Download Controlling a Three Meter Mirror Array Reflector to Track Stars

Controlling a Three Meter Mirror Array Reflector to Track Stars
Benjamin Adams
University of Utah Department of Physics and Astronomy
August, 2009
Abstract
The University of Utah Gamma Ray Group and the Department of Physics and Astronomy have
assembled two 3 meter optical reflector telescopes in the desert outside of Grantsville, Utah. This
thesis project was to provide software programming and associated hardware to control the
positioning and star tracking operations of the telescopes. The hardware included the use of
servo motors and position encoders, a communications link between the telescopes and
computer, and mechanical safety switches for position limits. The software was completely
written in National Instrument's LabVIEW. The end goal was to provide a system that would, at
a greater precision than the telescope's resolution, move the telescope to any fixed point, as well
as track a star's position over time.
Table of Contents
1.0 Introduction
2.0 The System Design
2.1
Hardware
2.1.1 Mechanical Limit Safety Switches
2.1.2 Communication Link
2.1.3 Servo and Encoder Wiring
2.2 Software
2.2.1 Communication Protocol
2.2.2 Tracking Algorithm with Servos and Encoders
2.2.3 Coordinate System Transformations
2.2.4 Precession and Corrections
2.2.5 Software Limit Safety Switches
3.0 Operations Guide
3.1 Power-up
3.2 Starting the program
3.3 Finding the Reference Zeros for Each Axis
3.4 Positioning
3.4.1 Track a Star
3.4.2 Go to a Position
3.4.3 Manual Entry
3.5 Ending Communication
3.6 Power Down
4.0 Conclusions and System Validation
5.0 References
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Table of Figures
Figure 1, Horizon Coordinate System
Figure 2, Equatorial Coordinate System
Figure 3, Safety Switch Wiring Diagram
Figure 4, Power Relays
Figure 5, Elevation Safety Switch
Figure 6, Azimuth Safety Plug
Figure 7, Communications Wiring Diagram
Figure 8, Servo and Encoder Wiring Diagram
Figure 9, Encoders, Encoder Unit
Figure 10, Servo Amplifier/Controller, Motor
Figure 11, Software Code – Example Servo Commands
Figure 12, Servo Movement – Velocity vs. Position
Figure 13, Servo Movement – Position vs. Time
Figure 14, Software Code – Calculating Sidereal Time
Figure 15, Software Code – Transf. from Equatorial to Horizonal Coord.
Figure 16, Software Code – Precession Function
Figure 17, Software Code – Corrections Function
Figure 18, Software – Main Tab
Figure 19, Software – Manual Control Tab
Figure 20, Software – Positioning Tab
Figure 21, Software – Track Selection Sub-Program
Figure 22, Software – Position Selection Sub-Program
Figure 23: Tracking Data – Azimuth Axis
Figure 24: Tracking Data – Elevation Axis
Figure 25: Tracking Data – Elevation Axis – Closer
Figure 26: Tracking Data – Sample from Data File
Figure 27: Star Images, Alp Lyr
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1.0 Introduction
The University of Utah Gamma Ray Group and the Department of Physics and Astronomy
acquired a number of mirror array reflecting telescopes that will be used for a wide range of
astronomical research. Two of these 3 meter antennas have been assembled in the Grantsville
desert to begin this work.
The telescopes are an altazimuth design which provides simple pointing in its native horizon
coordinate system. The horizon coordinate system consists of two axes, the azimuth and the
altitude or elevation. An object’s natural horizon is the primary plane and the zero degree
elevation point. The azimuth maps out 360 degrees around this primary plane. In the DuffetSmith convention, 0 degrees azimuth is North, and increases clockwise as you go East. Though
more simple to build and operate, the altazimuth design does not easily lend itself to tracking
stars.
Figure 1: Horizon Coordinate System
The equatorial coordinate system is what the Grantsville telescopes use to chart and track stars.
This system bases the star’s position on its location on the celestial sphere rather than on the
observer’s location on Earth. The celestial sphere is a sphere that places the Earth at the center,
and all celestial bodies at its surface. The Earth’s poles and equator are projected on to this
sphere to help with charting. The two axes for locating positions in this system is the declination
and right ascension. The vernal equinox, where the sun passes through the celestial equator in
March, is located at declination zero, and right ascension zero.
Right ascension is measured in hours, minutes, and seconds. It is much like Earth’s longitude. A
star sits on a line that goes from one celestial pole to the other and passes through it, and the
celestial equator. Right ascension is the angle between the vernal equinox and the point that this
line passes through the celestial equator.
Declination is much like Earth’s latitude. It is the angle between the stars position and the
celestial equator.
Figure 2: Equatorial Coordinate System
To use an altazimuth telescope to point at stars that are charted in the equatorial coordinate
system, a transformation must be done. Because the Earth constantly rotates, these two
coordinate systems are always changing positions in relationship to each other. To do the
transformation, it is necessary to use time in the calculation. To go from equatorial to horizon
coordinates:
Where A is for azimuth, a is for altitude or elevation. δ is for declination, H for hour angle. φ is
the observer’s geographic latitude. From hour angle we can find the right ascension (α), using the
local sidereal time (LST):
H = LST – α
Sidereal time is a time system that’s day is approximately 23 hours, 56 minutes, and 4.1 seconds
relative to our standard time. As opposed to basing a day on the time it takes for the Earth to
make a revolution relative to the sun, it bases it on the time it takes for the Earth to make a
revolution relative to the distant stars on the celestial sphere. Since sidereal time is required to
make the necessary transformations, it is also necessary to calculate this from standard time. In
the software section, the actual code containing the transformation is included.
When tracking stars using charts that are based on the equatorial coordinate system, depending
on the level of accuracy that is required, it may be necessary to correct for precession. Precession
of the Earth is the slow shift in the orientation of Earth’s axis of rotation over time. Its motion
can be described as a wobbling top that traces out a cone once every 26,000 years. This slow
change results in a stars location in the sky shifted slightly from the charts. So the process to
account for this shift looks at the position in the sky when the chart was made, and calculates
where it will be currently. The calculation for this is shown in the actual program code later on in
the thesis.
These are the basic elements that need to be understood when pointing at a star with an
altiazimuth telescope.
2.0 The System Design
2.1 Hardware
2.1.1 Mechanical Limit Safety Switches
The telescopes have mechanical limits to their movement. Due to data and power cables, the
telescope can't move more than 360 degrees in either azimuth direction. The mirror array's size
prohibits movement much below 0 degrees in elevation. Moving too far in either of these two
axes with cause tremendous damage to the structure and electronics. As a result, limit safety
switches are a necessary part of a control system.
Because software can not be fully trusted with the protection of the telescope and users,
mechanical safety switches have been installed to ensure that movement stops when limits are
reached. To be certain that movement stops when necessary, the mechanical switches directly
control the power source that powers the servo motors through relays.
Figure 3: Safety Switch Wiring Diagram
24 volts DC continually holds the relays in the on position, allowing power to flow to the servo
motors. This 24 volt loop includes a plug at the azimuth axis and a toggle switch at the elevation
axis. The 24 Volts is provided by a din-rail mounted power supply that also powers the serial
server, and the fiber optic extender.
Figure 4: Power Relays
The elevation axis has two metal brackets that move as the elevation moves, one for the upper
limit, and one for the lower limit. As a limit is reached, the bracket makes contact with the
switch, trips the relay, and stops movement.
Figure 5: Elevation Safety Switch
Since the azimuth limit is based on the cables being pulled too tight as the telescope spins, the
safety mechanism is connected directly to the cables. If a limit is reached and the cables are
pulled to tightly, the plug with pull apart, the relay trips, and movement stops.
Figure 6: Azimuth Safety Plug
2.1.2 Communication Link
Figure 7: Communications Wiring Diagram
Communication with the encoders and the servos are done with special serial cables. Wiring
diagrams for each type of cable is located in their operations manuals which will be made
available to the group. Those serial cables are plugged in an Ethernet Serial Server. This device
allows the serial data to be communicated over the network. On the computer side, this serial
data can be transmitted and received by either creating a virtual serial port (a driver provided by
the manufacturer of the serial server), or by TCP/IP. TCP/IP was selected as the method of
communication because of its stability and because it required no additional drivers or operating
system settings.
The network consists of a four port router that is connected to the workstation computer, the two
serial servers, and a GPS clock. It is not connected to a gateway. Between the serial servers and
the network router there are fiber optic extenders. The communication link takes up considerable
network bandwidth, so this primary network should not be added upon to provide internet access,
etc.
2.1.3 Servo and Encoder Wiring
Figure 8: Servo and Encoder Wiring Diagram
Figure 9: Encoder Unit
The Encoder system consists of a main display unit, and two position encoders. The main display
unit, located in the telescope rack, has a front panel display of the current raw degree position of
each encoder. It is the main unit that communicated the positions via serial as well. There is a
single cable that provides both low voltage power and data communication to each position
encoder located on the telescope. This is a pre-made cable with mil-style connectors.
Figure 10: Servo Amplifier/Controller, Motor
Each servo has an amplifier/controller that is located in the telescope rack. It requires 220V
power that is provided by a 3-phase generator that is installed behind the control shed. A breaker
is located in the rack next to the amplifier/controllers for safety. Two cables connect the servo
motor to the amplifier/controller. One provides power and uses a mil-style connector on the
motor end, and screw down terminals on the amplifier/controller side. The other provides control
data and uses a D-sub style connector on the amplifier/controller side, and a mil-style connector
on the motor side.
2.2 Software
2.2.1 Communication Protocol
Communicating with the servos and encoders is done through a TCP/IP connection to each serial
port on the ethernet serial server connected to the devices. Entering the serial server's local IP
address and the serial's port number is all that is required for addressing. All of the specific port
settings are saved in the non-volatile memory of the serial server. Both the servos and encoders
communicate using hexadecimal strings.
The encoder is very simple to communicate with. Sending a simple request signal, /02, you are
than able to read back a string of data that has position information for each axis. One iteration of
sending the command and reading the information takes 140 milliseconds.
The servo is a bit more difficult to communicate with. Though it has a serial port, it was designed
only to use with its own proprietary software. After signing a non-disclosure form, and obtaining
the communication protocol, I was able to determine what commands would make it work.
Every routine for the servo, from setting up communication, to changing velocity takes 3 steps.
The first step is a communications check. The second is a routine request. The third confirms the
request. Each step is answered by the servo acknowledging the requests. Once initial
communication is established, these 3 steps continue to repeat without break during the entire
session. This requires special timing and network resources. The following is an example of the
code for one routine.
Figure 11: Software Code – Example Servo Commands
2.2.2 Tracking Algorithm with Servos and Encoders
When the group acquired the telescopes, they came with some control hardware that had already
been designed to use. This was the case with the servo motors and position encoders.
The encoders are made by Heidenhain and have a resolution of 0.001 degrees. One is mounted
on each axis to provide continual position feedback. These are absolute encoders that have a built
in reference zero, so that repeatable positioning could be accomplished.
The servo motors are made by Sanyo-Denki. They are operated essentially by varying their
speed incrementally over a range slower that we would want to go, to much faster than the
telescope would want to move.
Using the combination of a motor and an encoder, positioning can be accomplished by writing a
programming algorithm commonly known as a servo loop. In this program, the speed of the
motor is a function of how far it is from where it needs to be as well as from where it started. For
example, when it is very close to its start position, its speed is slow. As well, as it gets further
away from its start position, the speed increases to a limit. Equally so with the end position, the
closer it gets, the slower it goes. This function is evaluated 5 times every second in a
programmed loop. This is depicted below.
Figure 12: Servo Movement – Velocity vs. Position
Figure 13: Servo Movement – Position vs. Time
This algorithm is the basis for all of the positioning that the telescopes perform. For the tracking
routine, the end position is not a fixed point, but changes over time based on position of a star.
The telescope follows this end position, and thus tracks the star. In repeated observations,
positioning can be accomplished with 0.001 degree precision, and tracking can be accomplished
with greater than 0.010 degree precision. This accomplishes the goal of positioning with a better
precision than the approximate 0.100 degree resolution of the telescopes.
2.2.3 Coordinate System Transformations
In the introduction, it was explained that in order to point at stars in the equatorial coordinate
system, it requires a transformation from the altazimuth telescope's horizontal coordinate system.
This transformation requires that both the current time and location be known. Below is the
actual code for this transformation.
Figure 14: Software Code – Calculating Sidereal Time
Figure 15: Software Code – Transformation from Equatorial to Horizonal Coordinates
2.2.4 Precession and Corrections
There are some corrections that need to be made so that after the transformation, the telescope is
pointing at the desired location.
Precession is the gradual shift of the Earth's axis of rotation. As a result of this shift, the stars
location is slightly shifted over time as well. Once the telescope is in the equatorial coordinate
system, a correction for precession must be made. The actual code for this correction is shown
below.
Figure 16: Software Code – Precession Function
Before the raw azimuth and elevation data from the encoders can be transformed to the
equatorial coordinate system, it needs to be corrected to the true azimuth and elevation. There are
a number of factors that cause the raw data to be incorrect. The first order is that the reference
zeros of the encoders are not at true elevation and azimuth zeros. This is relatively easy to
correct. The more difficult problems come from the telescope itself. Though I don't know all of
the sources of misalignment, there are a few common ones.
The telescope is not level. If the base in not completely level, this will cause a large
misalignment in the elevation axis as well as a change in the azimuth axis.
The two axes are not orthogonal. If the elevation axis is not exactly orthogonal to the azimuth
axis, this will cause incorrect reading in both the elevation and the azimuth axis.
This thesis makes an attempt to understand the main causes for misalignment, but does not
attempt to correct for it alone. Below is the actual code for some initial corrections that have
been applied to account for misalignment. This section of code will be adjustable as further data
is processed.
Figure 17: Software Code – Corrections Function
2.2.5 Software Limit Safety Switches
Programmed in to the code of the system are limit switches. These prevent the user from using
the software to move the telescope too far in any direction. The limits are as follows:
Azimuth:
Lower Limit = 0 degrees
Upper Limit= 450 degrees
Elevation
Lower Limit = -2 degrees
Upper Limit = 90 degrees
Just past these software limits, mechanical limit switches are installed as a backup. The limits
will manifest themselves to the user in a couple of ways. During the selection of a position or
star, the software will determine if it is within its moveable limits. If it is not, the user will be
notified, and movement will be denied. If the user is manually controlling the speed of the
movement with no programmed end point, the software will immediately cease communication
with motors if a limit is reached, causing all movement to stop. Software switches are the first
line of protection and work fine, assuming no software malfunction.
3.0 Operations Guide
3.1 Power-up
When the site is not in use, the power is shut off to all but the GPS clock unit.
Inside the control shed.
 Plug in the two 110V extension cords inside the control shed. This will provide power for
some of the electronics in the telescope racks.
 Power on the battery backup box in the control shed.
 Power on the workstation computer.
On the back side of the shed
 Pull the 220V power switch to the off position.
 Press the green start button on the 3-phase generator, and wait for 5 seconds for warm up.
 Pull the 220V power switch to the on position.
At the telescope rack location
 Power on the encoder main unit by flipping the main switch in the back.
 Press 'Ent' on the encoder main unit keypad to prepare to find reference zeros.
 Flip the breaker to the on position.
 The servo amplifier/controllers should indicate a ready signal by displaying three
horizontal bars.
3.2 Starting the program
On the workstation computer
 On the desktop of the computer, double click on the main telescope program.
 Click the white run arrow in the upper left hand corner to start the program.
 Select the telescope you would like to control.
 Click the 'Set Up Communication' button on the Main tab.
 Follow the onscreen prompts.
Figure 18: Software – Main Tab
At the telescope rack location
 Ensure that you see a figure 8 pattern on each of the amplifier/controllers signifying
successful communication.
3.3 Finding the Reference Zeros for Each Axis
When the telescope is in the home or park position, it is located just negative of the raw
reference zeros for each axis. When the antennas are powered up, it is necessary to manually
move the telescope with the software up and to the right to find each of the zeros. Finding
reference zeros is only necessary at the beginning of the session or if the encoder main unit has
power cycled.
On the workstation computer
 Go to the Manual Control tab.
 Click 'Start Manual Control'
 Click the 'UP' button, and the 'RIGHT' button.
 Set each axis speed to 10.
Figure 19: Software – Manual Control Tab
At the telescope rack location
 Note: the telescope will be moving slowly now in both axis.
 Watch the encoder main unit until the positions begin to register on each axis.
On the workstation computer
 Set each axis speed to 0.
 Un-click the 'UP' button and the 'RIGHT' button.
 Un-click 'Start Manual Control'.
3.4 Positioning
There are 3 different positioning activities: Track a Star, Go to a Position, or Manual Entry.
Figure 20: Software – Positioning Tab
3.4.1 Track a Star
On the workstation computer
 Go to the Positioning tab.
 Click on the 'Track a Star' button.
 Note: a sub-program will launch.
 Select a data file containing your star position data
 Add any position filters to narrow your search for a star.
 Select and confirm a star by double clicking on its line and clicking yes.
 Note: the subprogram will load the star data into the tracker.
 When you are ready to track, click 'Start'
 Note: if your selected position fall outside of the telescopes limits, it will notify you and
deny movement.
Figure 21: Software – Track Selection Sub-Program
At the telescope
 Confirm that the telescope is moving to your selected location.
 Caution: the telescope may move quickly at times, and it is much stronger than you.
On the workstation computer
 Click stop when you have completed your task.
3.4.2 Go to a Position
On the workstation computer
 Go to the Positioning tab.
 Click on the 'Go to a Position' button.
 Note: a sub-program will launch.
 Select a data file containing your position data
 Add any position filters to narrow your search for a position.




Select and confirm a position by double clicking on its line and clicking yes.
Note: the subprogram will load the position data into the tracker.
When you are ready to move, click 'Start'
Note: if your selected position fall outside of the telescopes limits, it will notify you and
deny movement.
Figure 22: Software – Position Selection Sub-Program
At the telescope
 Confirm that the telescope is moving to your selected location.
 Caution: the telescope may move quickly at times, and it is much stronger than you.
On the workstation computer
 Click stop when you have completed your task.
3.4.3 Manual Entry
This mode allows you to manually enter a fixed azimuth/elevation position, or a moving right
ascension/declination position.
On the workstation computer
 Go to the Positioning tab.
 Click on the 'Manual Entry' button.
 Toggle to either the azimuth/elevation side or the right ascension/declination side.
 Enter your position information
 When you are ready to move, click 'Start'.
 Note: if your selected position fall outside of the telescopes limits, it will notify you and
deny movement.
At the telescope
 Confirm that the telescope is moving to your selected location.
 Caution: the telescope may move quickly at times, and it is much stronger than you.
On the workstation computer
 Click stop when you have completed your task.
3.5 Ending Communication
On the workstation computer
 Follow the instructions in the 'Go to a Position' section to move the telescope to the park
or home position, using the main position data file.
At the telescope
 Confirm that the telescope is moving to the park or home position.
 Caution: the telescope may move quickly at times, and it is much stronger than you.
 On the workstation computer
 Go to the Main tab.
 Click the 'End Communication' button.
 Follow the same procedure for the other telescope if that one is also running.
 Click the 'End Program' button.
3.6 Power Down
At the telescope rack location
 Power off the encoder main unit by flipping the main switch in the back.
 Flip the breaker to the off position.
On the back side of the shed
 Pull the 220V power switch to the off position.
 Press the red stop button on the 3-phase generator.
Inside the control shed
 Unplug the two 110V extension cords.
 Power down the workstation computer.
 Power off the battery backup unit.
1.0 Conclusions and System Validation
To demonstrate that the system is stable and tracks stars at the desired precision, I performed a
one hour test in which I moved to a star from a stopped position and tracked its location. I
collected time, elevation and azimuth target and actual positions, and photos of the stars image at
the focal plane of the telescope. This test included only the first order corrections described in
the corrections section. As a result, the image of the star does not stay perfectly centered over the
hour of tracking.
Below are the graphs of the entire tracking session.
210
170
150
Az Position
130
Az Target
110
90
70
67171
66973
66776
66580
66383
66188
65991
65796
65599
65403
65207
65011
64815
64619
64422
64226
64029
50
63832
Azimuth Angle (degrees)
190
Time in Seconds (LST)
Figure 23: Tracking Data – Azimuth Axis
95
Elevation Angle (degrees)
90
85
80
75
El Position
El Target
70
65
60
55
67165
66979
66793
66608
66423
66238
66053
65868
65684
65498
65314
65128
64943
64758
64573
64388
64203
64018
63832
50
Time in Seconds (LST)
Figure 24: Tracking Data – Elevation Axis
In the graphs, you will see that at the beginning, the telescope moves towards the star and begins
tracking it. From the point that it reaches the star, it continues to track without interruption. To
better see the two traces, we can zoom in on the graph to show how well it tracks.
80.45
Elevation Angle (degrees)
80.4
80.35
El Position
El Target
80.3
80.25
63991
63989
63987
63984
63982
63979
63977
63975
63972
63970
63967
63965
63963
63960
63958
63955
63953
80.2
Time in Seconds (LST)
Figure 25: Tracking Data – Elevation Axis - Closer
The telescope does not have the ability to exactly match the speed of a star’s motion because it
has a finite number of different speeds. However, you can see that it still has the ability to track
with excellent precision and the variations are imperceptible since they are much smaller than the
resolution of the telescope.
To quantify how well it tracks, I calculated the angle between the target and actual positions over
the entire session. A sample of that data is below.
Time in Seconds (LST) 65488.9824 65489.98512 65489.98512 65490.98784 65490.98784 65490.98784 65491.99056 65491.99056 65492.99328 65492.99328 65492.99328 Az Position
(degrees)
106.519
106.521
106.524
106.532
106.541
106.551
106.558
106.561
106.562
106.564
106.566
Az
Target
(degrees)
106.536489
106.550043
106.550043
106.550043
106.56361
106.56361
106.577191
106.577191
106.577191
106.590787
106.590787
El
Position
(degrees) 85.021 85.022 85.023 85.025 85.027 85.03 85.032 85.033 85.034 85.034 85.035 El
Angle Target (degrees) (degrees)
85.028753 0.005586 85.03176 0.007127 85.03176 0.006397 85.03176 0.004906 85.034767 0.005664 85.034767 0.003458 85.037774 0.004248 85.037774 0.003518 85.037774 0.002826 85.040781 0.005067 85.040781
0.00436 65493.996 65493.996 65494.99872 65494.99872 65494.99872 65496.00144 65496.00144 65497.00416 65497.00416 65497.00416 65498.00688 65498.00688 65499.0096 65499.0096 65499.0096 65500.01232 65500.01232 65501.01504 65501.01504 65501.01504 65502.018 65502.018 65503.02072 65503.02072 65503.02072 106.575
106.584
106.602
106.618
106.625
106.625
106.625
106.626
106.628
106.63
106.632
106.636
106.645
106.654
106.663
106.668
106.67
106.673
106.675
106.679
106.689
106.711
106.72
106.721
106.721
106.604396
106.604396
106.604396
106.618019
106.618019
106.631656
106.631656
106.631656
106.645308
106.645308
106.658973
106.658973
106.658973
106.672652
106.672652
106.686345
106.686345
106.686345
106.700053
106.700053
106.713775
106.713775
106.713775
106.727511
106.727511
85.036 85.039 85.041 85.042 85.042 85.043 85.044 85.045 85.046 85.047 85.048 85.049 85.05 85.052 85.055 85.056 85.057 85.058 85.058 85.059 85.06 85.062 85.065 85.067 85.068 85.043787
85.043787
85.043787
85.046793
85.046793
85.049799
85.049799
85.049799
85.052804
85.052804
85.05581
85.05581
85.05581
85.058815
85.058815
85.06182
85.06182
85.06182
85.064824
85.064824
85.067829
85.067829
85.067829
85.070833
85.070833
0.005792 0.003607 0.001976 0.003389 0.003416 0.004825 0.004121 0.003411 0.004926 0.004209 0.005762 0.005015 0.004196 0.004951 0.002761 0.004264 0.003551 0.002821 0.005061 0.004313 0.005737 0.004125 0.002036 0.002739 0.002042 Figure 26: Tracking Data – Sample from Data File
It can be seen that in this sample, no angle is greater than .01 degrees. This is consistent with the
entire data set. In the figure below, you will see the image of the star. The diameter of its image
on the screen is ~0.5 cm. The focal length of the telescope is 300 cm. This is corresponds to a
roughly 0.095 degree resolution. Since the telescopes resolution is .095 degrees, the tracking
algorithm is very successful in tracking with roughly 10 times the resolution.
This session was performed with only first order corrections applied. As a result, the actual
position that is depicted above is not exact. As further corrections are added, the actual position
will better match the stars actual position. Below are some pictures of the star tracked during this
session. This is the telescope’s behavior with first order corrections.
63900
64522
64535
64726
64872
65090
65291
65582
65776
66165
66428
66591
66701
67075
Figure 27: Star Images, Alp Lyr
During a portion of the session, clouds covered the star. However, this gives you a good idea at
the telescope’s current alignment, and ability to track.
The software has been an evolving process over the past couple of years. Many features and have
been added that improve usability and functionality. Some of these features are outside of the
scope of this thesis, but were added as a contribution to the group. The original scope included
the setup of only one telescope, but I have put in extra time and effort to assist in getting a
second telescope up and running. I do this happily and have enjoyed my cooperation in the
project.
At this stage, the software is fully functional. A number of group members have been trained
first hand, and with the inclusion of the guide, they should be well supported. I have expressed to
the group that I will be available for support on this system after this thesis process is over. I
would like to see these telescopes become a valuable research asset for all of those involved.
5.0 References
1. Meeus, Jean (2005). Astronomical Algorithms, Second Edition. Richmond, Va:
Willmann-Bell, Inc.
2. Wikipedia, retrieved July 2009.
en.wikipedia.org/wiki/Precession_(astronomy)
en.wikipedia.org/wiki/Sidereal_time
3. University of Cincinnati Physics Department Website, retrieved July 2009.
www.physics.uc.edu/~sitko/Fall2002/1-Sky/sky.html
images only