Note since
great opposition occurs near perihelion, when
Mars is the hottest, planet-wide dust storms
could occur, so observe early.
Picture C.F. Chapin, http//www.astromax.com/pla
nets/ images/mars2003.gif
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Q What is Aristotles model of the universe?
A See figure.

• Aristotles (384-322 BCE) model placed the
  superior planets in right order using their speed
  on the celestial sphere.

• It explains simple phenomena such as daily rise
  and set of celestial objects, but not the details
  in longer time scales.
• In this model, the Earth is at the center the
  universe, surround by water, air, fire, etc.
• As more were known about the planetary motion
  through observation, ancient astronomy would
  transform slowly to a qualitative science, then a
  quantitative science.

Image showing Aristotles model.
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Q What does Ptolemys geocentric model look like?
A

• The epicycle is used to explain
  prograde/retrograde motion
• The epicycle center rotated uniformly about
  equant E, instead of the center of deferent M.
• The Earth is located off-center at the eccentric.
• Distances EM MO.
• This is the geocentric model that agrees
  quantitatively with observations of the time.
  From the time of Apollonius to Ptolemy, planetary
  theories changed gradually from qualitative to
  quantitative science.

http//www.venusoptics.com/AstroNotes/ files/Ptole
my1.png
37
Q Ptolemy model looks quite different from
Keplers, why did it work so well?
A Ptolemy was approximating Keplers law,
without knowing it.
More

• The reasons are
• the elliptical orbits of the planet are close to
  a circle
• the eccentric takes the role of a focus,
  approximating Keplers first law
• Ptolemys equant has the effect of approximating
  Keplers second law
• Using Tychos data, Kepler refitted Ptolemys
  model, which gave a maximum error of only 8 for
  Mars.
• Since uncertainty for Tychos data is only 1,
  Kepler was forced to give up the circles.

Eccentric/Sun
Equant
Comparing the elliptical orbit of Mars (red) to a
circle (blue).
38
Q How to transform between geocentric and
heliocentric models?

• The two models are equivalent if constructed as
  shown. The vectors pointing from the Earth to the
  planet are always the same between the two
  models.
• Copernicus used his own observation as well as
  Ptolemys data to obtain parameters to his model.
  
• The precisions of the two models are the roughly
  same.

Earth
Sun
39
Q One arcmin is about the size of a HK1 coin in
88 m away, how did Tycho Brahe achieve this
accuracy without telescopes?

• A Great care for accuracy, a whole lifetime of
  pursuit, and a lot of support.
• More
• He was the first one to notice the problem
  relating observation accuracy and have the
  ability to improve on them. He improved the sight
  with a slit design, and also added gradual scale
  to improve reading. Very large instruments help
  measuring smaller angles, but they requires
  stronger materials and mechanical parts. To
  support Tychos work, the King of Denmark granted
  him the estate of the island Hven, on which he
  built worlds best observatory called Uraniborg.

Left The sights aligned horizontally if the
star can be seen just on the CBGF edge and ADHE
edge at the same time. The vertical alignment can
be found similarly. For solar alignment, sunlight
is allowing to pass thru the hole in the front
and fall on a circle drawn on the ABCD plate.
Image showing Tychos sight device.
Image showing drawing of a very large
device (three meter diameter) of Tycho
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Q Did Galileo really invented the telescope?
A No. But Galileo did designed and made his own
telescopes, and improved on them. He was
ahead of others by a few months in telescope
quality, enough for him to claim most of
the discoveries.

• More A typical Galilean refractor had a
  plano-convex objective lens with 30-40 inches
  focal length plano-concave eyepiece of focal
  length about 2 inches focal length. It was good
  enough to discover Lunar features, Jupiters four
  moons, phase of Venus, as well as sunspots.
• (Note He became blind in his last years, due to
  observing the Sun directly through the telescope
  without proper filter or projection.)

http//galileo.rice.edu/images/ things/g_telescope
.gif
Galileos telescopes are quite unimpressive by
todays standard, with 0.5-1 inch effective
objective aperture, about 15-20x power, and a
very narrow (15) field of view, not to mention
significant aberrations. But they were the best
at the time.
41
Q Was Galileo jailed?
A He was found guilty in his trial and sentenced
to jail for life. However, his treatment was
closer to house arrest. He worked and published
during this time. More Some ideas Galileo
held, such as the Earth moves around the Sun, the
celestial bodies are not perfect, the Bible was
not meant to teach science, etc., were considered
heresy at the time. A less fortunate astronomer
named Giordano Bruno was burned at the stake. To
understand why Galileo was treated leniently,
perhaps one should understand that Galileo was
well known not only to those who practice
science, but to influential people of the society
and even to the Church. He made many discoveries
such as the law of motion, measured gravity,
invented a thermometer, studied the pendulum,
etc. The physics taught at the time stress
qualitative arguments, Galileo however believed
in the importance of mathematics and experiments.
He was thus called the father of modern
science. What made him stand out from other
scientist of his time, was the skill of mixing of
theory and practice. Galileo was also very
successful in getting supports from many people.
Although there were people who refused to even
look though the telescopes, Galileo succeeded in
introducing the telescopes to many nobles and
military officials who quickly understood the
practical and military applications of the
telescope.
42
Q Does the discovery of phase of Venus disproves
the geocentric theory?
A No. Models, such as Tychos model, which
require the Venus and Mercury to revolve around
the Sun give the correct phase of Venus.
43
Q What is a planet?

• A Definition by the International Astronomical
  Union (IAU) in 2006
• (1) A planet is a celestial body that
• (a) is in orbit around the Sun,
• (b) has sufficient mass for its self-gravity to
  overcome rigid body forces so
• that it assumes a hydrostatic
  equilibrium (nearly round) shape, and
• (c) has cleared the neighborhood around its
  orbit.
• A dwarf planet is a celestial body that
  satisfies, (a) and (b) but not (c), and is not a
  satellite.
• All other object orbiting the Sun, except
  satellites, are called Small Solar System
  Bodies.

More
Since some recently found minor planets are
similar in size or even bigger (Eris) than Pluto,
there was a need for redefinition. The new
definition is based on planetary formation theory
that, given enough time, a large enough object
would be able to collide with or scatter away
objects and dominate its orbit. The redefinition
has been criticized and remains controversial.
Note also that the line between (2) and (3) is
left for later meetings. For many small object,
the hydrostatic equilibrium condition (b) is not
easy to test.
44
Q After the invention of telescope, how was
position/angle measured?
A First by using wired micrometer eyepiece, then
by measuring photographic plate.
More The wired can be moved to match the stars
position. In some other eyepieces, a patterned
glass is placed at the focus for reading out
data. Angles can be measured from a photographic
plate using the focal length and the lengths
measured on the plate.
Image showing the view in a cross haired eyepiece.
45
Q Weve been focusing on the development of the
West, what about the work of Chinese?
A Ancient Chinese astronomers developed
sophisticated tools to observe the positions of
celestial objects. Unfortunate their work did not
affect the western astronomy development much.
More As an example, the drawing on the right
shows an invention in the Song Dynasty. The main
instruments (red, blue, and yellow) are driven by
water-powered gear systems to simulate Earths
rotation and tell time automatically.
Source HK Science Museum, ???????
46
Q1 Was Copernicus the first to think the Earth
moves around the Sun? Q2 Did Copernicus model
have epicycles?
A Q1 No. Q2 Yes.
More

• Ancient Greek and Indian astronomers had proposed
  heliocentric views. However, Copernicus model was
  the first to have the good length, time, and
  angle parameters. It was the reasonably close to
  modern model of the Solar System.
• In Copernicus model, the epicycles are used to
  account for elliptical orbits where as Ptolemys
  epicycles are used to account for Earths motion.
• Since the full Copernicus model is rather
  complex, the simplified heliocentric model is
  usually presented to students. This toy model
  does not have epicycles, but in practice, it has
  almost no predictive value.

47
Q What are the true advantages of the
heliocentric model?
A Easier to compute, correct orbital radii,
predicts stellar parallax.
More

• For those who computed using hand and tables, his
  simplification was much appreciated. Therefore,
  it was accepted first as a computational method
  rather than a physical model of the cosmos, even
  for those who are not willing to take a view
  different from the Church.
• Attempts to measure the distance to the planets
  were not successful at the time. In the
  geocentric models, the radii of deferent and
  epicycle of a planet are not obtained from
  observations (angle and time), only their ratios.
  Since the radii of planetary epicycles are the
  same as Earths orbital radius in the
  heliocentric model, Copernicus was able to
  determine the orbital radii (relative to Earth
  orbit) of all six planets.
• Heliocentric models predict stellar parallax,
  which is exactly why Tycho did not accept the
  heliocentric model. He could not observe parallax
  for stars, which are much further then he
  thought, and have a much smaller parallax (lt1)
  than he could measure.

48
Q What is the role of human/Earth in cosmology?
A It has been decreasing since history.
More Here are some paradigm shifts

• Earth is the center of the universe
• Earth is slightly off the center of planetary
  orbits. (Ptolemy)
• The Sun is the center of the universe
• The Sun is one of the stars in the Milky Way
  Galaxy
• The Milky Way Galaxy is just one of the galaxies
• The universe has no center
• We are not even made of the dominant form of
  matter (see nonbaryonic dark matter)
• The universe is made up of more energy (in the
  sense of E/c2) than matter (see dark energy).

49
Q Can you give us some references?
A Here are some of them

• NASA. The NASA site contain many useful
  information and images.
• Wikipedia. Note The Wikipedia is probably the
  quickest way to find information. However,
  because it can be edited by anyone, one should
  not trust the information without checking
  independent sources or risk getting wrong or
  misleading (intentional or not) information.
• HKU Physics Department, Nature of the Universe
  web site http//www.physics.hku.hk/nature/
• J. M. Pasachoff, Astronomy From the Earth to the
  Universe (1998).
• E. Chaisson and S. McMillan, Astronomy Today
  (2005).
• M. A. Hoskin, Cambridge Illustrated History of
  Astronomy (2000).
• J. Evans, The History Practice of Ancient
  Astronomy (1998).
• ??? ? ??? , ?? (2000).
• ??? , ??????? (2003).
• ???????????? (2000).

50
Sources of Pictures in this Talk
Sources of pictures Pictures are obtained from
the following sources unless given next to the
pictures.

• NASA. The NASA site contain many useful
  information and images.
• Wikipedia. Note The Wikipedia is probably the
  quickest way to find information. However,
  because it can be edited by anyone, one should
  not trust the information without checking
  independent sources or risk getting wrong or
  misleading (intentional or not) information.
• HKU Physics Department, Nature of the Universe
  web site http//www.physics.hku.hk/nature/
• J. M. Pasachoff, Astronomy From the Earth to the
  Universe (1998).
• E. Chaisson and S. McMillan, Astronomy Today
  (2005).
• J. Evans, The History Practice of Ancient
  Astronomy (1998).
• C. M. Linton, From Eudoxus to Einstein A History
  of Mathematical Astronomy (2004).
• Dr. Richard Hennig