[time-nuts] Danjon Astrolabe meridian transit timing errors

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Sat Sep 30 20:36:33 EDT 2006

Bill Hawkins wrote:
> OK, there are serious sources of error in making a one-time
> solar transit measurement.
> What I propose is a differential method, a favorite of
> instrument makers to reduce errors. This is possible
> because the equation of time makes a correction of only
> one percent or so.
> A steady platform with a single axis of motion is
> turned by a precision synchronous motor driven by a
> frequency derived from a cesium standard. This provides
> a fixed reference rotation speed.
> Use a mirror mounted so that it turns on the horizontal axis
> and is in turn turned on the vertical axis by the accurate
> frequency. Use a simple sun-tracking servo to keep the image
> of the sun on a mirror attached to a galvanometer assembly.
> Use an analog servo to generate a current that will keep the
> solar image from the galvo centered horizontally on a target.
> Use high frequency dithering to improve accuracy. Filter the
> galvanometer current to remove the dither and measure it with
> a computer. Use math tricks to subtract the equation of time,
> looking for a drift rate at a frequency much less than one
> cycle per day, but larger than the drift rate of the standard.
> Systematic errors in the instrument should be revealed. If they
> are temperature dependent, they can be compensated. The stability
> of the mounting for the apparatus becomes a problem over long
> periods of time. Perhaps ways can be found to compensate can be
> found, but I can't think of something that doesn't require a
> stable reference platform.
> The fact is, no other physical property can be measured to the
> same accuracy as frequency, because atomic motion provides a
> stable reference.
> The question is, then, can long-term averaging remove the small
> errors in measuring the position of the sun relative to a
> rotating reference platform?
> If this is feasible, where can I find a Maxwell clamp? Google
> can't find one.
> Regards,
> Bill Hawkins
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> time-nuts at febo.com
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The accuracy of a solar meridian transit measurement can be 
significantly improved if the position of the sun is continuously 
measured starting a short time before until a short time after the 
meridian transit.
A least squares fit to the sequence of positions can then be used to 
derive an accurate time for the actual transit. This can be done without 
using any moving components if the position sensor and associated optics 
have a sufficiently wide field of view.

A Maxwell clamp is a variant of the well known Kelvin clamp kinematic mount.
The classical Kelvin clamp employs 3 ball feet on one part which mate 
with a hole (ideally a 3 sided prismatic hole) a slot (V-groove) and a 
flat on the other part.
The Maxwell variant employs 3 radial V grooves instead of the hole, slot 
and plane. If the axes of the 3 grooves don't meet at a common centre 
then differential rotation occurs during differential expansion  between 
the mated parts. However this rotation is repeatable and can in 
principle be measured and corrected for. Friction should be low in a 
kinematic mount.
Suitable kinematic mount components are available from:


For heavier loads quasi-kinematic mounts such as spherolinders can be used:


If a suitable kinematic mount is used, two parts with different thermal 
expansions can be repeatedly mated whilst maintaining relative alignment 
to a small fraction of an micron.
With suitable components nanometer repeatability can be achieved.

For even higher stability with permanently mounted parts, 3 flexures can 
be used to mate 2 components with differing thermal expansions.
Well designed flexure mounts can have higher stability than kinematic 
mounts because friction is absent.
Integral flexures are used in moving stages with nanometer repeatability.


Whilst it is relatively easy to generate a precise frequency it is 
extremely difficult and expensive to make a platform that rotates with 
runout of not more than an arcsecond.
Roller bearings are inherently unsuitable, preloaded pairs of angular 
contact ball races are considerably better. Air bearings can be good 
enough but tend to be expensive.
A kinematic bearing design with extraordinary accuracy is possible.
Driving such a platform without destroying its inherent precision 
through the drive coupling can be problematic.
Backlash in gear reduction systems can also be a problem unless suitable 
preloads are used.
Periodic and other errors in gears can also be problematic unless the 
errors are repeatable, so they can be measured.
Drag from electrical cables connecting between the rotating platform and 
its fixed base can also be problematic.
You really need an angular position encoder with subarcsecond resolution 
and accuracy mounted on the rotating platform to allow most of the 
vagaries of the drive system to be eliminated.
Such encoders are not cheap. With an encoder one can also use feedback 
to improve the accuracy of the rotation speed of the platform.

For small rotations flexure pivots or integral flexure equivalents 
thereof can be used.

In principle one could use a pair of star trackers to monitor variations 
in the angular orientation of the instrument mount with respect to the 
An accuracy of around 1 arc second in determining  the  tilt, tip and  
rotation of the plinth. Although such measurements can only be made at 
night, with suitable insulation the movements of a well designed plinth 
would tend to be slow.


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