Fig'03'02

1
Fig.03.02
Planet seen with Sun P between E S only
relevant for inferior P
Planet seen with Sun S between E P
Planet seen 180º from Sun E between P S only
relevant for superior P
Planet seen 90º from Sun only relevant for
superior P
Planet seen near Sun only relevant for
inferior P
2
Fig.03.05
Very Early (Pythagoras 550 BC) Cosmology
3
Geocentric Astronomy

• Earth is a fixed sphere at the center of the
  universe (note that it is NOT flat to the ancient
  Greeks)!!
• Celestial sphere is outermost spherical shell to
  which stars are glued. It turns once a day, (23
  h 56 min), rising in east and setting in west
  about the axis NCP-SCP
• Suns sphere turns backward, once in 365 days,
  about the axis that normal to plane of the
  ecliptic (23.5º off previous axis)
• Inside suns sphere are Moons, Mercurys and
  Venuss spheres
• Outside suns sphere are Marss, Jupiters and
  Saturns spheres
• To account for retrograde, a system of four
  nested spheres for each planet is used (Eudoxus),
  with tilted axes, counterrotating

4
Fig.03.06
The Eudoxus model

• Two inner ones turn slowly in opposite
  directions, to account for retrograde, speedup,
  slowdown and ecliptic crossings
• Third one gives Mars year, with axis tipped a
  few degrees, slipping backward on the ecliptic
• Fourth one gives usual diurnal motion

5
Fig.03.07
Aristotles reasoning for why the earth is round

• Different stars can be seen, depending on
  location
• below Perfection demands that objects fall
  toward the Earth center, which is only down
  everywhere if Earth is sphere
• 3. right Eclipses would look strange (lunar
  depicted)

6
Fig.03.14
How Big Is the Earth? Eratostheness (200 BC)
clever idea

• On a day when the Sun is ON THE ZENITH in
  Syene,Egypt, a shadow in Alexandria is formed
• The angle subtended is 7.2º
• Know distance between
• Get radius of Earth!!

7
Fig.03.09
How Far To Moon? Aristarchuss (270 BC) clever
idea

• if you know the size of the Earth (not very
  well, actually)
• during a lunar eclipse, measure how many moon
  diameters
• fit into earths (slightly) cone-shaped shadow
  call that n diameters
• now you know the size of the moon too!!!
• so DM DE/n (its a bit trickier due to
  coniness of shadow)
• now you know the size of the moon too!!!
• knowing angular size of moon
• simple proportion, then dM DM q

8
Fig.03.12
How Far To Sun? Another of Aristarchuss clever
ideas

• at quarter moon, angle at M to E and S is 90º
• precisely measure angle between M and S
• he measured 87º correct answer is 89.83º
• in modern trigonometry, wed say
• dS dM sec A sec A 1/cos A
• he got dS 19 dM
• correct dS 390 dM

9
Fig.03.16
Precession of the Equinoxes

• Requires 26 ky these are 13 ky apart
• NCP moves by quite a bit!!
• Spring and Fall reverse roles, in a sense

10
Fig.03.17
Ptolemys Geocentric system of Deferents
Epicycles

• Preserves the beauty of the circle
• planet moves at steady speed on epicycle in a
  circle
• center of epicycle moves at steady speed on
  deferent
• in a circle result accounts for retrograde
  pretty well
• does not account for observed brightness
  variations

11
Fig.03.19
Refinements to the system

• deferent center is moved away from E
• motion on the deferent is variable speed only
• appears steady from a point called the equant

• I mean, cmon Ptolemy!!
• Isnt this getting a tad ridiculous?
• Who says the Earth has to be at
• at the center, anyway??
• And who says circles are the only
• shape??
• And whats all this about steady speed??
• I mean, really!! Get a grip!!

12
Fig.03.18
Note the order in which the celestial objects are
lined up and that Moon and Sun need no epicycles