As first dates go, Rita Petry thought this one was pretty great: a beautiful summer afternoon in the city, a matinee at Radio City Music Hall, drinks after, followed by a passionate, soon-to-be-iconic kiss.

Well, maybe not the kiss: Her handsome young suitor, it turns out, planted that on another woman.

Such is the incredible story behind one of the most romantic and enduring photos of the 20th century — and one of our most compelling mysteries.

Since Aug. 14, 1945, the identities of the smooching sailor and the nurse in Alfred Eisenstaedt’s Times Square V-J Day photograph have never been determined — until the publication, last week, of the book “The Kissing Sailor: The Mystery Behind the Photo that Ended World War II.”

There’s another person in the frame, one nobody even knew to look for, who makes the image that much more poignant: Rita Petry, the future wife of that sailor, George Mendonsa.

“I really liked him, but I didn’t know I was the future wife,” Rita tells The Post. “I guess I thought he looked nice or something.”

To this day, Rita insists that the kiss never bothered her and that the photo, while “nice,” hasn’t changed her life one bit. But much like the photograph itself, nothing is as it seems. “In all these years,” Rita says, “George has never kissed me like that.”

In August 1945, George Mendonsa was 22 years old, a Navy quartermaster on leave from the Pacific theater. He’d dropped out of school at 16 and worked with his dad, a commercial fisherman, in Rhode Island, enlisting in the Navy after the attack on Pearl Harbor: “Every kid my age wanted to get even with the Japanese.”

George didn’t like to talk about what he had seen, or his anxiety about what was coming, which everyone knew was the invasion of Japan. “I had just come back from the Philippines,” George says. “My ship had seen a lot of action. We were sent back to the States until the Army could get strong enough [to attack].”

So instead, he focused on his date with the pretty girl he’d met a few weeks before at a barbecue at his family’s house in Rhode Island; she was related to his new brother-in-law. Her name was Rita. She was just 20 years old and lived with her parents in Queens.

“She was beautiful,” George says. “I think I fell in love with her the first time I saw her.”

The morning of the 14th, George and Rita took the train into Midtown. He was nervous, and he wore his formal Navy uniform — the one he’d just had specially tailored at home in Rhode Island — and carried the chevron badge he hadn’t had time to affix.

They were going to Radio City Music Hall, to a 1:05 p.m. showing of “A Bell for Adano,” starring Gene Tierney as a fisherman’s daughter who falls in love with the US Army major assigned to her war-ravaged Italian village.

George and Rita never saw the end of the movie.

‘There was pounding on the doors from outside on the street,” George says. “They put the lights on and stopped the show and said, ‘The war is over, and the Japanese have surrendered.’ ”

George and Rita flew out of Radio City and right into Childs Bar, just a few blocks away. The bartenders had lined up glasses all along the bar and just kept pouring. “I popped quite a few drinks,” George says.

Then he and Rita went to Times Square, and as they crossed Seventh Avenue at 44th Street, George caught sight of a woman in a nurse’s uniform: “What I remembered about the nurses from five months earlier . . .”

Actually, George has it wrong. It had been three months before, out in the Pacific, aboard the USS The Sullivans. He’d watched on the morning of May 11 as two Japanese kamikaze planes, one after the other, smashed into the nearby USS Bunker Hill, setting off a series of explosions and killing 346 sailors (43 bodies were never recovered). George helped pull hundreds of men, some horribly burned, out of the water, and watched with awe as nurses went to work on them.

So on this joyous and unbelievable afternoon, George ran from Rita — the most beautiful girl he’d ever seen — grabbed the first nurse he saw, spun her around, dipped her and kissed her. Rita was just steps behind them, and in the photo she’s beaming.

“A lot of people want to know what I was thinking,” she says. “It was a happy day; I was grinning like an idiot. The kiss really didn’t bother me at all. If I had been engaged, maybe.”

The kiss did kind of bother someone else, though: the woman in the nurse’s uniform, Greta Zimmer, who wasn’t even a nurse. She was a 21-year-old dental assistant from Queens, who, having heard rumors about the end of the war, walked over to Times Square from her office on Lexington Avenue. George says he was so drunk, he doesn’t even remember the kiss. Greta says she’ll never forget it.

Greta Zimmer was born and raised in Austria, and in 1939, after much debate, her parents insisted that Greta and her two sisters flee to America. They were among the last refugees to make it out, and even on the afternoon of Aug. 14, as Greta read the illuminated news crawl declaring the end of the war, she had no idea where her parents were, or if they were even alive.

She isn’t sure how long she was standing there; maybe minutes. “And then I was grabbed,” she says. “That man was very strong. I wasn’t kissing him. He was kissing me.”

Just as suddenly, he let her go. George stumbled off towards the subway, Rita trailing behind, and Greta walked back to her office. George and Rita never discussed the kiss, nor did Greta tell anyone what had happened to her.

Back then, it was just one of those things: “Obviously, to do that today — it’s not such a good idea,” says Lawrence Verria, co-author of “The Kissing Sailor.” “But in Times Square, 1945, they hear the war’s over — it’s not such a bad idea.”

None of them knew they had just been photographed by Eisenstaedt, that their picture was about to be published in Life magazine, or that, decades later, multiple men and women would come forward claiming to be that sailor and that nurse.

Life magazine published the photo in the issue that ran right after V-J Day, but not on the cover — it was buried on page 27. Over the years, Life ran the image intermittently, but it wasn’t until 35 years later, after editors claimed to have discovered the nurse (they had it wrong), that the photo caught fire.

George saw the photo for the first time in that 1980 issue, and he says, “It was like looking in the mirror.”

Guess whom he didn’t spot?

“Rita saw the photo and goes, ‘I think that’s me,’ ” Verria says. “And George goes, ‘Rita, that’s not you. It can’t be you.’ ”

He laughs. “Rita’s very soft-spoken. She lets him take the limelight.”

Greta, by now married with children, had the same reaction as George: She knew it was her. “The seams in my stockings were perfectly straight — I was always careful about that,” she says. “And it was my figure, and my hairdo. I was carrying this little tapestry purse that I owned.”

Her husband, now deceased, noticed something else: The odd angle of the woman’s left thumb. According to Verria, Greta’s husband said, “You know, when you get very tense, your arm stiffens up and your thumb sticks out just like that.”

George and Greta were but two of several people convinced that they were Eisenstaedt’s subjects, and the mystery helped cement the image in the American psyche. Yet no real attempt was made to identify the sailor and the nurse until 1987, when Life magazine announced it was selling prints of Eisenstaedt’s photo.

Upset that he had effectively been edited out of history, George sued Time-Life, and though he was outspent legally, Yale University professor of photography Richard Benson agreed to examine the photo, along with three others Life made available. Benson concluded that the sailor was, indeed, George, as did the Mitsubishi Electric Research Lab in 1995 (they donated their services as a contribution to history) and forensic anthropologist Norman Sauer, who was contracted by the authors in 2009. Experts agree, through similar forensic analysis, that the “nurse” is Greta. “The Kissing Sailor” has collected all the research in hopes of being the final word on the subject.

The clincher for the authors is the presence of Rita, so long overlooked, quite recognizable in outtakes standing in the background.

She says the photo, like the kiss, has never been an issue in their marriage. “I never gave too much thought to it,” she says. “By the time I knew about it, I’d been married for years.”

Today, Greta Zimmer Friedman lives in Frederick, Md. After the war, she learned that her parents had died in the camps, and she has never returned to Austria.

George and Rita, now married for 66 years, live in Rhode Island, where a copy of the famous photo hangs in their hallway and another downstairs. George says he’d never hang it if his wife didn’t approve — “She’s the boss!” — and that it’s true the kiss has never been discussed, before the photo’s enshrinement or since.

After all, George says, “I’m still kissing Rita.”