Proper motion and parallax page



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As the earth orbits the sun the nearest stars appear to wobble back and forth relative to the much more distant background stars, an effect known as parallax. In addition, due to the star's own motion relative to the sun, a constant drift occurs in some direction, known as proper motion. For the nearest stars, both of these effects should be measureable with amateur equipment. Proper motion is easier to measure since it accumulates over the years. However, measuring a parallax requires estimating stellar positions with sub-arcsecond precision. Note that this does not necessarily require sub-arcsecond imaging resolution, though this would help. It is rather a question of signal-to-noise ratio and systematic errors.

The first successful parallax measurements were completed in 1838-1839 on 61 Cygni (11.4 light years) and α Centauri (4.4 ly). These measurements were performed without the aid of photography, using a special telescope (heliometer) that allows two images to be overlayed and adjusted using a micrometer, so that the angular distance between two stars can be precisely estimated. Using modern digital imaging, much more precise measurements are possible, and most recently the space-based Hipparcos satellite measured parallaxes of >100,000 stars with milli-arcsecond resolution.

This project has barely gotten off the ground since I have been too busy over the last year to take images every month or two as needed to obtain convincing parallax data. Neverthess I now have images of 61 Cygni and Barnard's Star (5.9 ly) taken one year apart, so it should be possible to see their proper motions. Although the relative velocities between stars are somewhat random, a large proper motion indicates that a star is probably relatively close. I have also taken images of ε Eridani (10.5 ly) but I think this target is too difficult with my equipment since the star (mag 3.7) is so bright compared with the sparse background stars nearby. Also I have one image of Lalande 21185 (8.3 ly) from nearly a year ago and hope to get another one this coming winter. This appears to be a good target because it is not too bright and is far enough north that it can be observed most of the year.

The next step will be to determine the magnitude and angle of proper motion of 61 Cygni and Barnard's star, and compare with the known values-- I hope to do this within the next few months if at all possible. One inconvenient issue with the current setup is that the camera angle is not controlled. So it will be crucial to properly scale (the camera pixels are not square) and rotate the images for comparison.

Click on any thumbnail to see the full-sized image.





Barnard's Star

Imax=1000 Imax=100

6 exposures, 10s each 9/25/08 Lake San Antonio, CA


This is the second-closest star system to our own, and the closest one that is observable from our latitude. This is a red dwarf star, with only 1/2500th the luminosity of the Sun. Distance: 5.94 ly (compared with 4.22 ly for Proxima Centauri). Magnitude: 9.54. Spectral type: M5. In this image, it is the bright orangish spot to the left of center.





Barnard's Star

Imax=1000

52 exposures, 1s each 9/25/08 Lake San Antonio, CA


Same as above except for shorter exposure.





Barnard's Star, 3X

Imax=50 Imax=500

6 exposures, 10s each 9/25/08 Lake San Antonio, CA


This image was obtained using a 3X Barlow to get the best possible resolution as needed for a parallax measurement. The elongation is probably due to tracking errors.





Barnard's Star, 3X

Imax=500

59 exposures, 1s each 9/25/08 Lake San Antonio, CA


Also with 3X Barlow, shorter exposures. Again there is some elongation, but at least the disk is smaller. It might be possible to do better with some changes to the image processing, by rejecting images with large spot sizes, or by processing the different colors separately.





Barnard's Star

Imax=50 Imax=100 Imax=500 Imax=1000

24 exposures, 10s each 9/19/09 Lake San Antonio, CA


Updated photo of the Barnard's Star, a nearby red dwarf, one of my targets for proper motion and parallax detection. A quick comparison with last year's image suggests it has moved noticeably, but I have not had a chance to start this analysis yet...





Barnard's Star

Imax=200 Imax=500 Imax=1000

59 exposures, 1s each 9/19/09 Lake San Antonio, CA


Another Barnard's star image, shorter exposures to avoid saturation.





Barnard's Star, 3X

Imax=100 Imax=500

169 exposures, 1s each 9/19/09 Lake San Antonio, CA


Barnard's star using 3X Barlow.





Barnard's Star

Imax=200

121 exposures, 1s each 10/8/10 Lake San Antonio, CA


This is part of my ongoing project to measure a stellar parallax...





Barnard's Star

Imax=100

297 exposures, 1s each 10/8/10 Lake San Antonio, CA


This is part of my ongoing project to measure a stellar parallax...





Barnard's Star

Imax=200

53 exposures, 1s each 9/3/11 Bonny Doon, CA


This is part of my ongoing project to measure a stellar parallax...





61 Cygni, 3X

Imax=50000 Imax=500

295 exposures, 0.1s each 9/27/08 Lake San Antonio, CA


61 Cygni is a magnitude 5 double star in Cygnus, famous for being the first star whose parallax was measured. This was accomplished by F. W. Bessel in 1838 using visual observation techniques, before photography existed! Distance: 11.4 ly. Individual magnitudes (A,B): 5.20, 6.05. Luminosities: only 0.065 and 0.038 compared with the Sun. Spectral types (A,B): K5, K7. The image here, obtained using a 3X Barlow, shows some color separation problems that I have noticed before with this camera. These effects tend to occur with very short exposures, especially if the object moves. Also, I cannot rule out that the Barlow could be causing some color effects.





61 Cygni, 3X

Imax=25000 Imax=500 Imax=100

198 exposures, 1s each 9/27/08 Lake San Antonio, CA


Same as above but longer exposures. The background stars (needed for parallax measurement) are brighter, but the price is saturation and enlargement of the 61 Cygni disks.





61 Cygni, 3X

Imax=5000 Imax=50

821 exposures, 1s each 12/29/08 Phoenix, AZ


The resolution here is a lot worse than in my previous sets. To compensate, I took a huge number of exposures in hope that it will still be possible to estimate the star center positions with < 1 arcsec accuracy.





61 Cygni

Imax=200 Imax=2000

55 exposures, 1s each 9/17/09 Lake San Antonio, CA


Updated photo of the nearby double star 61 Cygni, one of my targets for proper motion and parallax detection...





61 Cygni, 3X

Imax=200 Imax=20000

118 exposures, 1s each 9/17/09 Lake San Antonio, CA


61 Cygni using 3X Barlow lens.





61 Cygni, 3X

Imax=500 Imax=50000

252 exposures, 0.1s each 9/17/09 Lake San Antonio, CA


61 Cygni using 3X Barlow lens, shorter exposures.





61 Cygni

Imax=200 Imax=2000

59 exposures, 1s each 10/9/10 Lake San Antonio, CA


This is part of my ongoing project to measure a stellar parallax...





61 Cygni

Imax=2000 Imax=130000

267 exposures, 0.1s each 10/9/10 Lake San Antonio, CA


This is part of my ongoing project to measure a stellar parallax...





61 Cygni

Imax=130 Imax=13000

253 exposures, 0.5s each 10/9/10 Lake San Antonio, CA


This is part of my ongoing project to measure a stellar parallax...





61 Cygni

Imax=2000 Imax=130000

120 exposures, 0.1s each 9/3/11 Bonny Doon, CA


This is part of my ongoing project to measure a stellar parallax...





Epsilon Eridani

Imax=500 Imax=10000

59 exposures, 1s each 9/25/08 Lake San Antonio, CA


This is another nearby star. Distance: 10.5 ly. Magnitude: 3.7. Luminosity: 1/3 that of the Sun. Spectral type: K2. In this 1s exposure, the star image is already saturated, and yet there are very few background stars. This will make it difficult to attempt a parallax measurement. With the 3X Barlow, I doubt I could get any background stars without completely over-exposing the main target.





Epsilon Eridani

Imax=500 Imax=10000

59 exposures, 1s each 9/25/08 Lake San Antonio, CA


Same as above, shifted.





Epsilon Eridani

Imax=50 Imax=500

13 exposures, 10s each 9/25/08 Lake San Antonio, CA


Same as above, but longer exposure. Now there are more background stars, but epsilon is completely over-exposed.





Lalande 21185

Imax=10000 Imax=100

297 exposures, 1s each 12/29/08 Phoenix, AZ


This is another good candidate for a parallax measurement. It is called BD +36°2147 in the Observer's Handbook. It is 8.31 light years distant, is visible most of the year, and is not too bright relative to the background stars.