Barnard's Star project
Barnard's Star is a magnitude 9.5 red dwarf and, at 5.96 light years distance, is the closest star to the Sun visible from the UK. It is also a BY Draconis type variable star, V2500 Oph .
However, it is not here as a variable star but because it is the star with the largest proper motion in the sky. It moves about 10.39 seconds of arc against the background stars every year. This is rather more than half the apparent equatorial diameter of the disc of Saturn. This adds up to about half the apparent diameter of the Moon every 70 years. It moves so quickly that the catalogued positions are frequently in error. This project is to determine its position on the sky and to see if I can detect any changes to this. (This is 'astrometry' not 'photometry'.)
After reading an article the August 2018 Journal of the British Astronomical Association by Nick White about his project to determine the proper motion of 61 Cygni and Groombridge 1830 using an undriven 10-inch Dobsonian telescope, I thought I would have a go.
It just so happens that I have a 10-inch Dobsonian telescope (the grey wooden box shown here), and a stopwatch. All I needed was a suitable graticle/reticle eyepiece. I obtained a 12mm Illuminated Reticle eyepiece by Meade, and the inbuilt scale is shown below. When used with this telescope this resulted in a magnification of approximately x110.
However, it is not here as a variable star but because it is the star with the largest proper motion in the sky. It moves about 10.39 seconds of arc against the background stars every year. This is rather more than half the apparent equatorial diameter of the disc of Saturn. This adds up to about half the apparent diameter of the Moon every 70 years. It moves so quickly that the catalogued positions are frequently in error. This project is to determine its position on the sky and to see if I can detect any changes to this. (This is 'astrometry' not 'photometry'.)
After reading an article the August 2018 Journal of the British Astronomical Association by Nick White about his project to determine the proper motion of 61 Cygni and Groombridge 1830 using an undriven 10-inch Dobsonian telescope, I thought I would have a go.
It just so happens that I have a 10-inch Dobsonian telescope (the grey wooden box shown here), and a stopwatch. All I needed was a suitable graticle/reticle eyepiece. I obtained a 12mm Illuminated Reticle eyepiece by Meade, and the inbuilt scale is shown below. When used with this telescope this resulted in a magnification of approximately x110.
This project only uses the 0-50 scale, shown horizontal in the above image. This scale is calibrated by rotating the eyepiece so that the scale is parallel to the direction of drift of a star and then letting the star drift along its length and timing how long this takes. Ideally, the star should be near the celestial equator so that its track is virtually a straight line rather than a curve. Making corrections for the star's declination, and converting from seconds of time to seconds of arc of Right Ascension, gave a scale of 19.3 seconds of arc per small scale division (= approximately 16.1 minutes of arc for the whole scale length).
The eyepiece is now rotated so that the 0-50 scale is perpendicular to the direction of drift of the stars being observed. One of these stars is Barnard's Star, the other is a comparison star which is visible in the same field of view - at least in declination - so that the telescope can remain stationary during the following measurements.
The following diagram shows the view through the eyepiece; remember, the image is inverted in a Newtonian reflector.
With the help of the other scales on the reticle, the eyepiece is rotated until the diurnal motion of the stars is perpendicular to the 0-50 scale. The telescope is adjusted until the two stars (Barnard's Star and a comparison, in either order, depending upon the relative positions of Barnard's Star and the comparison) are on the east side of this scale and drifting towards it. When the first star crosses the scale the stopwatch is started and the position on the scale that the star crosses it is noted. When the second star crosses the scale the stopwatch is stopped and the position where this star crosses the scale is noted.
From this data we can calculate the Right Ascension and declination of Barnard's Star. The difference in time between Barnard's Star and the comparison star crossing the scale, after some calculation, give us the Right Ascension of Barnard's Star, and the distance along the scale between where the two stars cross, again after some calculation, gives us its declination.
So far, I have made these observations on four dates, 2019 August 25, 2020 September 13, 2021 September 7 and 2023 September 5. This procedure was carried out with two different comparison stars, HD163697 and UCAC4 474-068412. The average displacement from the comparison stars was calculated, and the results plotted in blue in the following diagram. This diagram also includes the positions of Barnard's star on the dates in question, as orange crosses, from GAIA data of its proper motion. These have been offset so that its 2019 GAIA position coincides with my 2019 estimated position.
The above chart is repeated below, but including the trendlines for the two sets of data
The above two diagrams have their axes scaled so that the data points are easily seen. However, this gives an incorrect impression of the relative proper motion in declination compared to the much smaller proper motion in right ascension. The scales in the following diagram have been adjusted so that the two axes have similar scales.
Assuming that the GAIA data is correct(!), it will be noticed that these sets of positions do not agree with each other, due to random and systematic errors.
Random errors are due mainly to the reticle scale being readable to only half a division at best, and the time being determined to 1/10 second at best. Even these estimates are optimistic. However, taking the averages of these two sets of readings generates the blue 'average' positions. Even these differ - on this scale - from the calculated positions of Barnard's Star on the dates the observations were made. The small divisions on the reticle scale represent approximately 19.3 seconds of arc on the sky. At this declination, which is near to the celestial equator, an error on 1/10 second on the stopwatch leads to an error of approximately 1.5 seconds of arc in Right Ascension. Taking many sets of measurements, using more than one comparison star, and checking the alignment of the scale with RA and dec help to reduce the final errors.
Systematic errors are evident in my estimates in the positions determined with respect to A and with respect to B independently, particularly in regard to the right ascension. Possibly due to my ineptitude at using a stopwatch, as well as some form of systematic error in aligning the eyepiece scales, these will be the subject of further investigation as more observations are made over the coming years. (The proper motions of the stars A and B have not been corrected for in the above analysis as they are very small compared to the proper motion of Barnard's Star.)
This page updated 2023 September 12.