Alfred Eisenstaedt's VJ Day in Times Square is one of the most iconic photos of the 20th century. Everyone's seen it, yet, seemingly, no one can answer two basic questions about it: who's in it, and when was it taken? Physics professor Donald Olson can't say who the jubilant couple is, but he is absolutely certain the image was snapped at exactly 5:51 pm.

Even Eisenstaedt couldn't pinpoint what time it was when he made the image, widely known as The Kiss, on August 14, 1945. And he never did identify the sailor and nurse, bent backward in a joyful, triumphant kiss celebrating the end of World War II. Dozens of people have claimed to be the lovers, and the book The Kissing Sailor hypothesized it was George Mendonsa and dental assistant Greta Zimmer that Eisenstaedt immortalized that day in Times Square. The question comes up every year on VJ Day, rekindling the debate. Every answer offered thus far has been circumstantial.

Olson doesn't have the first clue who is in the photo. But he has some serious science to back up his claim that Eisenstaedt snapped the shutter at 5:51 p.m.

The Texas State University professor joined his colleagues Steven Kawaler and Russel Doescher in making a meticulous study of vintage maps, aerial photos, and blueprints before building a scale model of buildings. Based upon the lighting and shadows and the position of the sun—more on this in a moment—they are quite confident in their findings. "It actually took me the better part of 4 years to figure it out," Olson says. "Does that sound crazy?"

Yes, actually.

If a physicist, an astrophysicist and an astronomer seem like unlikely candidates to solve this mystery, it's a surprise to learn they've been at it for more than 25 years.

They published their findings in the August issue of Sky & Telescope, laying out just how they were drawn into the mystery. It started with some surprisingly constructive Internet comments (yes, you read that right) posted in response to a 2010 New York Times article analyzing new evidence about the image. Kawaler, an astrophysics professor at Iowa State University, grew intrigued by a clock in the background when someone noticed a distinctive shadow in the top right corner of the photo. "Steve was the first to notice the Bond clock with its clues and other people noticed the shadow," Olson says. "Somebody said 'Well gee! Maybe we could figure out the time of that shadow.'"

The men set about determining the time based on the length and direction the shadow cast on the Loew's building in the background. Olson determined the shadow was created by an oddly shaped sign atop the Hotel Astor. He realized that the distance between the buildings and the line of shadow required the sun to be "at azimuth 270 degrees (exactly due west) and at an altitude of +22.7 degrees" according the case laid out in Sky & Telescope. Doescher's training as an astronomer surely helped here: To cast that shadow, the sun would have to be setting at a 5:51 pm Eastern War Time. It's as close to exact as you can get.

If a physicist, an astrophysicist and an astronomer seem like unlikely candidates to solve this mystery, it's a surprise to learn they've been at it for more than 25 years. Olson has a passion for dissecting key moments in history, art, and literature. He's figured out what time it was when Van Gogh painted Moonrise (9:08 p.m.), identified what inspired Walt Whitman's "Year of Meteors" (an Earth-grazing meteor procession), and determined just when Ansel Adams shot Autumn Moon, The High Sierra From Glacier Point (7:03 p.m. on September 15, 1948). Some projects take months, while others—the VJ Day mystery being an example—take years.

One mystery that may forever surround VJ Day in Times Square is the identity of the kissing couple. Olson still has no clue, but has potentially eliminated several likely candidates who claimed to be there before or after 5:51 pm.

Though he won't divulge details, he's working on some new puzzles — one involving the history of a German submarine that sank a British battleship in WWII and another analyzing the Tacoma Narrows Bridge collapse in 1940.

Olson and his fellow sleuths do more than peruse documents and review photos. They'll often go into the field to do their own research. Olson traveled to France to pinpoint exactly the time and location Monet planted his easel for The Cliff, Etretat, Sunset and visited Yosemite National Park to determine the exact date and time Ansel Adams stood to make Moon and Half Dome. While some people might find Olson's process mind-bogglingly tedious, he takes great joy in solving these puzzles. Knowing precisely when Eisenstaedt made The Kiss or how a volcanic explosion relates to The Scream deepens his appreciation of the work. "It makes my life richer to be able to look at these great things from art, history and literature and try to tie it to science,” he says.