The words Neil Armstrong uttered when he first set foot on the moon, "That's one small step for man, one giant leap for mankind" may have passed into legend - but the man himself remained something of an enigma, and is now the subject of Damien Chazelle's new biopic First Man.

To play Armstrong, an intense, but stoic figure that the film surmises was emotionally scarred by the death of his daughter Karen from a brain tumour before she turned three, Chazelle has cast his La La Land muse Ryan Gosling.

The actor is a great choice, few can do deadpanned, melancholic determination as well as Gosling, whose face is often shot in close-up allowing us to see every straining pore, grimace, and determined but doubtful glance.

We first see Armstrong in 1961 as a test pilot in a North American X-15 rocket-powered aircraft - displaying a cool head under incredible mental and physical pressure as he bounces off the outer reaches of the atmosphere. From afar, he and his wife Jan (Claire Foy) are a typical middle-American family - raising two sons in a studiously well kept home - but in intimate scenes we get to see the future astronaut's restlessness and determination to achieve, if only to forget his grief over his daughter.

Armstrong's engineering background lands him a place at NASA, who need men like him to embark on an outlandish and dangerous mission. Aware that the Soviet space programme is years ahead, NASA's experts, led by Robert R. Gilruth (Ciaran Hinds), and Deke Slayton (Kyle Chandler) set their recruits the task of landing on the moon - reasoning that the endeavour is so difficult that both they and their Russian rivals will effectively be starting from scratch.

What really stays with you when watching First Man is Chazelle's depiction of the sheer mechanical complexity and constant danger of space travel. Films traditionally show spacecraft as technological marvels, with even the Tom Hanks classic Apollo 13, whose events took place the year after Armstrong's successful lunar trip, depicting its astronauts' journey as fairly serene until things went disaster struck. In First Man, we really get the sense of what it's like, in the words of David Bowie, to be sitting in a tin can - aware that if a wire malfunctions or a switch fails, you will not return home. Chazelle builds the tension as each stage of the moon voyage, like docking one craft with another (which had never been done before) has to be completed successfully before the main journey.

The focus on the mechanics of the achievement, and the camaraderie between men heading into the unknown, like the brash Buzz Aldrin (Corey Stoll), and Armstrong's close pal Ed White (Jason Clarke), means that Foy is largely kept in the background, as a nervous, exasperated wife.

However, she turns what could be a thankless role into a tour de force, with Jan articulating the emotions her husband feels unable to - providing the film with heart it might otherwise have lacked without straying into mawkishness. One scene, in which she demands her reluctant husband say goodbye to their boys before his famous 1969 trip is heartbreaking, even though history tells us he lived until 2012.

Like Armstrong himself, First Man is understated, technical, underpinned by real emotion, and in boastful times, a timely reminder of the diligence and intelligence of those who really made America great.