Brad Pitt is an intergalactic Captain Willard, taking a fraught mission up-river in James Gray’s Ad Astra, an outer-space Apocalypse Now which played to rapt crowds at the Venice film festival. In place of steaming jungles, this gives us existential chills. Instead of Viet Cong soldiers, it provides man-eating baboons and pirates riding dune-buggies. It’s an extraordinary picture, steely and unbending and assembled with an unmistakable air of wild-eyed zealotry. Ad Astra, be warned, is going all the way - and it double-dares us to buckle up for the trip.

Set in the near future, this casts Pitt as Major Roy McBride, a lonesome samurai who prides himself on the fact his pulse rate has never climbed beyond 80. He’s travelling out to Neptune in search of his lost father, a man he barely knows, and seeking to halt a series of unexplained cosmic rays that threaten life on Earth. Pitt embodies McBride with a series of deft gestures and a minimum of fuss. His performance is so understated it hardly looks like acting at all.

“In the end the son suffers the sins of the father,” McBride explains in hushed voice-over as his ship noses onward through the blackness. This is because McBride Sr (Tommy Lee Jones) is the film’s Colonel Kurtz, a brilliant astronaut who went AWOL years before and may in some way be responsible for the current crisis. Roy’s bosses at SPACECOMM say they simply want his father brought home whereas in fact they are secretly planning to terminate his command. Roy receives this information with barely a flicker of emotion. His feelings about the old man have always been conflicted; he’s not even certain he wants to find him alive. But he still fires out messages and waits for a response.

Gray (who also wrote the script alongside Ethan Gross) is an established purveyor of big, brooding, ambitious cinema, from The Yards through The Immigrant to 2017’s Amazonian adventure, The Lost City of Z. But he’s never made anything as ambitious as this soaring psychological space-opera, with its cool surfaces, dark pockets and sudden flashes of violence. Ad Astra is so deadly serious that it verges on the silly; so immaculately staged and sustained that it sweeps us up in its orbit.

Roy docks at Mars, after which he lights out on his own, 2.7bn miles from home. And it’s at this point that the film begins to fold in on itself, jettisoning its sci-fi paraphernalia (man-eating primates and all) to become an unblinking parable of desperate fathers and damaged sons. Having kept his cool for so long, the astronaut finds that his pulse rate is spiking. So he cuts communication with Earth and prepares to face his demons. He’s travelling deeper and deeper into his own heart of darkness as Ad Astra pitches from full-blown horror to the thunderclap of closure. In space, it transpires, no one can hear you scream for your dad.

• Ad Astra opens in the UK on 18 September, in Australia on the 19 September and in the US on 20 September