Drift Method
This page gives a brief overview of the drift method used to polar align the PANOPTES unit.
Astronomical Coordinate Systems
There are a few different coordinate systems used in astronomy to define the positions of celestial objects on the celestial sphere, such as:
Horizontal system
Equatorial system
Ecliptic system
Galactic system
Supergalactic system
Equatorial Coordinate System
One of the most widely used coordinate system is the equatorial coordinate system, which is the projection of the Earth's latitude and longitude coordinate system onto the celestial sphere. The Earth's equator, North pole, South pole, latitude and longitude are projected onto the celestial sphere and referenced as the celestial equator, North celestial pole, South celestial pole, declination (dec) and right ascension (RA), respectively.
Stars appear to move along lines of declination that run parallel to the celestial equator. The declination of a celestial object on the celestial sphere is measured similar to the terrestrial latitude of a place on Earth. The declination of a celestial object indicates how far north or south of the celestial equator the object lies:
The plot below shows the path stars appear to follow on the celestial sphere as seen from Earth. The concentric circles (colored points) correspond to stars of different declinations, moving parallel to the celestial equator (grey line).
The plot is interactive. Use a mouse to pan, rotate or zoom into the plot. Click on Edit Chart button at the bottom of the plot to open the plot in plotly studio.
Horizontal Coordinate System
The horizontal coordinate system, also called the alt/az system, is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles: altitude and azimuth.
Altitude is the angular distance of an object above the local horizon. It ranges from 0 degrees at the horizon to 90 degrees at the zenith. Azimuth is the angular distance of an object from the local North, measured along the horizon in the eastward direction.
Mount Polar Alignment
The equatorial mount can be rotated on two axis for polar alignment, the altitude and azimuth. For polar alignment, the altitude adjustment knob on the mount has to be set to the latitude of your location. The azimuth knob has to be set to point towards true North.
When the mount's axis of rotation is perfectly aligned to the Earth's axis of rotation, the mount can track the stars for very long durations of time without any drift. See plot shown below for a star at declination = 25 degrees. The mount is perfectly pointed to the North celestial pole (altitude error al = 0.00 deg, azimuth error az = 0.00 deg). The mount tracks a path on the celestial sphere (black line) that overlaps with the star's path on the celestial sphere (colored points).
When the mount's axis of rotation is not aligned to the Earth's axis of rotation, the misalignment can be in altitude, or azimuth, or both. This misalignment causes the mount to track the stars poorly. This difference in the star path and mount tracking path is observed as a star drifting in the PANOPTES observations. By observing and calculating the direction and magnitude of the drift in stars, we can estimate how much offset in polar alignment the PANOPTES mount has.
See plots shown below for how a misaligned mount tracks a star at declination = 25 degrees, on the celestial sphere.
Case 1: Plot shows the path tracked by a mount misaligned in altitude by 15 degrees. The difference in the path tracked by the star and the mount manifests as stars appearing to drift in the PANOPTES observations.
The path traced by the mount on the celestial sphere can be computed from the observations taken by the PANOPTES unit, by measuring the magnitude and direction in which the stars appear to drift. This is then compared with models to determine the extent of misalignment in mount altitude and azimuth.
Python Notebooks
The equations used for drift alignment and for making the plots shown above, are derived and explained in detail in Python notebooks available on this link. There are three Python notebooks to help understand and visualize the drift method:
Notebook 1: Model Derivation
Derive the equations necessary to predict the offset in the equatorial mount pointing on the celestial sphere, when it is misaligned in altitude and azimuth.
Notebook 2: Model Visualization
Using equations derived in Notebook 1, we see how stars would drift as seen by a PANOPTES unit when the equatorial mount is misaligned in altitude and azimuth.
Notebook 3: Fitting Model to Data
Fit the models derived in Notebook 1 to observations taken by your PANOPTES unit to compute the offset in the mount alignment in altitude and azimuth.
Then use the computed offsets to do the polar alignment of your PANOPTES unit.
Note: It is not critical to understand the equations derived in Notebook 1 and Notebook 2 to do the polar alignment of your PANOPTES unit. You only need to follow Notebook 3 to polar align your PANOPTES unit.
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