THERE’S a delightfully old school feel to the screwball chemistry enjoyed by Scarlet Johansson and Channing Tatum in Fly Me to the Moon, Greg Berlanti’s new mid-century rom com. It’s a repartee that recalls the likes of Cary Grant and Rosalind Russell or, perhaps, Rock Hudson and Doris Day. There’s fizz and friction aplenty.

Set at the height of the 1960s space race, Tatum plays Cole Davis, the NASA director in charge of Apollo 11. Johansson is Kelly Jones, the marketing specialist brought in to fix NASA’s public image and oversee the production of a back up Moon landing - just in case Neil Armstrong and co. don’t actually make it. They’re not natural bedfellows.

Now, clearly, and in spite of 50 years of endless conspiracy, Fly Me to the Moon is a work of complete fiction. Not only was the Moon landing absolutely not faked but NASA never produced a just-in-case back up. Viewed with the benefit of hindsight, that element of the plot is all part of the fun. A splash of irony or “an alternative version” of history.

While the literal truth of the film is hazy - students would be better sticking to Damien Chazelle’s worthier First Man - a degree of sociological truth lies within. The cynicism behind Kelly’s recruitment has, for instance, always been there. What was the Space Race if not a PR exercise in asserting the moral superiority of capitalism over the commie Russians? Kelly’s instructions, as the film has it, come right from the top.

Woody Harrelson plays Moe Berkus, the agent with orders from D.C., with Stranger Things’ Joe Chrest as just one Senator unconvinced of Apollo’s value for money. Ray Romano joins as Cole’s engineer in chief, while Jim Rash has a ball as Lance Vespertine, the second-choice director (they wanted Kubrick) brought in to shoot the fake.

All the while, Tatum reels in horror. Weighed down by his own inability to fly, Cole’s vested interest runs far deeper than politics and gimmicky. It’s a touching journey and well played. That Tatum sings so well with Johansson is rocket fuel enough.

Originally penned for streaming, Fly Me to the Moon made the big screen leap following a wealth of praise from test audiences. It’s not hard to see why. Stylish, clever, funny and warm, this is crowd pleasing stuff.