Repeating the Experiment that Made Einstein Famous


An attempt to measure the solar deflection of stars during the August 21, 2017 total solar eclipse to the highest precision ever realized.



Commercial equipment today is better than ever!


Society for Astronomical Sciences, Ontario, CA, USA June 2016: Presentation Abstract


In 1919, astronomers performed an experiment during a solar eclipse, attempting to measure the deflection of stars near the sun, in order to verify Einstein’s theory of general relativity.  The experiment was very difficult and the results were marginal, but the success made Albert Einstein famous around the world.  Astronomers last repeated the experiment in 1973, achieving an error of 11%.  In 2017, using amateur equipment and modern technology, I plan to repeat the experiment and achieve a 1% error.  The best available star catalog will be used for star positions.  Corrections for optical distortion and atmospheric refraction are better than 0.01 arcsec.  During totality, I expect 7 or 8 measurable stars down to magnitude 10, based on analysis of previous eclipse measurements taken by amateurs.  Reference images, taken near the sun during totality, will be used for precise calibration.  Preliminary test runs performed during twilight in April 2016 and April 2017 can accurately simulate the sky con­ditions during totality, providing an accurate estimate of the final uncertainty.


(Click here to download the technical paper.)


Ctrl+click here to open a new window and view the video presentation on YouTube  (Note the video was taken with an infrared camera to keep the room dark, so my visual appearance is a little funny!)



A feature article for Sky & Telescope Magazine appeared in the August 2016 issue, with additional description on their web site.




The Sky & Telescope update has a graph of test results analyzed without distortion.  More work to include this effect resulted in the left-hand graph shown here:  the RMS error is now 0.023 arcsec!  The graph shown here was used to calibrate the optical distortion in the Tele Vue NP101is telescope, so stars were imaged near zenith, and 10 frames were averaged to reduce noise.  While not a perfect comparison to the eclipse data, it shows excellent performance.  Note that the entire outline of the graph is about the size of one pixel.  Since no sun was present, the red circles should all be zero, and the average is fact only 0.00004 arcsec.  The blue symbols show the deflections expected in 2017 on the same scale.  The right-hand graph shows the results from the 1973 experiment by the University of Texas.  Note that most of their stars are at larger distances, so their deflections are smaller.  Analysis of the 1973 data gives an uncertainty of 11%, so I expect to do much better.






Site selection trip in August 2016


Steve Lang and I travelled to sites near Casper and Alliance to find the best spots to set up the telescope.  Requirements include a good base for the tripod, clear view toward south, wind protection, electrical power, nearby lodging, and overnight security.  We found an ideal site near Casper, so we will plan on traveling there well before the eclipse date.  In case of a cloudy forecast, we plan on driving east to some place between Alliance and Grand Island on Saturday or Sunday, giving at least one night for polar alignment.  We found one site in Alliance that meets most of the requirements, and will be looking for a better site before next August.



Optical Distortion in the Tele Vue NP101is Telescope


Distortion in the Tele Vue NP101is needs to be corrected to a very high precision, since it will not be averaged away by measuring lots of stars.  In addition, the optical axis needs to be measured, since a slight change in the coordinate will result in a different correction for distortion.  The graph here shows the allowed change in the optical train that will produce an error of 0.5% in the deflection.  Since most of the stars are near the edge of the field of view, the change in the optical axis needs to be tracked within 10 microns.



The CCD camera is attached to the Tele Vue focuser, and gravity in different orientations will cause it to sag.  Attaching and re-attaching the camera to the Tele Vue focuser, as well as the simple act of refocusing the camera, will also cause a small change in the optical axis seen by the camera.  My precise measurements of the optical axis using an artificial star showed that the Tele Vue focuser is very rigid!  The optical axis shifts less than about 5 microns when the camera is refocused, or the camera is re-attached, or the telescope points to different parts of the sky.  With this excellent performance, the distortion calibration can be reliably used, with resulting systematic deflection errors less than 0.002 arcseconds.



In December 2016, all of the semi-automatic analysis routines were completed.  I can now read the various calibration files and apply those coefficients to a simulated experiment.  The optical distortion is well-defined and rigorously corrected.  The plate scales and camera orientation can be found from fields near the central eclipse field, and those corrections applied to the eclipse images. This is the technique to be used for the August 21 eclipse.



In March, one of my technical papers was published in Applied Optics.  This paper describes the use of Arago’s spot to monitor the change in the optical axis due to mechanical motion.  You need to purchase the paper or be a member of the Optical Society of America to read the entire article.  It will also appear in the printed journal.



A detailed paper in Applied Optics describes my entire calibration procedure.  It will be published in the August 1 issue. Any other interested astronomers can follow my procedure to their experiment.  That will increase their chance of success.  Thanks to my nephew for co-authoring and helping with all the equations!


In May, I have completed an accurate end-to-end simulation of the experiment, using all of the same hardware, software, and procedures that will be used in August.  Data sets were taken at night and during twilight in March, when the same stars that will be used in the eclipse were about the same altitude as they will be in August.  The only thing missing is the gravitational influence of the sun, so that was included artificially.  The results are encouraging, as shown in the figure here.  The error in Einstein’s coefficient for 16 data tests averaged to 1.00, with 11 of the 16 tests having an error less than about 3%.  In the figure, the blue triangles and the green diamonds were nighttime tests, while the red circles were taken during twilight, when the skies were about as dark as expected during totality.


When the data for one twilight test (the first red point) is plotted to compare with the 1973 experiment, it is obvious that using stars closer to the sun is important, and the scatter in the data is much reduced.  This gives me confidence that I will be successful in August.  I’ve already made a short list of improvements to the data analysis that might also give slightly better results.



Dress Rehearsal trip in May 2017



Steve and I returned to Casper Mountain to set up the telescope and verify everything was in working order.  There was still snow on the ground from a recent storm, and we had to set up the tripod in a wet puddle of water.  Unfortunately, the nighttime weather was cloudy, so I couldn’t get new calibration images.  The equipment is safely stored in Casper, ready to set up in August.  The dim figure in the background is the director of the IMAX documentary on Einstein.  He seemed to like what he saw, so there is a good chance that we will appear in the movie to be released in 2019, the centennial of Eddington’s original eclipse adventure.




Presentations and publications:


Society for Astronomical Sciences, paper and lecture, completed June 2016.

Sky & Telescope Magazine, article published August 2016.

Sky & Telescope Magazine special Eclipse issue, August 2017.

Applied Optics journal articles, published March 2017 and August 2017.

Discover Magazine blog, interview posted May 5, 2017

Astronomy Magazine list of cool experiments, posted May 15, 2017. interview – August 2017.

New York Times – included in map of interesting activities during eclipse – August 2017


Still to come:


Presentation at AstroCON, August 17, 2017, in Casper, WY. (

Repeat presentation on August 18 at the Lion’s Camp for interested students and astronomers.

Live video interview with ( just after totality on August 21.

Final eclipse report, 2018.

Presentation at NEAF, 2018.

Included in IMAX Einstein documentary movie 2019.




Al Nagler, Tele Vue Optics, Inc., for loan of the NP101is telescope and optical raytracing.

Greg Terrance, Finger Lakes Instrumentation LLC, for loan of the ML8051 CCD camera.

Stephen Bisque, Software Bisque, Inc., for loan of the MyT Paramount tripod.

George Kaplan and John Bangert, both formerly of USNO, for astrometric advice and help with NOVAS.

Norbert Zacharias, USNO, for astrometric advice.

This research has made use of FORTRAN version of NOVAS, the Naval Observatory Vector Astrometry Software package.

This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23.

Suresh Rajgopal, for help in setting up gfortran.

Corey Bruns, for help in automating the data analysis with linear algebra advice.

Ted Pecoraro, for help in improving the Paramount field tripod feet.

Steve Lang, for help setting up in Wyoming.

Jerry Kassebaum, for suggesting locations near Casper.

Greg Kinne, for help in scripting TheSky.

Ron Bruns, for calibrating weather instruments and operating an auxiliary experiment.


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Web page last updated July 21, 2017.