Quote:
Originally Posted by OICURMT
I suspect you meant cone error?
|
Hi.
No, that is a totally different.
"Cone error" is the name used by Chinese mount manufacturers in their
instruction manuals for optical axis to declination axis non-orthogonality.
Historically that particular phenomena is referred to professionally
as "collimation error".
The use of the term goes back at least to the early days of surveying
with optical theodolites.
When the optical axis of the theodolite's telescope is not at right angles
to the theodoite's horizontal axis it is referred to as "collimation error".
With transit theodolites surveyors would take two readings, one with the
telescope on the left side of the vertical circle and the other with the
telescope flipped to the right side of the vertical circle.
They would then average these "face left" and "face right" readings
to eliminate any "collimation error".
Collimation error is often a significant source of pointing error particularly
in German Equatorial Mounts (GEMs).
Since the end-user is usually the one responsible for ensuring the OTA
is "square" in the rings or with respect the dovetail plate and they are
in turn "square" to the mount, the simple act of mating the OTA with the
mount often brings it about.
To get back to what I am referring to is not collimation error but
field rotation due to the "stretching" brought about within the FOV
from atmospheric refraction.
Unless you are standing precisely at the north or south poles on Earth,
if you take a time-lapse photograph of the stars apparent rotation around
one of the celestial poles, the trails don't form a perfect circle.
That is because refraction "lifts" the position of the star in elevation
as a function of the stars non-refracted elevation.
Stars on the horizon appear about 1/2 degree higher than they actually
are if Earth had no atmosphere.
At 45 degrees elevation, the amount of lift is only about 2 arc minutes.
At the zenith, the lift caused by refraction is zero.
The ‘true’ polar axis is the one around which the Earth actually rotates.
To appreciate this, a question to ask oneself is if there were a star with
a catalog declination of -90 degrees, i.e. right on the ‘true’ south celestial
pole, where would it appear to an observer, say in Adelaide?
Because refraction causes the apparent place of an object to be ‘lifted’
above its ‘true’ position, a star exactly on the ‘true’ pole will, to an observer
at Adelaide, appear lifted to a position known as the ‘refracted pole’.
So then one might ask, how much higher is the apparent refracted pole
compared to the true pole?
It depends on many factors.
Latitude is one of the most important.
At Singapore, which is at +1° north latitude, the true north celestial pole
will be nearly on the northern horizon, so the refracted pole will be lifted
by refraction by about ½ a degree. That’s 1800 arc seconds!
At Adelaide, the latitude is -35° south and so the true SCP is at 35° above
the southern horizon and the apparent refracted pole is about 85 arc seconds above that.
At Scott Base at the South Pole, the true pole is directly overhead and the
refraction is zero at the zenith. So the refracted pole and the true pole
appear at the same point.
There are other factors that affect refraction and therefore how much
higher the refracted pole is compared to the true pole.
Amongst these are :-
* Ambient temperature
* Atmospheric pressure at the observing site
* relative humidity
* Temperature lapse rate through the troposphere
* The wavelength you are observing at (red, yellow, radio, etc.)
One problem is that for any given elevation in the sky, the amount of
“lifting” to a star caused by refraction is different when compared to a star
at some different elevation.
What’s more, as the star advances across the sky in elevation, the amount
of “lift” is continually varying.
Plus within the FOV, points in the sky that are at lower elevations are
“lifted” more than those at higher elevations. The wider the FOV, the more
the “compression” within the image.
That also means there will still be some field rotation within
the FOV on an equatorial telescope.
The bottom line is that for any given point in the sky you wish to image,
the optimal polar axis will be slightly different and unfortunately continually changes with time.
So the fact that your equatorial mount moves around its polar axis in a
perfect circle can, in some ways, be considered a mechanical compromise,
as the stars don’t circle the sky in perfect circles.
Since the amount of “lifting” to a star caused by refraction is different
when compared to a star at some different elevation, that also means the
tracking rate will continually vary.
One of the first to consider this problem was Arthur Alcock Rambaut who
was a Trinity College Gold medallist mathematician and Royal Astronomer
of Ireland in 1892.
Andrew Robert Hinks who was at Cambridge Observatory elucidated the
problem further in 1898.
These guys were amongst the pioneers of long exposure astrophotography.
The slow emulsions on their plates meant they would require long
exposure times and the problem of field rotation due to refraction became
a real practical problem for them which they endeavoured to analyze and
solve.
These days amateur astrophotographers enjoy the benefit of higher
virtual ISO numbers and can keep exposure times relatively modest
and the FOV small to avoid it becoming an artefact.
Many, I suspect, are not even aware of it despite it being well appreciated
by astronomers over 127 years ago.
Image, Rambaut, 1893 paper :-