Quote:
Originally Posted by ausastronomer
At an altitude of 5 degrees above the horizon the effects of atmospheric refraction will cause the target to be visually incorrectly positioned by about 10' (1/3rd the diameter of the full moon ) in relation to its true actual position.
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John
It is derived from a formula known as the "surveyors algorithm" for determining position on earth astrometrically in absolute coordinates, using a theodolite to observe the stars, and a precision time source. A theodolite is just a precision altaz telescope where the azimuth circle is accurately aligned to north using a terrestrial reference mark (from a map) and, with the base precisely levelled, the altitude measurements are also accurate.
In the surveyors case:
- the star positions are known (from an ephemeris);
- the mount is dead level, and
- the measurements from the circles are accurate, so
the problem is to determine the telescope's lat and long.
In the astronomical case, however:
- the star positions are known,
- the telescope position is known (thanks to GPS) and
- the orientation of the circles is unknown, so
the problem is to determine the orientation of the circles relative to the sky.
In both cases the algorithm is curiously the same apart from transposing some variables. The algorithm works by projecting the polar axis ( EQ mount) or azimuth axis (altaz setup) on the sky then:
a) for an EQ setup, it has to find the altitude of this point above the horizon and its azimuth; or
b) for an altaz setup, it determines the declination of the point on the sky, and the hour angle (east/west).
It then calculates the offset from the correct values, based on your longitude and latitude, assuming the mount is level, determines the errors and stores these for later coordinate conversions to find any object at some future time. This is why - if you enter incorrect date/time/lat/long data, the resulting alignment and GOTO's can be WAAY off. Levelling the mount/tripod head is also important - something many may not be aware of.
In the EQ setup, the star near the horizon primarily determines the azimuth of the polar axis relative to the star. Refraction affects the altitude, not the azimuth, and any error from refraction is thus negligible for this - well below the desired precision.
The star on the meridian is used to determine the altitude of the polar axis and hence it does need to be reasonably high to avoid an error due to refraction, andn ideally on the meridian because during the actual observation, as the star crosses the meridian its altitude is constant, to a first approximation.
When surveyors use this to calculate an astrometric position they do include a correction for refraction in the measure altitude of a star, using the site altitude, barometric pressure and humidity and a lookup table from the USNO Almanac. But they are trying to achieve sub - minute of arc accuracy, whereas I’m content with being within 15 arc min, so there’s no point worrying about it - especially when a telescope mount has greater mechanical errors between the axes.
There are cases where the algorithm is vulnerable to errors:
a) two stars close together;
b) two stars more-or less opposite due east and west; in this case the azimuth error is small but the altitude correction will be poor.
c) both stars at about 45 degrees elevation or more and neither near the meridian, in which case the both altitude and azimuth accuracy will be poor.
The latter case does seem to arise frequently in practice with a Synscan, due to the limited choices of bright stars.
Lastly there is a significant difference in the quality of an alignment done by just eyeballing the reference stars vs aligning with an eyepiece with crosshairs - the latter invariably achieves a much better result. The subsequent GOTO's are also sensitive to non-perpendicularity between the optical axis of the scope and the dec axis of the mount, and between the dec axis and RA axis. The Skywatcher EQ mounts complete with telescope+mount combinations may well have cone errors of the order of a degree.
