Jim Krehbiel was up past midnight making a piece of art by layering maps and field notes onto photos he had taken of an ancient ritual site high on a cliff ledge in the desert Southwest.
He looked at the image of the kiva and remembered how the ruins were nearly inaccessible. Krehbiel had to lower himself on a rope to reach them.
Why, he wondered that night in the fall of 2007, would anyone build something so important in such a remote spot among the canyons and mesas?
It was then that the chairman of Ohio Wesleyan University's art department found himself at the conjunction of archaeology and astronomy.
Perhaps, he thought, the site was an observatory; a place to help religious leaders keep track of the solstices, time rituals and plantings.
"Their world around them is absolute, total chaos," Krehbiel said. "They were really at the mercy of the elements.
"So where do they go for something that's predictable, that remains the same, that you can count on: The sky and the relationship of those things on the horizon."
A discussion with Barbara Andereck, a professor of astronomy and physics at Ohio Wesleyan, put Krehbiel on a path that would help him test his ideas about the remote kivas he visited each summer.
Krehbiel was stepping into archeo-astronomy, the study of the ways ancient cultures tracked the sky's movements. The science has been gaining acceptance as a branch of archaeology since the 1970s.
England's Stonehenge, for example, is well known for its alignments with astronomical phenomena. In Ohio, archaeologists agree that ancient mound builders lined up some works with the movements of the sun and the moon.
In the Southwest, the most famous site is the Chaco Sun Dagger. The sun and moon shine through the spaces between slabs of rock to make slashes of light on a spiral carving in conjunction with the solstices and the movements of the moon.
But no one had identified such alignments at hundreds of remote ruins that dot the canyons of southeastern Utah.
One of Andereck's students, Natalie Cunningham, was looking for a senior project in 2008 and agreed to help Krehbiel.
"I had to do a lot of math to go back into the past and see where the sun and moon were," said Cunningham, who was studying English and astrophysics.
In the summer of 2008, Krehbiel took Cunningham to Utah to take readings.
Back at the kiva he'd pondered on that fall night, Krehbiel set up his transit and sighted in on a gap in the opposite canyon rim where he thought the winter solstice sun might rise.
Instead, he found that the moon rises there during an event called the major lunar standstill, which occurs every 18.6 years.
The major standstill occurs when the moon rises and sets in its longest arc across the horizon -- the lunar version of the annual summer solstice when the sun makes its longest arc across the sky.
But they also found that the calculations Cunningham made in relatively flat Ohio only went so far in the canyons of Utah.
The cliff-top kiva is on a relatively flat plane with the features on the opposite canyon rim and with the horizon, so the calculations were close enough to work there. But they didn't work for kivas deep inside a canyon.Because the canyon rim is high above, the sun and moon don't appear to observers at those sites until they're far above the true horizon. Since they cross the sky in an arc, the sun and moon appeared in a different spot than Cunningham had calculated.
"I said 'Oh, crap, it's not nearly good enough,' " said Cunningham, who is now at the University of Arizona pursuing a graduate degree in nonfiction writing.
She found a better model that summer in a book published in 1942 by the U.S. Navy: Spherical Trigonometry with Naval and Military Applications.
Now she could derive an equation that took the arc of the sky into consideration.
"We went back out in October of 2008 and re-examined the sites," Krehbiel said. "We had the spherical trig charts in hand, and everything just fell into place."
They have found alignments for solstices, equinoxes and major and minor lunar standstills at 29 sites so far.
Krehbiel takes sightings only from spots where the cliff-dwellers left a sign, such as a spiral carving or a basin chipped out of the rock.
He doesn't always find alignments with distinct features on the horizon. About 30 percent of the sites he's checked showed none, he said.
Jeff Dean, a professor at the University of Arizona in Tucson, has spent decades using tree-ring data to fix when archaeological sites throughout the Southwest were built. He took a look at Krehbiel's work recently and said it makes sense to him.
"I don't know of anybody that actually measured these things to the extent that he and his colleagues are doing," Dean said.
"He picks plausible places to set up the equipment, they're making calculations based on certain techniques and they're also concerned about any variation put in place by the date."
Noreen Fritz, an archaeologist with the National Park Service, has asked Krehbiel to write reports on his findings on seven sites in the parks she oversees in southeastern Utah.
"He's looking at these sites with fresh eyes," she said. "One was a site we work at regularly. You always walk by these upright stones, but it turns out they're sighting stones."
In June, Cunningham hiked up to a kiva with Krehbiel to watch the sun set on the summer solstice. She calculated that they'd see it set through a rock window if they set up near a handprint marking.
They arrived about a half an hour early, but the position of the sun worried them.
"It was pretty far to the left," Cunningham said. "We kept saying 'It's not going to hit that window.' We were in a bit of a panic."
Still, they set up the camera and the tripod. Then, just at the right time, the sun blazed through the rock window, shining onto the shrine.
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