Joachim,
See here, about 1/2 page down. <https://en.wikipedia.org/wiki/Sidereal_time>
"Greenwich Mean Sidereal Time (GMST) and UT1
<https://en.wikipedia.org/wiki/UT1> differ from each other in rate, with
the second of sidereal time a little shorter than that of UT1,
so that (as at 2000 January 1 noon) 1.002 737 909 350 795 second of mean
sidereal time was equal to 1 second of Universal Time (UT1).
The ratio varies slightly with time, reaching 1.002 737 909 409 795 after a
century.[3] <https://en.wikipedia.org/wiki/Sidereal_time#cite_note-3>"
What I need for the timepiece is a way of not only generating a
non-standard gear ratio, in this case, 1:1.002737909350795, but something
that
also modifies that gear ratio over time to the latter value, and beyond, to
account for the celestial drift errors over centuries. Much like the
Clock of the Long Now Foundation does this with their equation of time cam
for 10,000 years drift variation calculated in stack
<http://demonstrations.wolfram.com/VariationOfTheEquationOfTimeWithThePrecessionOfTheEquinoxes/>
.
Now that I see it is possible to make a non-standard gear ratio with
helical spur gears, that can help, but I can't make a set that will fit in
a watch-
maybe a large clock. It also isn't continuous, there is no way to keep it
running in the same direction when it reaches the end of it's gear spiral.
The ratio was going to be approximated to as many places as possible for
normal gearing- it has been done out 6 or so places with only a few gears
by G. Daniels. That was why I wanted to learn Python- that program I
started was a gear calculation program to calculate that ratio out as many
places as possible. That was directly for a geartrain in a watch that
showed sidereal time derived from a solar (mean) time gear train, as
accurately
as possible to theory ratios with as few gears as possible. The python
program I have also showed the deviation from that ratio and calculated
the error in time difference over centuries for a given set of gears.
I have no idea if it is possible to modify a gear ratio in running over
time. I know there are progressive lead screws, where pitch gradually
varies,
but I've never seen a progressive geared mechanism that gradually changes
gearing ratio a specific amount over time. Most people would never
need such a thing mechanically. I do.
Not sure if it's possible, but learning python would help more...
-Andrew
