In “Slingshot,” a space travel thriller directed by Mikael Håfström, the title refers to a risky flight maneuver involving orbital mechanics. Astronauts journeying more than a billion miles to one of Saturn’s moons, Titan, will need a gravity assist — the “slingshot” in question — from Jupiter’s orbital velocity to make it all the way. Why are they going to Titan? It’s the only other planet that has liquid on its surface, methane that they intend to harvest for clean energy to combat climate change on Earth.

But despite the seemingly action-oriented premise, this psychological character study starring Casey Affleck is a slog. The film isn’t about the slingshot, or the methane gas or even climate change, but about the challenges of the journey itself. In order to endure the yearslong trip, the crew needs to “hibernate” in three-month-long chunks, their sleep aided by heavy doses of drugs, which cause disorientation every time they wake up.

John (Affleck), an ambitious pilot, spends most of his time on board trying and failing to shake off dreamy visions of a former lover, Zoe (Emily Beecham), one of the designers of the cutting-edge spacecraft. Every time he goes to sleep, he dreams of Zoe rolling around in bedsheets, and every time he wakes up, he’s fighting through brain fog in order to discern what’s real and what’s not, or fighting with his colleagues.

The situation with the other crew, Captain Franks (Laurence Fishburne) and scientist Nash (Tomer Capone) becomes increasingly untenable as their mental health devolves over many taxing hibernation cycles. When the ship is mysteriously damaged, Franks is determined to finish the mission, while Nash wants to turn back, with John caught in the middle. Despite this central tension, “Slingshot” is undeniably sleepy, in which a groggy Affleck stumbles around a spaceship for most of the running time.

As Nash sows the seeds of mutiny, Franks attempts to violently wrest back control. Ultimately, it plays out a bit like “Gaslight” in space, with Fishburne playing Charles Boyer to Affleck’s Ingrid Bergman. Screenwriters R. Scott Adams and Nathan Parker don’t bother digging into the themes or big ideas, and instead throw twist after twist into the script just to keep things from getting too somnambulant.

The desire to know what’s real sustains enough interest to keep us engaged, but the continual flashbacks to a syrupy and unconvincing romance in which John and Zoe lie on the floor talking about moths have a devastating effect on the momentum. The terrific Beecham is saddled with a dismal role, her character simply an object of wan yearning for the John. Affleck seems lethargic even in flashback, and is entirely implausible as a hotshot pilot in his late 30s. Affleck sleepwalks through this film in more ways than one.

Håfström’s direction is equally sluggish. While there’s some pretty lighting in the hibernation pods, the creative choices made around John’s hallucinations are predictable and pat. There’s just nothing to hook into aside from Fishburne’s performance, which is the only captivating element of the film, and even that is derivative of his iconic Morpheus role in “The Matrix.” Despite the twists and turns that never let up, there are no signs of life in “Slingshot.”

MPA rating: R (for language and some violence/bloody images)

Running time: 1:49

How to watch: In theaters Aug. 30