NexStar alignment and tracking: spreadsheets and diagrams
These spreadsheets and diagrams are a byproduct of discussions John Carlyle, Alain Fraysse, Mike Swanson
and I had while John was preparing his alignment FAQ for Celestron's NexStar telescopes: we used them
to try out ideas about how alignment might work in principle, and to test theories about it.
Most interesting to start with might be the alignment-simulating spreadsheet. With it, you can
try out the effects of inaccuracies during the alignment procedure; and you could
contribute to the group's understanding of the issues by finding cases where alignment
is particularly sensitive, or insensitive, to setup errors. The ideal is to back up recommendations
of which stars to use, etc., by showing that small setup errors result in only small GOTO errors
for those alignment stars. Also useful would be suggestions about stars to avoid!
The diagrams show, geometrically, how the alignment is carried out: they might be useful
for thinking about where to look for good/bad alignment configurations.
These remarks are --- at least at the moment --- fairly terse; but comments or questions
are welcome.
Carroll Morgan
carrollm@cse.unsw.edu.au
22 February 2001
The spreadsheet alignment
is a simulator for testing various 2-star alignment
choices; and tracking simulates tangential tracking (to see how bad it can be...)
Also, look at these diagrams for an "in principle" explanation of how alignment is done,
and its sensitivity to errors. The diagrams are drawn as if one is looking at the celestial sphere
"from the outside", that is, as if you were looking at a stellar atlas displayed on a globe.
- Diagram 1 shows an alignment done with two stars
S1 and S2, with S1 being close to the pole and S2 far away. It illustrates how --- at least
conceptually --- the scope finds the pole at the intersection of two circles, one drawn around each
alignment star. Then...
- Diagram 2 shows what happens if there is a "make the OTA perpendicular
to the base" error: the circles no longer intersect; the scope cannot find the pole; and the
display reads "Bad Alignment". (For simplicity, call that a "levelling error" even though,
as the FAQ points out, it is the right-angle, not the levelling, that matters.)
- Diagram 3 illustrates the case when a levelling
error makes even the original alignment stars difficult to GOTO. In this case,
the levelling error of S1 (and S2) makes the subsequent GOTO S1 --- that is,
even a GOTO back to one of the alignment stars --- miss by the amount
shown as a blue arrow.
- On the other hand, Diagram 4 shows that you can escape much
of the error introduced by levelling if you use stars on opposite sides of the meridian,
and GOTO a star in between: in effect, the levelling error cancels itself out.
- Diagrams 5, 6 and 7 show what data are gathered by the scope during
the alignment process, and how it is used.
In Diagram 5 the three main data are shown: the pole's
altitude and azimuth, in scope coordinates; and the sidereal time. Those are all that's needed
for subsequent GOTOs.
- Diagram 6 shows how the scope uses the data to perform
a preliminary calculation necessary for a GOTO to that star; and finally...
- Diagram 7 shows how the scope uses the results of that
calculation to determine the correct altitude and azimuth for pointing the OTA.
