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Astronomicum Caesareum. The astronomy of the Emperors. Recreating the astronomy of the Renaissance. Produced by the Unilab Project at the California Institute of Technology with assistance from the Digital Media Center and the SURF Program. www.unilab.caltech.edu.
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Astronomicum Caesareum The astronomy of the Emperors Recreating the astronomy of the Renaissance Produced by the Unilab Project at the California Institute of Technology with assistance from the Digital Media Center and the SURF Program. www.unilab.caltech.edu
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 Apian’s 1540 Astronomicum Caesareum (“Astronomy of the Emperors”).
Apian’s 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 Copernicus’s great work, Apian’s book thus marked the pinnacle of more than a millennium of scientific practice.
A Renaissance astronomer’s 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.
Astronomers assumed that the earth was motionless at (or very near) the center of the cosmos. • They then reckoned that a planet’s 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 deferent’s circumference.
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 deferent’s motion was regular. • Apian’s book allows us to retrace how all these concepts were used.
Apian simplified the astronomer’s 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.
This image shows Mars’s 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 Apian’s 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.
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 Earth’s own rotation.) • To incorporate precession into our procedure, we use this planisphere - a movable map of the universe.
Incorporating the precession for 1500 means deciding where to place Mars’s line of apsides. This is the straight line on which the equant point, the center of Mars’s deferent circle, and the Earth’s 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.
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.
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.
Step 3 • Now we rotate the disk again so that the second pointer, marked AUX Communis, meets the thread.
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. Mars’s line of apsides will point to this location.
Step 5 • First, we rotate the outer disk so that its pointer indicates 183˚31’ - 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.
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.
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.
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 Earthto cross this point.
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.
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.
Step 11 • We now need to take this amount of precession into account in setting the actual deferentdisk - our third disk, and the one which carries the epicycle. • We do this by tracing one of the oblique lines from the first disk’s 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.
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.
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 epicycle’s motion for the period between 0 AD and February 23, 1500.
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.
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.
Step 16 • Now we rotate the epicycle’s index until it meets our thread. • The epicycle is now in position for the end of 1499.
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.
Step 18 • Then we rotate the disk until the epicycle’s 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 Emperor’s birthday.
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.
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 V’s birthday, February 23, 1500.
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 Apian’s procedure. It is within a degree or so of the actual position. (The green line is the ecliptic.) • Apian’s book could clearly produce a remarkably accurate prediction.
