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Subject: Re: [M]: 2-Star Alignment Problem (Long again!)
From: PAugello@aol.com
Reply To: mapug@shore.net
Date: Thu Dec 12 00:01:06 1996

In a message dated 96-12-11 17:43:24 EST, you write:

<< In 2-star alignment you get 4 observations (alt and az of two stars), so
you end up with 4 equations in 5 unknowns; something has to give. I'm
pretty sure Meade assumes N-tilt is zero and generates corrections for the
other 4 >>

Jim:
Whew! My experience is limited to writing a program to run DobDrivers.
It started in BASICA in '91 on a lunchbox style 8088 diskette system I had
lying around, and ended up in VB -- I don't use it much since I got my
LX-200, but the main reason I bought the Meade was for imaging. The system
worked fine for visual use, and I even ended up adding voice control -- I
would wear a wireless mic and talk to the 'scope, and it would listen. It
supports both my 8" and 13" Dobs.
The basic method I use has stayed the same the whole time, though. I
just took a code fragment that came with the DobDrivers that converted HA-DEC
to ALT-AZ and do a one star alignment. That gives me all the info I need to
run the motors and to slew. As I looked at the formulas in the code
fragment, it looked to me like 2 equations in 2 variables. I saw that if
LAT, LON, LST, ALT and AZ (got 'em all, right?) were replaced by arbitrary
variables, two intersections would be needed, and I wouldn't know where the
horizon was, but I would have all the info needed to solve. I am just
solving for the transformation angles between the two coordinate systems.
When I start my program I first pick which 'scope I am using. This lets
me set the # steps/deg constants that I have measured for both 'scopes. Then
I enter LST -- I first start TheSky and get it from it -- and I calculate an
offset of LST from system time. I just ignore the difference between a
siderial second and a civil second while the program runs and just use the
system clock + offset for LST. It's good enough for visual use. Next I
enter the RA-DEC of an object and and hit my SYNC command. I locate the
object and lock the clamps. When I SYNC, I calculate the constants for the
two equations for now -- the system clock + offset. I didn't bother to
differentiate the equations WRT time, I just do an approximation. I solve my
equations for now and again for now + 10 seconds. I subtract for delta ALT
and delta AZ, convert to # steps, and run the motors. I then wait 10 sec and
do it again. For "Photo" tracking I get a step rate from the deltas and set
timers to step the motors at that rate.
I am really making little straight lines, but the point is that to only
SYNC on one star I need accurate site information because the RA-DEC - >
ALT-AZ of the zenith is the second intersection I need. Put an other way --
these two equations are both functions of time and I have two of them. It is
only a matter of convenience that I use the zenith at the same instant as the
second intersection. Thats where the dependance on accurate site info and
LST / HA comes from, otherwise they are all arbitrary. To get slew rates
from the equations is math even I took, once -- not a big deal.
So: I just assumed that if I could see this, and that all of the
digital setting circles that came out at about the same time used two-star
alignment, they were doing the same thing -- RA-DEC -> ALT-AZ with an
arbitrary clock and two intersections. All Meade would need to do is get
tracking rates. If this is the case, then the only need for accurate site
and time info is for refraction correction and finding planets, and that if I
do a one-star align and then sync on another star, the system should now be
two-star synced at a know site. I suppose they could keep the first
intersection (the zenith at power-up) but that would be pretty silly.
Naturally, the issues of using poorly placed alignment stars would be
evident, and the pointing would be best when the second intersection is very
close in ALT-AZ (ergo time) to where you are going.
I gotta try this. Next clear night, I am going to go ALT-AZ (I usually
use the wedge myself) and do a careful two-star alignment. Then I will do a
long slew and see how close I get. Next, slew to south and 0 and shut off.
Wait a minute, turn on and use the same stars for 0-star with two syncs by
GOTOing and then try the same slew. More to the point -- after several slews
and syncs, does it make any difference how I started?
Wadd'ya think?

Later,
Peter Augello

ps: I don't know what you mean by azimuth encoder bias and altitude encoder
bias. I use stepper motors, not encoders, but same diff.