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# Trigonometrical parallax measurment is it possible?

15 replies to this topic

### #1 Giorgos

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Posted 30 January 2020 - 03:02 AM

Hi all!

Is it possible to measure with amateur equipment the trigonometrical parallax of at least the nearest stars?

Any practical information? I could not find anything on the net but I know that during the 19th century

the first parallaxes were measured with 4" and 6" refractors.

I'd like an amateur project like this!

Edited by Giorgos, 30 January 2020 - 03:06 AM.

### #2 sg6

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Posted 30 January 2020 - 04:40 AM

Seems to be reasonable as lomg as the datum from the initial reading can be maintained - one measurement would be 6 months seperate from the second. So whatever the first angular pposition was made on/with/against would have to be maintained until 6 months later.

Quick read of Earthsky say the distance to the nearest is 300,000 time that of the distance to the sun.

So the parallax would be the angle that 2/300,000 so 1/15000 degrees.

so angle = tan-1(1/150,000)

Quick run through a calculator and you get a parallax of 1.375 arcsec.

Which seems within the performance of present equipment.

Unsure of an easy way to do it. One that comes to mind is center a more distant star that is in line with our nearest and measure the angular separation, wait 6 months, repeat measurement. Nearest star should have changed position by 1.375 arc min, further star should not have moved owing to the increased distance and it's hopefully negliable parallax.

As in most of this expect to get several measurements, then I guess discard the lowest and highest and average the remainder. Could also discard the 2 highest and 2 lowest, might tighten up the final "average" measurement. Maybe take 20 measurements and discard the highest 10% and lowest 10% is probably what I would consider, so from 20 only 16 go forward.

Will depend on the number of measurements taken and how good you are. If the measurements are a general mess and all over the place then something has gone wrong.

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### #3 happylimpet

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Posted 30 January 2020 - 05:05 AM

Definitely.  Look at the methods used by the asteroid people, they determine positions accurate to a very small fraction of an arcsecond with quite coarse resolution. I would have thought that concentrating on high resolution with good image sampling will get you to <0.1" position quite easily.

I saw a plot some years ago where someone had plotted the position of Barnard's star to watch its proper motion across the sky, and they were surprised and delighted that the sinusoidal parallax motion was also clearly visible!

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### #4 pbealo

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Posted 30 January 2020 - 08:50 AM

If you wish to measure parallax, participate in this!

http://pluto.jhuapl....arallax-Program

Peter

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### #5 robin_astro

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Posted 30 January 2020 - 09:22 AM

Tougher by visual observation in the "old days" but relatively straightforward I would have thought with imaging and the precision of today's plate solving services like astrometry.net. Just follow a star with high parallax taking lots of images of the field for a season (or all year if circumpolar), plate solve, plot the positions  and fit a sine curve.

Robin

### #6 Sportflyer

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Posted 30 January 2020 - 09:29 AM

sg6 has an error in the math.  One should divide 1 AU by the estimate of 300 000 AU not one half of that.  Using 300 000 AU you get about 0.68  arc sec  closer to the accepted value of 0.78 arc sec.

### #7 robin_astro

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Posted 30 January 2020 - 09:36 AM

Tougher by visual observation in the "old days" but relatively straightforward I would have thought with imaging and the precision of today's plate solving services like astrometry.net. Just follow a star with high parallax taking lots of images of the field for a season (or all year if circumpolar), plate solve, plot the positions  and fit a sine curve.

Since you are looking to measure the postion to a precision much higher than the size of the star image, there would be some things to watch for though. eg off the top of my head

Keeping the psf (ie the shape) of the star images constant would be important so best to use the same setup all the time.  Distortion of the star image shape and the relative positions in the field due atmospheric dispersion could be a problem, particularly near the horizon so using a narrow field (though still with enough reference stars) and a filter to limit the wavelength range might be a good idea. Exposures would need to be long enough to eliminate scintillation but not saturate any of the stars

Edited by robin_astro, 30 January 2020 - 09:40 AM.

### #8 robin_astro

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Posted 30 January 2020 - 09:45 AM

Before embarking on a long project, a number of images measured over a few (near) consecutive nights would give you an idea of the measurement uncertainty and how many points you might need to average to see the movement against the scatter of individual values

Edited by robin_astro, 30 January 2020 - 09:46 AM.

### #9 robin_astro

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Posted 30 January 2020 - 10:06 AM

I saw a plot some years ago where someone had plotted the position of Barnard's star to watch its proper motion across the sky, and they were surprised and delighted that the sinusoidal parallax motion was also clearly visible!

Ah yes, that could be the fly in the ointment.  If the proper motion is high,  untangling the two could be difficult without a long series of measurements. (Over several years the star would describe a spiral path in the sky instead of a (near) circle)

Cheers

Robin

### #10 robin_astro

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Posted 30 January 2020 - 10:24 AM

The English translation of Bessel's letter to John Herschel published in the MNRAS in 1838 on his measurement of parallax of 61 Cyg makes interesting reading.

Edited by robin_astro, 30 January 2020 - 10:26 AM.

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### #11 DEnc

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Posted 30 January 2020 - 01:04 PM

Here are my results from 438 days, analyzed with MPO Canopus.  The top shows scaling of 0.005* on both axes, the bottom shows RA rescaled to emphasize the parallax.  I haven't yet figured out how to fit an expression having a linear and elliptical component to the data, WIP!  Stellarvue SV-110ED, SBIG STT-8300M

Search for these PDFs for practical info:--

The Proper Motion and Parallax of Barnard's Star: Errors and Precision in Small-Telescope Astrometry, Richard Berry

Measuring the Parallax of Barnard's Star, Robert Vanderbei

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### #12 pejorde

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Posted 18 February 2020 - 02:34 AM

As other have pointed out, this is indeed possible, at least for the nearest stars. A number of years ago I measured Barnard's star and the pair 61A and 61B Cygni with a 6" Maksutov and my homebuilt "Cookbook" CCD camera. I imaged the respective star fields twice a year, autumn and spring, over two years. Positions were measured relative to other more distant stars in the same field using astrometric software (I used fitsblink but there should be more and better software available now). My measured positions are shown in the plots below, yielding parallaxes of 0.69" for Barnard and 0.33" on average for 61A and B. You can easily see the seasonal zig-zagging motions due to the combination of parallax and proper motion.

Regards,

Per Erik

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### #13 catalogman

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Posted 18 February 2020 - 02:47 PM

Accurate parallax can't be found from blinking unreduced apparent positions. They include the
aberrational ellipse and other effects which vary throughout the year.

For 61 Cygni, Bessel used Herschel's idea to measure the displacement relative to faint
background stars within 12' of 61 Cyg, which were assumed to be of negligible parallax and
affected by the same aberration and other effects as 61 Cygni itself. See Chauvenet's
A Manual of Spherical and Practical Astronomy, Vol. I, Art. 441, or the examples below:

An easier method is Rambaut's formula for binary stars, which requires a few orbital elements
and the spectroscopic velocity:

--catalogman

Edited by catalogman, 18 February 2020 - 05:18 PM.

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### #14 drpaneas

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Posted 21 June 2020 - 12:22 PM

Suppose I take 2 photos of the same star with 6 months difference, using the same dslr equipment.

How do I know the angle? All I have is pixels.

### #15 pejorde

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Posted 30 June 2020 - 03:17 PM

Popular graphics that illustrate parallax due to Earth's movement around the Sun, such as the one in Wikipedia

https://en.wikipedia...tellar_parallax

give a very misleading impression of the magnitude of the parallax. Typically with amateur equipment the parallax will be less than one pixel and it is not possible to visually see such a tiny shift in position. Instead, astrometric software is needed to measure the target star and reference stars and the software will calculate and report position relative to catalog positions of selected reference stars in the same image. Subpixel precision is possible in such measurements because the software measure the centroid of the star image.

Per Erik

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### #16 StupendousMan

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Posted 03 July 2020 - 07:58 PM

Suppose I take 2 photos of the same star with 6 months difference, using the same dslr equipment.

How do I know the angle? All I have is pixels.

The very basic idea is

• measure the position of the target star, and a set of 10-20 other stars, in each image.  You must determine the position of each star to sub-pixel precision, so you'll need to use some software that can do that job.
• next, determine the offset of the target star from each of the reference stars in image A
• then determine the offset of the target star from each of the reference stars in image B
• finally, look for a systematic difference in these offsets.  For example, you might find that in image A, the target is 91.56 pixels East of one reference star, but only 91.26 pixels East of that star in image B -- that's a shift of 0.30 pixels.   Look at the offset of the target from a second star -- does it also shift by 0.30 pixels from image A to image B?

In essence, you must measure the position of the target relative to all the reference stars in each image, and then look for a shift in that position.

It's a complicated business.   I'd recommend using a piece of software such as "Astrometrica" to do most of this dirty work for you.   Good luck!

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