Houston, we have a romantic comedy (and a good one at that)

If you’ve seen the trailer for “Fly Me to the Moon,” you might think you know what movie you’re in for: a classic romantic comedy that casts its leads — Scarlett Johansson and Channing Tatum — in a silly period comedy, decked out in staid clothes, mid-century modern furniture, big bouffant hair and gunmetal glasses from 1969.

You might expect the light-hearted hyperbole and witty performances of 2002’s “Down with Love,” whose reinterpretation of Rock Hudson and Doris Day by two early-2000s megastars brimmed with satire and a warm admiration for its source material.

Unlike that film, “Fly Me to the Moon” is not a love letter to the ’60s, other than the fact that it is set in the same misogynistic era.

Kelly Jones, played by Johansson, is an anomaly and an entirely fictional person. She is a formidable combination of Holly Golightly, the hyper-feminine but emotionally distressed character played by Audrey Hepburn, and Frank Abagnale Jr., the famous con man played by Leonardo DiCaprio who, had the fictional worlds collided, would have teamed up with this mythical Miss Jones to form a formidable Bonnie and Clyde-style con duo.

Kelly Jones works in the male-dominated world of advertising, surrounded by Don Draper types. Her success is largely due to her ability to mold truth into a prettier package than her monochrome dresses and shape-shifting accent. Typically, she repositions cars or household items to appeal to a broader audience, American consumers. But her next assignment is a much bigger project that requires a much bigger lie.

Moe Berkus (Woody Harrelson) approaches Kelly at a bar with the job of a lifetime: The United States government, then under President Richard Nixon, needs Kelly to sell NASA’s latest space mission to a country exhausted by the civil rights movement and the Vietnam War. The Cold War with Russia is also at its height, and the space race is in its final stages. Public awareness, they believe, would lead to greater congressional support and, therefore, more money for the program. Kelly is up for it, though she faces suspicion and resistance from NASA’s serious and very attractive launch director, Cole Davis (Tatum).

Directed by acclaimed television writer-director-showrunner Greg Berlanti, “Fly Me to the Moon” takes off thanks to Rose Gilroy’s smart, punchy script and Keenan Flynn and Bill Kirstein’s original story.

Ray Romano takes on Henry Smalls, the launch’s deputy director, with his trademark misanthropic angst, though there’s an unexpected touch of tenderness that fully fleshes out his performance. Harrelson is little more than a toothless Rottweiler, spitting out orders with vaguely ominous repercussions in the actor’s trademark tone of raised eyebrow and sardonic smile.

Like the Hudson-Day duo, the Johansson-Tatum couple is the undeniable attraction of this film, which, despite the many compliments in this review, lasts 20 minutes too long, a flaw camouflaged by the charm and charisma of its protagonists.

Johansson oscillates between a high-heeled businesswoman, sharp, smart and deadly, and a sweet, endearing woman lost in her character’s flaws. She’s the powerful force that drives every scene, even dictating her chemistry with Tatum, who might otherwise be a paper cutout with the same effect. She’s just that good.

But Tatum is a megastar in his own right, and he brings a breath of mischief to the otherwise solemn character of Cole Davis, who is still haunted by the deaths from his previous (again fictional) work on Apollo 1, which suffered a cabin fire before takeoff and killed all three astronauts on board. Apollo 11 is a personal mission for Cole, which is why he is not included in a plot conceived by the White House and executed by Kelly: to create and film a fake moon landing in an abandoned hangar at the Kennedy Space Center to ensure that the live television broadcast is not marred by the vagaries of space travel. Tatum brings a breath of mischief to the otherwise solemn character

Kelly hires his favorite sales manager, a flamboyant cynic played with perfect execution by Jim Rash. With the help of his loyal assistant Ruby (Anna Garcia), Kelly nearly pulls off the coup of his life until his heart and dormant moral ethics are awakened by the kindness of his new friend and colleague, Cole Davis.

As the film progresses, those 20 minutes of sub-editing become more apparent. The delay toward a resolution, which we know from the history books is a success, is mitigated by the performances and the humor that doesn’t flag in the third act as one might expect.

Kelly changes her mind. Cole learns to accept help. The movie’s lessons aren’t exactly new, and its vision of 1960s America is probably more progressive than the real thing. But if we’re going to shoot for the fictional moon, we might as well spend some quality time with some beautiful stars.

Houston, we have a romantic comedy, and a good one at that.

“Fly Me to the Moon” is in theaters.