[time-nuts] Danjon Astrolabe meridian transit timing errors

[Dr Bruce Griffiths]

Tom Van Baak wrote:
>> Accuracy still won't be much better than1% of the solar diameter or 
>> about 1 second of time nowhere near the o.1 sec or better hoped for.
>> Bruce
>>     
>
> Bruce,
>
> Can you show us how to derive the accuracy number?
>
> I would have guessed that with fractional degree Al-El
> steering, a rotary encoder, 12 hours of sampling, and
> curve fitting that one could calibrate solar time against
> a local UTC standard to a bit better than that.
>
> /tvb
>
>
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>   
Tom

First I'll deal with some of the problems of the various proposed 
transit methods:
For a time error of 100 millisec or less the corresponding error in the 
sun's azimuth is about 1.5 arcseconds.

When viewed from the bottom of the atmosphere the sun and stars appears 
to move about randomly due to the effects of atmospheric seeing.
The amplitude of this random image displacement in the visible depends 
on the altitude of the object being observed it can be as large as 
several arc seconds when observing stars with an altitude of 45 degrees 
at night. This random image motion due to atmospheric turbulence is even 
greater during the day (as much as 10 arc sec rms on Mauna Kea).
http://adsabs.harvard.edu/abs/1990ursi.symp...75C
The solar image is not uniformly bright across the disk, there is a 
noticeable darkening towards the limb.
There is no sharply defined solar limb, prominences and other outbursts 
can extend arc minutes from the edge.
Local seeing effects such as turbulent air over structures warmed by the 
sun such as buildings, concrete pads, roads etc will also have 
significant effects.
Internal instrument turbulence due to solar heating can also be problematic.
Scintillation in the solar irradiance will also have an effect on the 
noise in solar meridian transit measurements.
At solar meridian transit solar heating of the ground will produce worse 
seeing than earlier in the day when the suns altitude is lower.

The accuracy of a transit method that uses a pair of photodetectors to 
compare the light from two small sections of the solar limb will be 
adversely affected by atmospheric seeing and bright prominences.
The angular size and declination of the sun vary throughout the year.
Thus the position of the limb sensing detectors have to be adjusted to 
accommodate the variation in the sun's altitude at meridian transit.
Making such adjustments without changing the effective azimuth defined 
by the detectors and associated optics, gnomon or slit is difficult 
especially when the maximum variation in azimuth due to such adjustments 
has to be no more than 1 arcsecond or so.

It has also been implicitly assumed that azimuth of the transit 
instrument remains fixed over time and temperature variations. it is 
actually difficult to ensure the azimuth remains constant to an 
arcsecond or so over time without taking heroic measures to ensure the 
instrument mounting plinth is sufficiently stable. Uneven solar heating 
of the instrument plinth can cause it to the instrument to tilt and 
twist its azimuth through several arc seconds. Joints between dissimilar 
materials are prone to cause the instrument azimuth to rotate as it 
warms up. A suitable kinematic joint such as a Maxwell clamp can reduce 
the thermal rotation significantly but even then it is difficult to 
ensure an azimuth stability of an arcsecond or so.

The pointing stability of an instrument using plastic (fibers, etc) 
parts can be problematic especially when it is subject to temperature 
cycling.

Bruce