My Do-It-Yourself Relativity Test

Here's an update on an amateur astronomer's amazing effort to prove that Einstein really was right during the 2017 total solar eclipse.

Equipment for Don Bruns' relativity testt

The author’s “relativity test kit” consists of a Tele Vue NP101is refractor, FLI Microline 8051 CCD camera, and Software Bisque MyT Paramount and field tripod.
Donald Bruns

As you've perhaps read in Sky & Telescope's August 2016 issue, I'm gearing up for an experiment during next year's total solar eclipse that will use off-the-shelf equipment and software to measure the deflection of starlight due to the Sun's gravity — and thus prove that Einstein's general theory of relativity really is correct!

Since I wrote that article, there's good news on my data analysis for the eclipse experiment: I have demonstrated that I can measure the deflection of stars in a twilight sky to 0.05 arcsecond. This result shows that the equipment I am using will work! My test came too late to include in the S&T article, but I'll be updating my forthcoming presentation at the SAS Symposium with the new results shown below.

Here is what I did:

On April 20th, just after the sun set at 7:25 p.m., I focused my Tele Vue NP101is refractor on Procyon and locked the focuser. I then slewed my Bisque Paramount MyT to the location of the "right" reference star field (indicated in the sky chart below) and waited 15 more minutes. At 7:45 p.m., the Sun had dropped to 6° below the horizon. This produces a twilight sky as bright as during a typical total eclipse.

Reference fields for relativity test

The author intends to record three star fields during 2½ minutes of totality during the 2017 total solar eclipse. Stars are shown to magnitude 10.5.
S&T: Leah Tiscione; source: Donald Bruns

I captured 7 frames on the Finger Lakes ML8051 camera, each 3 seconds long, and then immediately slewed 8° to the area where the Sun would be during the eclipse. I captured 25 frames there, each 1 second long. I then immediately slewed 8° on the other side to the "left" calibration field and captured 7 more frames in 30 seconds.

The total time to accomplish all this was 2 minutes 20 seconds, just as long as totality in Wyoming during the 2017 eclipse. This is a good dress rehearsal — all that was missing was the Sun’s gravity and the corona.

I processed the star centroids from all 39 images using MaximDL, Pinpoint, and Astrometrica. I was able to find 26 measurable stars in the eclipse images, and 36 and 42 good stars in the reference fields. I calculated the plate scale in the reference fields, and averaged them to get the plate scale to use in the eclipse field. This preliminary analysis can be considered as a “sanity check” on the entire experiment.

Bruns' test observation from April 2016

This is a plot of the star positions derived during a test run in April 2016. Because the Sun was not in the field, the stars' deflections should cluster near zero.
Donald Bruns

Then I plotted this data to show the deflection as a function of radial distance from the simulated Sun. Since there was no Sun, the gravitational deflection should be zero. The blue line in the graph at right  is the deflection expected with the Sun in place in August 2017, and the orange dots are the deflections measured in April. The black line is the case for no gravity; as expected, the measured points cluster around this line.

For comparison, look at the data plot from a similar experiment, conducted in 1973, that had an 11% uncertainty. In that graph, shown below, the larger circles have the most confidence. Note that in the 1973 data, most of the stars are more than 4 solar radii away, while the stars in my plot are concentrated between 2 and 4 radii. This means that I will be measuring much larger deflections next year.

Deflection data collected in 1973

During a total solar eclipse in 1973, a team from the University of Texas measured the positional deflection of stars near the Sun.
Donald Bruns

During the eclipse in 2017, I expect there will be fewer stars than in this “pretty good” simulation, but even if half of these stars are measurable, I think the results prove the capability of the equipment, my technique, and the data analysis.

The scatter in the data shows the measurement accuracy, and I'm working on a few improvements to reduce this scatter. The points toward the right side of my graph do not average to zero, for example. It turns out that these are stars near the edge of the camera frame. To simplify this preliminary data analysis, I did not include optical distortion, which (according to my zenith tests) is about 0.25 arcsecond — just about what is showing in the graph. Once I include this data correction, I am confident that those data points will also average to zero.

I will be making some other minor changes in the coming year to reduce the uncertainties even further. My final tests will be next spring, using the optimized configurations and updated software and procedures I am starting to write. I think my goal of measuring the deflection to the highest precision ever realized from the ground, using amateur equipment based on modern technology, is proven to be realistic.

If you want to learn more about my experiment, please read the detailed article that I prepared for the SAS Symposium. Also please contact me if you want to try to duplicate this project or offer help.