Sky and Telescope - August 2018 - 25

t DEFLECTION ANGLE The author used data collected in 1973 (yellow
circles) and his own data collected in 2017 (blue squares) to calculate how
the deflection angle changes with position. The apparent positions of stars
farther from the Sun's limb are deflected less than those nearer the Sun,
and the constant describing this relation in relativity is 1.7512. The author's
data line up nearly perfectly with Einstein's prediction.

Deflection (arcseconds)

2.0
1.5
1.0
0.5
0.0

- 0.5

Distance from Sun (solar radii)

of the analysis in just a few months. I used both MaxIm DL
and Astrometrica software to measure the precise positions
of stars, including only those stars that gave good signals
and weren't distorted by the corona or neighboring stars. The
two programs use different methods for their calculations,
and because I had no reason to prefer one over the other, I
averaged their outputs. This procedure led to an amazingly
accurate result.
I used calibration images taken during the brief totality
to improve the accuracy of the analysis. For these, I had the
telescope point about 7° from the Sun, where there is little
gravitational deﬂection. The computerized mount, controlled
via automatic scripting, enabled me to take these calibration
images on both sides of the Sun. Sufﬁcient calibration had
proved a problem for previous eclipse expeditions, due in part
to the time involved for manual setup, but modern technology easily resolved that issue.

After careful analysis of my eclipse
images, I measured a deﬂection constant of exactly 1.7512 arcseconds.
A perfect conclusion to a perfect
eclipse! Granted, it's a coincidence
that my measurement landed exactly
on the correct value - my uncertainty is about 3%. But it's still
reason to celebrate: The measurement
achieved the best precision ever by a
wide margin. The results are available
in a more technical format as a paper
published in the April 12th issue of
Classical and Quantum Gravity.
By coincidence, the best-ever optical measurements of the gravitational
deﬂection of starlight came only four
days after LIGO detected the ﬁrst
gravitational-wave signal from a collision of two neutron stars (S&T: Feb.
2018, p. 32). These two astounding
phenomena had both been predicted
decades earlier by the equations of
relativity: All in all August 2017 was
a good month for Einstein!

Moment of Truth

DEFLECTION DATA: DON BRUNS

According to the mathematics of relativity, deﬂection caused
by the Sun's gravity decreases with the distance from the
Sun's center as 1.7512 arcseconds divided by the distance in
solar radii. But past attempts at measuring the deﬂection constant weren't very good, averaging 1.9 arcseconds and ranging
from 1.2 to 2.7 for previous eclipses.

during, and after totality. The camera
was set to cycle through exposures of
varying length every 10 seconds, starting
8 minutes before totality began until 8
minutes after it ended. Afterwards, I analyzed only those images from each cycle
that were not under- or overexposed.
I arbitrarily selected pixels at radii
5°, 15°, and 25° from the Sun to measure sky color. I saw a small increase in
redness as the eclipse progressed, but
seconds before totality began, that trend
reversed to an increase in blueness. But

¢ DONALD BRUNS, a retired physicist, received the American Astronomical Society's 2018 Chambliss
Amateur Achievement Award for his
careful work in replicating Eddington's
famous experiment.

the latter change, as measured by the
ratio of the intensity of blue pixels to the
red pixels, was only about 5% at 15°
from the Sun. Was that enough to notice
with the naked eye? Halley may have
noticed it, but I was too intent on enjoying the diamond rings and coronal views
to check for any visual color change - it
certainly wasn't obvious to me.
The same set of photos showed that
the sky had darkened at the same rate
that the Moon had covered the Sun. At
mid-totality the sky was 6,000-10,000

Another
Chance
The next decade
will see four solar
eclipses with
longer durations
of greatest
eclipse:

July 2, 2019
(4 min, 33 sec)
South America

April 8, 2024
(4 min, 28 sec)
North America

August 2, 2027
(6 min, 23 sec)
Africa

July 22, 2028
(5 min, 10 sec)
Australia/
New Zealand
I hope other
amateurs will
take these
opportunities
to undertake
some science
of their own and
experience the
same excitement!

times darker in the blue filter, depending
on the angular distance from the Sun -
equivalent to a drop of 9.5 to 10 magnitudes. Meanwhile, the sky darkened
another 0.4 magnitude in the red filter.
Future eclipse experiments could build
on this first set of observations: Astronomers might make measurements closer
to the Sun, collecting more frequent
data points to include any effect from
limb-darkening. I would be interested in
comparing your results with mine.
- Ronald Bruns
sk yandtelescope.com * AUGUST 2 018

http://www.skyandtelescope.com

Sky and Telescope - August 2018

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