three star alignment

Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.
A.Z.

On Thu, 06 Jan 2005 16:46:05 GMT, Antonio Zanardo wrote:

Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.
A.Z.

I am not familiar with three star alignment. My Meade Magellan setting
circles use a two star alignment with a horizontally leveled scope as a
third reference point.


--
Martin R. Howell
"Photographs From the Universe of Amateur Astronomy"
http://members.isp.com/universeofama...nomy%40isp.com

Antonio Zanardo wrote:
Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.
A.Z.


I have a MathCad document which illustrates the concept somewhere. Would
you like it

Steve

On 2005-01-06, Antonio Zanardo
wrote:
Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.

Your telescope mount provides a coordinate system for the direction
your telescope is pointing. The celestial coordinate system provides
the directions to stars. The computer in your telescope does the math
to transform the coordinate system of the sky to the coordinate system
of your telescope. When you do the alignment you are measuring the
positons of the alignment stars in your telescope's coordinate system.
The computer uses the measurements you made during the alignment
process to compute the direction to any other star in the telescope's
coordinate system. You can see the math required in a note by Tomishi
Taki that appeared in the Sky & Telescope Astronomical Computing
column in February, 1989. There is an update on the World Wide Web at
http://www.asahi-net.or.jp/~zs3t-tk/aim/aim.htm.

On 2005-01-09, William Hamblen wrote:
On 2005-01-06, Antonio Zanardo
wrote:
Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.

Your telescope mount provides a coordinate system for the direction
your telescope is pointing. The celestial coordinate system provides
the directions to stars. The computer in your telescope does the math
to transform the coordinate system of the sky to the coordinate system
of your telescope. When you do the alignment you are measuring the
positons of the alignment stars in your telescope's coordinate system.
The computer uses the measurements you made during the alignment
process to compute the direction to any other star in the telescope's
coordinate system. You can see the math required in a note by Tomishi
Taki that appeared in the Sky & Telescope Astronomical Computing
column in February, 1989. There is an update on the World Wide Web at
http://www.asahi-net.or.jp/~zs3t-tk/aim/aim.htm.


When aligning on more than the minimum 2 stars your computer can do a fit
to the data to minimize pointing errors. Some computers let you do an
alignment update when you are pointing the telescope at known stars.
Pointing errors happen because the telescope mount is not perfect,
your pointing at known stars is not perfect and the math done by your
computer is not infinitely precise.

Thanks William for your answer.

Your suggestions were helpful, but are not what I am looking for.
I'd like to know what is the algorithm wich enables tracking a celestial
object, after doing a three star alignment with a mount not aligned to pole.
This is what can be done, i.e., with the Vixen Skysensor controller.
Is such a program available on the Web?

Regards.

Antonio Zanardo

"William Hamblen" ha scritto nel messaggio
...
On 2005-01-09, William Hamblen wrote:
On 2005-01-06, Antonio Zanardo

wrote:
Does anybody know how the three star alignment works?
I'd appreciate any hints on the alghorithm basics.

Your telescope mount provides a coordinate system for the direction
your telescope is pointing. The celestial coordinate system provides
the directions to stars. The computer in your telescope does the math
to transform the coordinate system of the sky to the coordinate system
of your telescope. When you do the alignment you are measuring the
positons of the alignment stars in your telescope's coordinate system.
The computer uses the measurements you made during the alignment
process to compute the direction to any other star in the telescope's
coordinate system. You can see the math required in a note by Tomishi
Taki that appeared in the Sky & Telescope Astronomical Computing
column in February, 1989. There is an update on the World Wide Web at
http://www.asahi-net.or.jp/~zs3t-tk/aim/aim.htm.


When aligning on more than the minimum 2 stars your computer can do a fit
to the data to minimize pointing errors. Some computers let you do an
alignment update when you are pointing the telescope at known stars.
Pointing errors happen because the telescope mount is not perfect,
your pointing at known stars is not perfect and the math done by your
computer is not infinitely precise.

On Sun, 09 Jan 2005 14:24:10 GMT, "Antonio Zanardo"
wrote:

Thanks William for your answer.

Your suggestions were helpful, but are not what I am looking for.
I'd like to know what is the algorithm wich enables tracking a celestial
object, after doing a three star alignment with a mount not aligned to pole.
This is what can be done, i.e., with the Vixen Skysensor controller.
Is such a program available on the Web?

I think you will find that the Tomishi Taki reference is what you are looking
for (which includes code). The point is, there is really no such thing as a
three-star alignment. Two stars are all that are required to align the two 2-D
coordinate systems (the scope and the sky). Three star (and higher) alignments
are doing one of two things- they are either picking the two stars with the best
geometry for calculating an alignment, or they are fitting the positions to
minimize the error. In either case, that basic calculation is the same as for a
standard two-star alignment.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On 2005-01-09, Antonio Zanardo
wrote:

Your suggestions were helpful, but are not what I am looking for.
I'd like to know what is the algorithm wich enables tracking a celestial
object, after doing a three star alignment with a mount not aligned to pole.
This is what can be done, i.e., with the Vixen Skysensor controller.
Is such a program available on the Web?

Taki's web site has the math to permit you to do this. You are doing a
coordinate transform from the celestial coordiate system to the telescope
coordiate system. The celestial coordinate system rotates around the
polar axis once per sidereal day. This causes an apparent motion of the
star in the telescope coordinate system. The computer in your telescope
has a built-in clock and updates the motions of the star in the telescope
coordinate system many times a second, sending the result to the motors
in the mount so you get continuous tracking.

"William Hamblen" ha scritto nel messaggio
...
On 2005-01-09, Antonio Zanardo

wrote:

Taki's web site has the math to permit you to do this. You are doing a
coordinate transform from the celestial coordiate system to the telescope
coordiate system. The celestial coordinate system rotates around the
polar axis once per sidereal day. This causes an apparent motion of the
star in the telescope coordinate system. The computer in your telescope
has a built-in clock and updates the motions of the star in the telescope
coordinate system many times a second, sending the result to the motors
in the mount so you get continuous tracking.


Many thanks to everybody for your help. It looks like the TAKI's code is
what I was looking for.

Antonio Zanardo

Statistically its like fitting a straight line to more than 2 points(minimum
required). The more points the greater the accuracy because random errors are
starting to be reduced.