An Optical Measurement of the Deflection of Light by Jupiter’s Gravity

Dr. Donald G. Bruns (dbruns@stellarproducts.com)

San Diego, CA 92129

Abstract

General Relativity predicts that starlight will be deflected by 0.016 arcsec if its light passes close to the planet’s limb. Astronomers measured this at radio frequencies, but no one has accomplished this in the visible spectral region. A fortuitous alignment of three bright stars with Jupiter in October 2023 should make this measurement possible using only small telescopes placed almost anywhere in the Western Hemisphere. The data collection will require continuously recording images over several hours over two nights. The data analysis will extract the star positions from thousands of images, followed by averaging the values in 30 minute intervals to reduce the measurement noise. A test in November 2021 demonstrated the required precision. If successful, this measurement will fulfill one of Einstein’s wishes.

Introduction

Stellar deflections due to General Relativity have been measured near the Sun since 1919, where the deflection coefficient is 1.75 arcsec for stars located near its limb [Refs 1, 2, 3]. Einstein suggested this in 1916, but astronomers were understandably frustrated because observing during a total eclipse was necessary. Those events are not very common or convenient, and the observations had to be completed during the few minutes of totality. Einstein also suggested that these measurements could be done during the daytime without an eclipse, but that has proven unsuccessful [Refs 4, 5, 6].

Einstein’s third suggestion was to use Jupiter as the gravitational source. Deflections there would be about 100 times smaller than those near the Sun, so technology was not good enough during his lifetime. The Hubble telescope attempted to measure the deflection of a star near Jupiter in 1995, but no results were obtained [Ref 7]. While the Gaia analysis included Jovian deflections in calculating the positions of stars for its catalog [Ref 8], a direct optical measurement has never been completed.

One convenience of using Jupiter to measure stellar deflections is that an observer can use a telescope almost anywhere in the world, as long as a bright star passes within 100 arcsec of Jupiter while at high elevation in a clear sky. The Jovian passage takes several hours, so timing is not critical and the measurement noise can be reduced by analyzing thousands of images. It is also essential that the target star be accompanied by two bright reference stars so that an accurate plate scale can be calculated. Because every instrument slowly changes with temperature, the best possible reference stars would be in a line, minimizing changes in the relative plate scale.

By coincidence, such a conjunction did appear the night of October 27-28, 2023. Figure 1 shows the target star and the two reference stars near Jupiter. The closest approach of SAO 93016 is at 7:15 UT, when it will be only 25 arcsec from Jupiter’s limb. Jupiter’s gravity should generate an apparent outward deflection of 0.007 arcsec in the direction of SAO93015. This close conjunction last occurred in 1928 and does not repeat until 2106, so this opportunity needs to be measured!

Figure 1. SAO 93016 (magnitude 7.1) should show a 0.0085 arcsec gravitational deflection as Jupiter passes nearby in October 2023 (0.007 arcsec in the direction of SAO93015). SAO 93015 (magnitude 7.6) and SAO 93020 (magnitude 8.3) provide good references to calibrate the plate scale. The slow motion of Jupiter with respect to the stars allows several hours to acquire images. [Image from Guide 9.]

The view from Jupiter in Figure 2 shows Earth at the time shown in Figure 1. Jupiter shines high near the meridian in much of the US, but southern sites with good seeing will provide better measurements.

Figure 2. Earth’s Western Hemisphere is perfectly placed to view SAO 93016 as Jupiter makes its closest approach. Image collection over several hours reduces the measurement noise. [Image from Guide 9.]

Updated Notes:

Attempt to Measure Gravitational Light Bending by Jupiter (submitted to Sky and Telescope in early 2024)

Don Bruns and Stan Moore

March 6, 2024

The Jupiter-star triplet conjunction of Oct 27-28 2023 was an attempt to measure Jupiter’s gravitational effect on the light path of distant stars. A similar experiment in 1919 using the Sun instead of Jupiter led to making Einstein famous. He earlier suggested using Jupiter instead of the Sun, since that should have been easier. Now the answer is known – it’s much harder than using the Sun!

This project started a few years ago as a collaboration between the authors. Thanks to a short note in Sky&Telescope just before the event, more observers joined the effort and also helped automate the Python programming analysis. Special thanks go to Bill Fisher (especially programming), Francesco Meschia, Greg Duncan, Jonathan Lawton, Richard Senegor, Robert Minor, Joe Izen, George Silvis, Nikola Nikolov, Terry Dixon and Kenneth Carrell. Some of these observers were clouded out, while others had equipment problems, but I hope they all enjoyed the experience and learned something new! Hundreds of e-mail exchanges among the participants showed the strong social component of this collaboration, which was a delight to witness.

Data Collection

Amateur telescopes, cameras, and mounts are perfectly suited to capture the images needed for this project. The instrument requirements are summarized here.

In moderate (1 - 2 arcsec) atmospheric seeing, the best star position measurements result from using a plate scale near 0.5 arcsec/pixel. A Luminance filter acceptably reduces atmospheric chromatic aberrations since the targets are at high altitude. The bright targets means that 100 mm apertures can operate using 1 sec exposures. For 2.4 micron CMOS pixels, the telescope should have a focal length near 1 meter, just right for a 127 mm F/8 refractor. For 3.8 micron CMOS pixels, the ideal telescope focal length is 1.6 meters. A 200 mm F/8 Ritchey-Chretien telescope design also generates minimum distortions, providing the best calibrations. Since the imaging takes place all night long, a carbon-fiber design helps minimize focal shifts. Other telescope and camera combinations might work well, but should be tested as described in the Results section.

The imaging camera should be a CMOS design, so that a 1 frame-per-second (FPS) rate can be maintained. Only a small sub-frame needs to be saved, but this still requires Gigabytes of storage space. Since 13 arcminutes separates the reference stars, the CMOS sensor needs to be at least 1600 pixels wide. Most amateur units meet that requirement. A cooled camera is not essential, since the exposures are so short. On the other hand, a cooled camera might be more stable, important for the precise measurement.

Since the imaging lasts all night long, the ideal mount would be a fork style. A German equatorial mount requires pausing for a few minutes while the observer flips the mount across the meridian. Good tracking keeps the stars nearly in the same location on the sensor, avoiding potentially difficult optical distortion corrections. If Jupiter or one of the stars is used to auto-guide the telescope mount, then the optical distortion corrections will be small, allowing most telescopes to work OK.

Another approach to get ideal data is to use a methane filter to reduce the glare from Jupiter. If a wide bandwidth is used, then Jupiter is still pretty dark, and the other three stars are still easily recorded with a 200mm aperture telescope. I will probably be using two telescopes, one with the filter and another one without the filter. This is a unique opportunity, so I don’t want to waste it!

Updated Notes after the Conjunction

Jupiter’s gravitational deflection constant is 100 times smaller than that of the Sun, but it was hoped that the experiment could be carried out for a few hours at night from one’s home, instead of a few minutes from some remote location during a solar eclipse. The use of CMOS cameras and modern optics should make up the difference, it was hoped. Unfortunately, Jupiter is still much brighter than the target stars, and coping with that problem probably caused the poor match with the theoretical values. The likely problem is probably due to the difficulty of subtracting the strong glare from Jupiter before measuring the star’s position in the images. A composite of images taken every hour from 3UT to 9UT is shown in the image below.

Subtracting the bright background glare from Jupiter was more of a problem than expected from simulations. It turned out that the data from the reflectors with secondary mirror supports were all very poor and not used in the analysis. Even a slight mis-collimation of the secondary mirror in an SCT skewed the glare enough to ruin the results. The graph below shows the results of processing the data from three refractor telescopes. The best fit 4^th-order polynomial curve to the data points is shown by the dotted line, while the theoretical curve is shown in red. It is obvious that even this data is far from the theory. The largest error bars occurred when Jupiter was low in the sky, so the relative turbulence was large.

The averaged data curve is eerily similar to the theoretical curve, but at about 1.7x the value. Even though several Jupiter-background-subtraction techniques were used, they all resulted in deflections about the same magnitude. Maybe there is still some subtle diffraction from the CMOS pixels, or scatter from Jupiter’s rings?

Conclusions

The next experiment is going to use the Jovian moons instead of the distant stars. The moons are much brighter, so the Jupiter background subtraction is less of a problem. Starting in late 2024 and through 2025, Jupiter will be even higher on the ecliptic, so getting better Jovian moon data might be easier for observers in the northern hemisphere. Please stay tuned! If you are interested in contributing, please contact me at dbruns@stellarproducts.com.

The two telescopes I used last October in San Diego are both mounted on a single MyT mount. The total weight is close to the MyT limit, but it still worked! For the moon version, I will be using only one telescope, probably the 127mm refractor. I am still comparing results with a methane filter to further reduce Jupiter’s scatter.

Figure 4. Two telescopes will be used in San Diego. Front and side views are shown here. Hidden is a third camera with a small telescope between these two, for use in autoguiding.

References

1. Einstein, A. “Die Grundlage der algemeinen Relativitätstheorie“, Annalen der Physik 354, # 7 pp. 769-822 (1916).

2. Dyson, F.W, A.S. Eddington, and C. Davidson, “A Determination of the Deflection of Light by the Sun’s Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919”, Philosophical Transactions of the Royal Society of London, Series A, 220, pp. 291-333 (1920).

3. Bruns, Donald G. “Gravitational starlight deflection measurements during the 21 August 2017 total solar eclipse”, Classical and Quantum Gravity 35 (2018) 075009 (21 pp).

4. Lindemann, A.F. and F.A. Lindemann, “Daylight Photography of Stars as a means of testing the Equivalence Postulate in the Theory of Relativity”, Monthly Notices of the Royal Astronomical Society 77, pp. 140-151 (1916).

5. Handler, F.A. and Richard A. Matzner, “Photographic Astrometry against a Bright Sky: Theory and Application”, The Astronomical Journal 83, # 10, pp. 1227-1234 (1978).

6. Bruns, Donald G. “On the Difficulty of Measuring Star Deflections near the Sun Without an Eclipse”, Research Notes of the American Astronomical Society 3, # 12, article ID 197 (2019)..

7. Personal communications with Bill Jeffreys and Art Whipple regarding their oral paper at a 1996 AAS convention.

8. Prusti, T. et. al. “The Gaia mission”, Astronomy and Astrophysics 595, A1, (2016).

9. Han, Inwoo, “The Accuracy of Differential Astrometry Limited by the Atmospheric Turbulence”, The Astronomical Journal 97, # 2, pp. 607-610 (1989).

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