[time-nuts] Measuring sidereal/solar time?

Chris Albertson albertson.chris at gmail.com
Fri Dec 30 16:30:35 EST 2016

On Fri, Dec 30, 2016 at 2:42 AM, Attila Kinali <attila at kinali.ch> wrote:
> On Fri, 30 Dec 2016 10:59:03 +0200
> Anders Wallin <anders.e.e.wallin at gmail.com> wrote:
>> out of curiosity, are there any amateur/semi-pro experiments that can
>> measure the length of the solar or sidereal day to sub-millisecond
>> resolution?

Yes.  It is not hard at all to measure the Earth's rotational period,
if all you needs is "sub millisecond"  It would get harder if you
cared about nanoseconds.

I worked on an amateur project with some others and while measuring
the Earth was not the goal we had to know the Earth's rational period
to do the work.   The project was about stellar photometry.  But I
leave that part out.....

Basically what we did was mount a camera made out of a small CCD
sensor and a 135mm f/2.8 camera lens salvaged from  an old 35mm film
camera.  The camera was fixed to the roof of my garage. (This was THE
big cost saving feature:  The camera could not move.  The mount as
fixed at one location in the sky forever, right at the equator)  I
placed it in one end of a long wood crate and it looked up at the
equator through a square hole on the upper end of the box.   The box
provided some protection from the elements and provided a lot of light

To measure Earth's rotation all you need to do in know exactly when
you took an image and to have a GOOD catalog of star locations.  Let's
say your image captures 200 stars.   They are rather blurry and each
covers maybe 5 pixels but even so you compute the centroid of each
"gaussian blob" and then do a least squares fit of all those centroids
to the astrometric catalog.  The catalog is "good" to several
milliacrseconds and with hundreds of centroids you can figure out were
the camera was printed to a few  "MAS" (Milli Arc Seconds).     We
took many images every clear night for several years.    Hardware cost
today is "not much" and you can use salvaged camera equipment  Almost
all of the software is available for free. Certainly matching stares
to catalog images is.  Yes the lens has geometric distortion and the
CCD is likely not exactly 90 degrees to the optical axis but the
software models this.  This is possible because millions of star
positions are known to insane levels of accuracy and if they appear in
the "wrong" place in your image you can bet the cause is geometric
distortion in your camera, especially after seeing the same error in
hundreds of images.  We used narrow filters to limit the image to just
one "color" so the chromatic aberration in the optics i not an issue,
filters are cheap.

As part of our processing we time-tagged each image and also recored
where the optical xis was pointed at.

So you'd need a small telescope or big camera lens and a camera that
can be triggered by a computer and software.  Not really expensive.
I'd invest in the best used optics you can and get a monochrome

Some people in the past century used transit telescopes to manually
measure the time a star crossed a hairline in an eyepiece.  Then the
next night to observe the same star again.  Now you know the length of
the day (after you reduce the data)   Put you can measure a dozen
stars every night and take an average.   In concept it is very simple.
  But today we can measure a tens of thousands of stars per day from a
suburban roof top.

Almost all other methods of measuring the Earth's rotation do not
collect enough data.  You need tens or hundreds of thousands of data
points. if you want to know the sidereal period to Time Nut standards


Chris Albertson
Redondo Beach, California

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