Astronomicum Caesareum

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Astronomicum Caesareum
The astronomy of the Emperors

• Recreating the astronomy of the Renaissance

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Program. www.unilab.caltech.edu
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• This system introduces a central aspect of
  astronomical practice during the Renaissance.
• We will retrace the steps by which an astronomer
  found the position of a planet for a given date.
• To do so, we will use a sophisticated scientific
  instrument - but one made out of paper and bound
  into a book. This is Peter Apians 1540
  Astronomicum Caesareum (Astronomy of the
  Emperors).

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• Apians volume, perhaps the most beautiful of all
  early scientific books, used the principles of
  the ancient astronomer Claudius Ptolemy. Those
  principles dated back to antiquity, and they
  remained definitive until Copernicus argued that
  the Earth orbited the Sun in his On the
  Revolutions (1543).
• Issued just three years before Copernicuss great
  work, Apians book thus marked the pinnacle of
  more than a millennium of scientific practice.

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• A Renaissance astronomers main duty was to
  predict where a planet would be on any given
  date. In particular, he wanted to know its
  longitude its position on the great circle
  called the ecliptic (or Zodiac) that spanned the
  heavens and was divided into the twelve signs
  still familiar to us today.
• This picture shows the ecliptic as portrayed by
  seventeenth-century map-maker Johann Blaeu.

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• Astronomers assumed that the earth was motionless
  at (or very near) the center of the cosmos.
• They then reckoned that a planets apparent
  movements around the earth resulted from the
  combined motions of at least two circles. The
  first of these was called the deferent. The
  planet itself moved on the rim of an epicycle
  that moved around the deferents circumference.

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• But astronomers found they needed to use two more
  techniques.
• First, they said that the deferent circle could
  be eccentric - that is, the earth could be
  slightly off-center.
• Second, they invented the equant. This was a
  separate point in space, about which the
  deferents motion was regular.
• Apians book allows us to retrace how all these
  concepts were used.

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• Apian simplified the astronomers task by
  building for each planet a device called an
  equatorium.
• An equatorium was a kind of circular slide-rule
  or, if you prefer, a Renaissance computer.
• It reproduced in physical form all the
  mathematical concepts of astronomy - the
  epicycle, the eccentric deferent, and the equant
  point.

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• This image shows Marss equatorium in its
  starting position. It is composed of seven
  rotating disks.
• We will use this equatorium to discover where
  Mars was on February 23, 1500 - the birthday of
  Apians own imperial patron, the Holy Roman
  Emperor, Charles V.
• In doing this we are reproducing the steps taken
  by Apian himself when he did this calculation in
  1540.

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First, however, we need to take account of
precession. Precession is a very slow movement -
less than 1 per century - that all stars and
planets appear to share. (We now know that it
comes from a variation in the Earths own
rotation.) To incorporate precession into our
procedure, we use this planisphere - a movable
map of the universe.
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Incorporating the precession for 1500 means
deciding where to place Marss line of apsides.
This is the straight line on which the equant
point, the center of Marss deferent circle, and
the Earths center all lie. We can find where
this line lies by rotating the blue disk and
looking at the positions of the pointers on its
edge.
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Step 1 First, we rotate the disk so that the tab
on the far right (which is marked X) matches
the 1500 point on a scale beneath the disk.
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Step 2 Now we extend a thread from the center of
the disk through the 1500 point on a small oval
scale printed on the face of the disk. This
scale is called a trepidation oval. It provides
for an extremely slow variation in the rate of
precession that medieval astronomers thought they
had observed. It is now known that trepidation
does not exist.
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Step 3 Now we rotate the disk again so that the
second pointer, marked AUX Communis, meets the
thread.
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Step 4 Now we read off the location of the
pointer to the top left of the disk, which is
marked with the symbol for Mars, ?. Its location
is 15 in the sign of Leo. We will need to
remember this and use it later. Marss line of
apsides will point to this location.
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• Now we turn to the equatorium itself.

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• Step 5
• First, we rotate the outer disk so that its
  pointer indicates 18331 - a value obtained from
  a separate table.
• This sets the basic position of the deferent for
  1400.
• We now need to move it further to take account of
  99 more completed years, plus the 53 days
  sufficient to bring us to February 23.

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• Step 6
• To advance 99 years, we use a scale on the edge
  of the outer disk.
• We find the point on this scale marked 99. Then
  we extend a thread from the Earth through this
  point.

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• Step 7
• Now we rotate the outer disk until its marker
  meets this thread.
• We have set the deferent for the end of 1499.
• We now need to add the remaining days.

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• Step 8
• This we do by using a second scale on the outer
  disk (here it is hidden beneath the next disk).
• We find the point on this scale corresponding to
  February 23.
• Then we extend the thread from the Earth to cross
  this point.

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• Step 9
• Now we rotate the outer disk until its pointer
  meets the thread.
• The deferent is now set for the correct date.
• Next, we need to incorporate precession, which we
  found earlier to be 15 in the sign of Leo.

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• Step 10
• To do this, we move to the second disk, and
  rotate it so that its pointer moves to 15 in Leo
  - the value we found earlier using the
  planisphere.
• Note that the small central disk rotates in line
  with this second disk. This means that by moving
  the second disk, we are indeed setting the line
  on which the earth and the equant lie. This is
  the line of apsides.

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• Step 11
• We now need to take this amount of precession
  into account in setting the actual deferent disk
  - our third disk, and the one which carries the
  epicycle.
• We do this by tracing one of the oblique lines
  from the first disks pointer to the scale on the
  inside of the second. There we find a value of
  8 in the sign of Aquarius (or 308). We extend
  a thread from the equant through this point.

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• Step 12
• This is where the center of the epicycle must go.
• So we rotate the third disk, the deferent, until
  the center of the epicyle falls on our thread.

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• Step 13
• Then we rotate the outer of the two epicycle
  disks so that its zero point marked with a
  cross, ? - also meets this line.
• This means that the epicycle is correctly placed
  for 0 AD.
• We are now ready to introduce the epicycles
  motion for the period between 0 AD and February
  23, 1500.

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• Step 14
• First, we rotate the inner epicycle disk so that
  its pointer indicates 105 on the scale on the
  outer disk. The value of 105 is obtained from
  separate tables, and corresponds to the total
  rotation for 1400 years.
• This sets the epicycle to its position for 1400
  AD.
• We now need to add 99 years plus the days
  corresponding to February 23.

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• Step 15
• Next, we locate the point on the scale of the
  inner epicycle disk marked 99.
• We extend a thread from the center of the
  epicycle through this point.

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• Step 16
• Now we rotate the epicycles index until it meets
  our thread.
• The epicycle is now in position for the end of
  1499.

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• Step 17
• Now we located the point on the inner scale of
  the inner epicycle disk that corresponds to
  February 23.
• We extend the thread from the center of the
  epicycle through this point.

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• Step 18
• Then we rotate the disk until the epicycles
  pointer meets our thread.
• The pointer is now at 20 in the 8th sign (260).
• The disks are now in place to reveal the position
  of the planet Mars on the Emperors birthday.

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• Step 19
• The planet Mars is indicated by a rosette printed
  on the pointer on the inner epicycle disk.
• To find its observed place from the Earth, we
  extend a thread from the Earth, through the
  center of this rosette, to the Zodiac scale
  printed on the page itself.

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• Step 20
• This gives a reading of 54 (or 24 in the sign
  of Taurus).
• This, then, is where Mars will appear in the
  Zodiac on Charles Vs birthday, February 23,
  1500.

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Here you can see where Mars actually was on the
evening of February 23, 1500. The red cross marks
the position that we have just calculated using
Apians procedure. It is within a degree or so
of the actual position. (The green line is the
ecliptic.) Apians book could clearly produce a
remarkably accurate prediction.