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Using Jupiter to measure gravitational deflections in 2023

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#1 dbruns

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Posted 17 January 2022 - 12:38 AM

In 1919, Einstein's General Theory of Relativity was demonstrated during a solar eclipse by measuring arcsecond shifts in several star positions near the Sun. This test was successfully performed using amateur equipment in 2017. However, Jupiter has never been used to measure gravitational deflections, although that was originally requested by Einstein. The advantage here is that the measurements can be done at night, over several hours. The disadvantage is that the deflections are 100 times smaller! Bright stars pass close to Jupiter every year or so, but on October 27-28, 2023, three bright stars form a perfect alignment that that won't be repeated for many decades. The close conjunction will be visible from the entire Western hemisphere, but the best places would be in the Southwestern US. I have been doing tests with small telescopes and CMOS cameras to show that the necessary precision is possible. If anyone would like to participate by using their own equipment, I would be happy to provide more details on the recommended setup and procedures.

 

Don Bruns

San Diego


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#2 Taosmath

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Posted 17 January 2022 - 01:37 AM

How accurate would the measurements need to be to detect the deflections?



#3 happylimpet

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Posted 17 January 2022 - 03:55 AM

The deflections close to the sun were of the order of 1" as I recall, so presumably these are around 0.01"?



#4 LauraMS

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Posted 17 January 2022 - 05:12 AM

I guess this is junction with the 7.3mag star HD16 150? I would be interested to join observations but would observe from Central Europe where sunset interferes with minimum distance:

20220117_110435.jpg

Would you comment about the size of the effect as a function of angular distance from Jupiter?

#5 dbruns

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Posted 17 January 2022 - 01:14 PM

Thanks for your interest!  The deflection of HD16150 would be about 0.008 arcseconds as it passes Jupiter, so measurements need to be accurate to about 0.003 arcseconds to show the effect. The deflection decreases as 1/distance. My preliminary experiments show this measurement is possible, and good seeing helps. The images need to be averaged over about 30 minutes intervals to reduce the noise. The observing session would need to start a few hours before closest approach, and last a few hours after closest approach, so sites in the Western hemisphere would be best, although any place would get some data. Since this conjunction occurs when two other bright stars are nearby, the change in the separation of those star pairs is what makes this measurement possible. Absolute positions, or positions relative to Jupiter or its moons would not work. Another unique feature of this event is that the three bright stars (SAO 93015, 93016, 93020) are nearly in a line, so camera tilt and other secondary effects cancel! This vastly reduces measurement errors.

 

The optimum equipment for this experiment uses apertures from 100mm to 300mm, with focal lengths between 0.5 m and 2 m, depending on the camera. A plate scale between 0.3 and 1 arcsecond per pixel is probably best. This star trio is still visible after sunset for the next month or so. Jupiter is far away, so the deflection of the middle star should be zero. I am making progress on a program that automatically extracts the needed data from thousands of images in a long series, so don't worry about that, for now.

 

Don Bruns

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#6 LauraMS

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Posted 17 January 2022 - 05:35 PM

Thanks for the explanation! Yes, I have seen that there are actually three stars in a row, but only one will get near Jupiter. I guess imaging is done using lucky imaging over CA 30min, or at least with rapid readout (1/sec, or whatever one needs to get down to 8th-9th mag?

That sounds interesting. I may try in the next days if I'll be able to catch some clear sky.

Best, Laura

#7 dbruns

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Posted 17 January 2022 - 10:58 PM

All three stars need to be imaged. The outer two stars set the plate scale, since they will be far from Jupiter all the time. The middle star will apparently move with respect to the outer two stars. The ratio of the distances will be calculated, and will slowly change as Jupiter approaches, and then goes back to the original value by the next evening. Since the stars are in a line, camera tilt or other errors will cancel, allowing very precise measurements. I have a detailed pdf on my web page that might help explain: see http://www.stellarpr...on Paper V2.pdf

 

Don Bruns

San Diego



#8 happylimpet

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Posted 18 January 2022 - 05:50 AM

Thanks for your interest!  The deflection of HD16150 would be about 0.008 arcseconds as it passes Jupiter, so measurements need to be accurate to about 0.003 arcseconds to show the effect. The deflection decreases as 1/distance. My preliminary experiments show this measurement is possible, and good seeing helps. The images need to be averaged over about 30 minutes intervals to reduce the noise. The observing session would need to start a few hours before closest approach, and last a few hours after closest approach, so sites in the Western hemisphere would be best, although any place would get some data. Since this conjunction occurs when two other bright stars are nearby, the change in the separation of those star pairs is what makes this measurement possible. Absolute positions, or positions relative to Jupiter or its moons would not work. Another unique feature of this event is that the three bright stars (SAO 93015, 93016, 93020) are nearly in a line, so camera tilt and other secondary effects cancel! This vastly reduces measurement errors.

 

The optimum equipment for this experiment uses apertures from 100mm to 300mm, with focal lengths between 0.5 m and 2 m, depending on the camera. A plate scale between 0.3 and 1 arcsecond per pixel is probably best. This star trio is still visible after sunset for the next month or so. Jupiter is far away, so the deflection of the middle star should be zero. I am making progress on a program that automatically extracts the needed data from thousands of images in a long series, so don't worry about that, for now.

 

Don Bruns

San Diego

Do you think you can derive positions to 1/100 to 1/300 of a pixel (photosite) as per your numbers above? That sounds unrealistic. My planetary imaging rig is typically 0.0993"/pix, which still needs 1/30 of a pixel.

 

I would also be VERY wary of the image scale warping across the field of view. This is very easily detectable with my system (barlow or powermate and ASI290 for example) even just using winjupos to align to (eg) jupiter and moons - the effect is maybe 1% of pixel scale across the field of view. this would be extremely hard to disentangle from the grav effects, unless the stars were kept absolutely motionless on the detector.


Edited by happylimpet, 18 January 2022 - 05:51 AM.


#9 LauraMS

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Posted 18 January 2022 - 07:58 AM

@happylimpet: I guess, the point is to have good guiding on the star/stars such that the positions on the CCD chip are more or less constand, as is the error. In consequence there may be a total error in the relative change of deflection but  in absolute terms this may be much less (approx. 1% of the deflection).

 

I checked for central European observers and saw that the at sunset/sunrise the distance between edge of Jupiter and HD16150 is on the order of one diameter of Jupiter or more. Moreover, they will be low at the horizon, resulting in suboptimal seeing, significant atmospheric extinction and chromatic aberration which cannot be controlled suffciently with a filter (narrow band would cut away to much light, i.e., significantly lengthen exposure time). An ADC will probably increase distortion. Moreover, differential aberration for stars at different elevation may introduce further errors. Do you have a plot on the effect as a function of distance of Jupiter? I didn't find literature. I'm afraid that this will mean that in Europe no meaningful observation may be feasible for this reason.

 

Even in the US where elevation Is high during the day, will differential aberration by the atmosphere be an issue considering the extremely high angular resolution needed and achievable in principle for this experiment? This may be particularly relevant when elevation is much less than that at peak culmination.


Edited by LauraMS, 18 January 2022 - 08:01 AM.


#10 dbruns

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Posted 18 January 2022 - 02:55 PM

Hi all,

 

Regarding 1/100 pixel precision: You are correct that this is a problem for single images. Each image might be accurate to 0.1 pixel, based on centroiding an image that is 3 or 4 pixels wide. When calculated for each image, then the calculations averaged together (not an averaged image), the uncertainty for 10,000 calculations is reduced by 100, approximately. Turbulence causes each image to move slightly, but an average position after many images is OK. I've been doing tests of this, and the resulting accuracy is just good enough. Better seeing should help.

 

Image warping is not too bad for the telescopes I am using. I measured the cubic distortion in both telescopes, and they agree with the ray-tracing results. A Ritchey-Chretien 200mm telescope is my primary instrument, and the measured distortion is less than 0.001 arcsec over the star triplet FOV. This means the stars can wander over 10 or 20 arcsec, and the distortion is negligible. The other telescope I am testing is a APO refractor, and it should have similar numbers. Preliminary tests show a distortion of 0.0009 arcsec over the field. Precision guiding is not really required.

 

The unique alignment of these three stars means that focus shift or camera sag will cancel. The *ratios* in each image should stay the same. That is why this Oct 2023 conjunction is so important, compared to other close passes of single stars near Jupiter.

 

Differential refraction of the stars is important, even for such a close pair at high elevation. I am compensating for this using the best astrometric program that includes proper motion, parallax, stellar aberration, and refraction; it is the US Naval Observatory program called NOVAS. By using this program on the data I took in December, the calculated separations of the stars agreed with my images (averaged over 30 minutes) to 0.003 arcseconds. So far, so good!

 

Don Bruns

San Diego


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