Double Star KUI82AB,C Measurements with Astrometrica David Haworth and Tom Frey

Astrometrica software has been used for double star analysis by Robert K. Buchheim [1], [2] and James L. Jones for double star analysis. Astrometrica runs on Windows computers and it has a 90 day free trial for you to try it before spending money on it. The Astrometrica Yahoo group is a good forum for discussing how to use Astrometrica.

Astronetrica is used to measure the RA and Dec of each the double stars in the image. Next the distance and position angle is calculated from the RA and Dec with a Python script.

The double star KUI82AB,C separation (rho) and position angle (theta) were measured on five Canon DSLR images 5970, 5971, 5972, 5973 and 5974 with Astrometrica by Tom Frey using a MacBook with Apple Boot Camp running Microsoft Windows 7. The images were taken buy Tom Frey using his alt-azimuth Dob and DSLR.

Astrometrica reads 8, 16 and 32 bit FITS (Flexible Image Transport System) files. The Canon DSLR camera CR2 RAW image files are converted to FITS files in order to be use in Astrometrica.

Below is the double star KUI82AB,C separation (rho = 50.127 arcseconds) and position angle (theta = 313.460 for J2000) based on the mean RA and Dec of the Astrometrica measurements. The rho and theta measurements have not been precessed to the observation date of May 30, 2013.

The plots are equirectangular map projections of the sky on a flat plot. The plots have been adjusted to that RA distance is equal to the Dec distance. As a result a circle of fixed radii will be round and not distorted by the map projection.

Below is a plot of the five images (5970, 5971, 5972, 5973 and 5974) KUI 82 AB RA and Dec positions based on the individual RA and Dec measurements. The average of the RA and Dec is in the center of the plot and is called primary average. All five RA and Dec measurements were within about 2.4 arcseconds radius of the RA and Dec average.

Below is a plot of the five images (5970, 5971, 5972, 5973 and 5974) KUI 82 C RA and Dec positions based on the individual RA and Dec measurements. The average of the RA and Dec is in the center of the plot and is called secondary average. All five RA and Dec measurements were within about 2.8 arcseconds radius of the RA and Dec average.

Below is a data analysis output KUI82_20130927_184710_DataOut.txt file created by the Python script DoubleStarsAnalysisV22.py.zip with the KUI82AstrometricaDataIn.txt file.
The Python script was created by David Haworth to calculate and plot the the separation (rho) and position angle (theta) of double stars given the double stars RA and Dec in a CSV txt file. The Python script was developed with the free Python Canopy Express programming environment. David uses Canopy Express on computers with the Mac OS X and Windows 7 operating systems. Canopy Express simplifies using Python because it installs and manages the updates to over 30 preconfigured Python packages.

```Date: 2013-09-27 time: 18:47
Python script file name: DoubleStarsAnalysisV22.py

Data file: KUI82AstrometricaDataIn.txt has 5 rows
Data file contains:

Row 0:KUI 82, 5-30-2013, 9:46:46, Image, 5970, Primary RA, 17, 29, 19.86, Dec, 29, 23, 27.0, Secondary RA, 17, 29, 17.11, Dec, 29, 24, 1.4, P Label XY offset, 0,  1, S Label XY offset, 0, 1, Plot Size, 7, Circles, 6, 1, Astrometrica Plate Solve for RA & Dec
Row 1:KUI 82, 5-30-2013, 9:51:33, Image, 5971, Primary RA, 17, 29, 19.84, Dec, 29, 23, 28.8, Secondary RA, 17, 29, 17.03, Dec, 29, 24, 3.0, P Label XY offset, 0,  1, S Label XY offset, 0, 1, Plot Size, 7, Circles, 6, 1, Astrometrica Plate Solve for RA & Dec
Row 2:KUI 82, 5-30-2013, 9:51:43, Image, 5972, Primary RA, 17, 29, 19.76, Dec, 29, 23, 28.2, Secondary RA, 17, 29, 16.97, Dec, 29, 24, 2.2, P Label XY offset, 0,  1, S Label XY offset, 0, 1, Plot Size, 7, Circles, 6, 1, Astrometrica Plate Solve for RA & Dec
Row 3:KUI 82, 5-30-2013, 9:46:46, Image, 5973, Primary RA, 17, 29, 19.92, Dec, 29, 23, 27.9, Secondary RA, 17, 29, 17.17, Dec, 29, 24, 2.4, P Label XY offset, 0,  1, S Label XY offset, 0, 1, Plot Size, 7, Circles, 6, 1, Astrometrica Plate Solve for RA & Dec
Row 4:KUI 82, 5-30-2013, 9:55:31, Image, 5974, Primary RA, 17, 29, 19.63, Dec, 29, 23, 27.3, Secondary RA, 17, 29, 16.81, Dec, 29, 24, 2.6, P Label XY offset, 0,  1, S Label XY offset, 0, 1, Plot Size, 7, Circles, 6, 1, Astrometrica Plate Solve for RA & Dec

Double star name:KUI 82
Comment: Astrometrica Plate Solve for RA & Dec

Image 5970.0 analysis:
Primary RA = 17h 29' 19.86"
Primary RA = 262.33275 degrees
Primary Dec = 29 degrees 23' 27.0"
Primary Dec = 29.39083 degrees
Secondary RA = 17h 29' 17.11"
Secondary RA = 262.32129 degrees
Secondary Dec = 29 degrees 24' 1.4"
Secondary Dec = 29.40039 degrees
Rho = 49.75039 arcseconds, theta = 313.74514 degrees

Image 5971.0 analysis:
Primary RA = 17h 29' 19.84"
Primary RA = 262.33267 degrees
Primary Dec = 29 degrees 23' 28.8"
Primary Dec = 29.39133 degrees
Secondary RA = 17h 29' 17.03"
Secondary RA = 262.32096 degrees
Secondary Dec = 29 degrees 24' 3.0"
Secondary Dec = 29.40083 degrees
Rho = 50.18317 arcseconds, theta = 312.96124 degrees

Image 5972.0 analysis:
Primary RA = 17h 29' 19.76"
Primary RA = 262.33233 degrees
Primary Dec = 29 degrees 23' 28.2"
Primary Dec = 29.39117 degrees
Secondary RA = 17h 29' 16.97"
Secondary RA = 262.32071 degrees
Secondary Dec = 29 degrees 24' 2.2"
Secondary Dec = 29.40061 degrees
Rho = 49.85563 arcseconds, theta = 312.99770 degrees

Image 5973.0 analysis:
Primary RA = 17h 29' 19.92"
Primary RA = 262.33300 degrees
Primary Dec = 29 degrees 23' 27.9"
Primary Dec = 29.39108 degrees
Secondary RA = 17h 29' 17.17"
Secondary RA = 262.32154 degrees
Secondary Dec = 29 degrees 24' 2.4"
Secondary Dec = 29.40067 degrees
Rho = 49.81953 arcseconds, theta = 313.82830 degrees

Image 5974.0 analysis:
Primary RA = 17h 29' 19.63"
Primary RA = 262.33179 degrees
Primary Dec = 29 degrees 23' 27.3"
Primary Dec = 29.39092 degrees
Secondary RA = 17h 29' 16.81"
Secondary RA = 262.32004 degrees
Secondary Dec = 29 degrees 24' 2.6"
Secondary Dec = 29.40072 degrees
Rho = 51.03360 arcseconds, theta = 313.76493 degrees

5 Rho & theta measurements analysis:
Image 5970, rho = 49.75039 arcseconds, theta = 313.74514 degrees
Image 5971, rho = 50.18317 arcseconds, theta = 312.96124 degrees
Image 5972, rho = 49.85563 arcseconds, theta = 312.99770 degrees
Image 5973, rho = 49.81953 arcseconds, theta = 313.82830 degrees
Image 5974, rho = 51.03360 arcseconds, theta = 313.76493 degrees

Rho mean = 50.12846 arcseconds
Rho standard deviation = 0.47646 arcseconds
Rho standard error of the mean = 0.21308 arcseconds
Rho mean - standard deviation = 49.65200 arcseconds
Rho mean + standard deviation = 50.60492 arcseconds
Maximum rho = 51.03360 arcseconds in image 5974.0
Minimum rho = 49.75039 arcseconds in image 5970.0
Rho spread = 1.28320 arcseconds, rho spread percentage of rho mean 2.56%

Theta mean = 313.45946 degrees
Theta standard deviation = 0.39304 degrees
Theta standard error of the mean = 0.17577 arcseconds
Theta mean - standard deviation = 313.06642 degrees
Theta mean + standard deviation = 313.85250 degrees
Maximum theta  = 313.82830 degrees in image 5973.0
Minimum theta  = 312.96124 degrees in image 5971.0

Mean of 5 images RA & Dec analysis:
Mean of primary RA & Dec:
RA mean = 262.33251 degrees
RA standard deviation = 0.0004170 degrees, 0.0250200 arcminutes, 1.5011995 arcseconds
RA standard error of the mean = 0.0001865 degrees, 0.0111893 arcminutes, 0.6713568 arcseconds
Dec = 29.39107 degrees
Dec standard deviation = 0.0001780 degrees, 0.0106771 arcminutes, 0.6406247 arcseconds
Dec standard error of the mean = 0.0000796 degrees, 0.0047749 arcminutes, 0.2864961 arcseconds
Mean of secondary RA & Dec:
RA = 262.32091 degrees
RA standard deviation = 0.0005180 degrees, 0.0310805 arcminutes, 1.8648324 arcseconds
RA standard error of the mean = 0.0002317 degrees, 0.0138996 arcminutes, 0.8339784 arcseconds
Dec = 29.40064 degrees
Dec standard deviation = 0.0001474 degrees, 0.0106771 arcminutes, 0.6406247 arcseconds
Dec standard error of the mean = 0.0000659 degrees, 0.0039553 arcminutes, 0.2373184 arcseconds
Rho = 50.12729 arcseconds, theta = 313.46007 degrees
Plot 6 circles in radii increments of 1.00 arcseconds.

Double star AB plot size is 132.32 by 115.29 arcseconds.
Primary plot size is 8.03 by 7.00 arcseconds.
Secondary plot size is 8.03 by 7.00 arcseconds.
Equal angular adjustment of plot RA is True.

End of data analysis.

```