skyandtelescope.com • JANUARY 2020 29
Equation
of timeOrbital
eccentricityTilt of
axisJan. 1 Apr. 1 July 1Time^difference^(minutes)–15–10–5051015Sundial
reads earlier
than clock.Sundial
reads later
than clock.Oct. 1 Jan. 1a biting cross-examination. By referencing the inaccuracy of
weather predictions as well as the mass hysteria surrounding
the recent passage of Halley’s Comet, he built an air of absur-
dity around the scientifi c method. The technique worked; at
the second trial the jury convicted and sentenced Yeisner’s
client to 15 years in prison.
But Yeisner wasn’t going to let an innocent man rot in
prison. He appealed the sentence to the Supreme Court of the
State of Nebraska, whose fi ve judges were less susceptible to
rhetorical fl ourishes than the local jury; they threw out the
conviction on the basis of insuffi cient evidence.
The prosecution made one more attempt to discredit Rigge
by hiring an independent astronomer, hoping that he would
derive a different time for the photo. But the two results
agreed within less than a half minute.
In the lead-up to May 22, 1912, two years after the day of
the incident, Rigge wrote an article in the local newspaper
inviting people to come to the church where the photograph
was taken to see for themselves the veracity of his method. A
group of students and journalists, as well as a photographer
from the Omaha Daily News, took him up on his offer. As the
promised shadow passed its expected point at 3:21.5 p.m., the
photographer snapped a photo that matched the 1910 picture
perfectly. Photos taken one minute earlier and later showed
the shadow in visibly different positions. A piece congratu-
lating Rigge was written up with great fanfare. Publications
around the country and the world began to reprint the story,
recounting how Rigge — and the discipline of astronomy —
won a well-deserved victory on their day in court.¢ JEFFREY DOBEREINER is a science communicator and
documentary TV producer, with a PhD in anthropology and a
particular passion for space.pRigge used this 3-inch transit telescope to measure the positions
of stars with sub-arcsecond accuracy, roughly 1,000 times better than
needed for his shadow measurements. Creighton Observatory was
Omaha’s offi cial timekeeper, using the transit times of standard reference
stars to synchronize the public clocks.pEarth rotates once every 23.934 hours. The extra 0.066 hour in the 24-
hour day comes from the Sun’s apparent motion through the stars, which
is in turn caused by Earth’s revolution around the Sun. Unlike Earth’s ro-
tation, the west-to-east motion due to revolution varies considerably de-
pending on the season. That’s due partly to the fact that Earth’s orbit is
not a perfect circle, and partly to the fact that its axis is tilted. This graph
shows the two separate components and how they add up to form the
equation of time, the difference between apparent solar time, as shown
by sundials, and mean solar time, the basis of our civil time system.one or two minutes. The main error results from shad-
ows’ fuzziness, which is caused by the fact that the Sun
is an extended object rather than a point source.
Determining the date is harder, because it results
from Earth’s revolution around the Sun, which is roughly
365 times slower than its rotation. Moreover, the Sun’s
declination changes very slowly near the solstices, as
you can see on the ecliptic chart on page 44. Finally,
the Sun reaches any given declination (except the
extremes) twice a year, once on its way north and again
on its way south. In the case of the church photo, of
course, Rigge already knew the date ahead of time.
Having determined a local apparent solar time of 2:54
p.m. for the shadow in the church photo, Rigge then
added 24 minutes because Omaha is 6° west of the
center of its time zone, plus 3½ minutes for the equa-GR tion of time, as shown at right.
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