On Sunday, August 9, 2015 at 10:57:57 PM UTC+1, Brian Denzer wrote:
In the posthumously-published 18th century manuscript, Descriptio Automati Planetarii, Christian Huygens described the motions of the planets in degrees traveled in one Earth year.

So, for example, he said that Earth travels 359° 45' 40" 31''' in one year, but Saturn travels just 12° 13' 34" 18''' in one year.

What is he talking about, how did he arrive at those numbers, and what is the unit used in the last term (thirds?)?

The degrees traveled by other planets are also listed, but the document is in Latin, so it's very difficult to extract those ratios.

I rather like his approach as an exercise in the math of astronomy. I'd like to understand it better.


There is no reason you should like it, Huygens was using the original geocentric framework where everything moved through the Zodiac including the Sun -

"Here take notice, that the Sun or the Earth passeth the 12. Signes,
or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49
min. or there about, and that those days, reckon'd from noon to noon,
are of different lenghts; as is known to all that are vers'd in
Astronomy.

http://adcs.home.xs4all.nl/Huygens/06/kort-E.html


This is what was known as the periodic times argument where the original heliocentric astronomers switched the time and position of the Sun with the time/motion of the Earth around the Sun and where Isaac was getting his disruptive double modeling from -

"That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun.This proportion, first observed by Kepler, is now received by all astronomers; for the periodic times are the same, and the dimensions of the orbits are the same, whether the sun revolves about the earth, or the earth about the sun." Newton

Kepler said no such thing as the original heliocentric approach to the periodic times was always going to be awkward when dealing with the motions of Venus and Mercury which do not answer to that method.

" The 10th argument,taken from the periodic times, is as follows; the
apparent movement of the Sun has 365 days which is the mean measure
between Venus' period of 225 days and Mars' period of 687
days.Therefore does not the nature of things shout out loud that the
circuits in which those 365 days are taken up has a mean position
between the circuits of Mars and Venus around the Sun and thus this is
not the circuit of the Sun around the Earth -for none of the primary
planets has its orbit arranged around the Earth,as Brahe admits,but the
circuit of the Earth around the resting Sun,just as the other
planets,namely Mars and Venus,complete their own periods by running
around the Sun." Kepler

Seen from a moving Earth, the motion of the inner and outer planets are divided by perspectives and the different type of inputs the Earth supplies to the observed motions of those planets.

The appreciation of the motion of the outer planets around the Sun relies totally on relative speeds of a faster moving Earth overtaking these slower moving planets -

http://apod.nasa.gov/apod/ap011220.html

The inner planets are different as is the input supplied by the orbital motion of the Earth hence the periodic times as understood and used by Kepler and Huygens breaks down.

The major input of the Earth's orbital motion for discerning the heliocentric motion of the inner planets uses the annual motion of the stars behind the Sun thereby setting the Sun up as a central reference for the annual motions of Venus as a grandstand view. There will be a small orbital input from the Earth where the maximum elongations of the inner planets will be accelerated or delayed .

https://www.youtube.com/watch?v=MdFrE7hWj0A

Pay no attention to these 'year time' magnification dunces who have nothing to say about the actual workings of the original geocentric and heliocentric astronomers even though these things have been up for discussion for a few decades in this forum.