Over the years, a great many actors have taken a turn at playing one of the Kennedy brothers (in made-for-TV movies, on “Saturday Night Live,” in big-screen historical dramas). The vast majority of these performances have been mediocre, a handful have been quite good, and a few have been memorable — like Bruce Greenwood’s cuttingly terse and commanding JFK in the Cuban Missile Crisis drama “Thirteen Days,” or Peter Sarsgaard’s tender and battle-scarred Robert F. Kennedy in “Jackie.” To that short list of singular and superb Kennedy performances, we can now add the Australian actor Jason Clarke’s portrayal of Edward M. Kennedy in “Chappaquiddick.”

Clarke, with a bit of makeup, looks the part to an astonishing degree: the squint, the hawkish profile, the wedge of hair combed gently over from the left side, the lips that hang slightly open as if pondering a question, giving Kennedy an aura that’s more tentative, less forceful than that of his two legendary older brothers. Clarke also nails the voice — not just the familiar Boston accent but the dry understatement of it. He inhabits Ted Kennedy with the softly halting charm of an aging preppie who can seize up with self-doubt, but who still treats the world as his oyster.

There’s no contrivance in watching this actor; you simply accept the reality of his presence as Ted Kennedy. And that goes for the film as well. “Chappaquiddick” is exactly what you want it to be: a tense, scrupulous, absorbingly precise and authentic piece of history — a tabloid scandal attached to a smoke-filled-room travesty. It recounts and anatomizes, with riveting detail, the tragic car accident and its aftermath that cast its shadow over the political career of Edward Kennedy and, in many ways, came to symbolize his existence. The movie is avidly told and often suspenseful, but it’s really a fascinating study of how corruption in America works. It sears you with its relevance and, for that reason, has every chance to find an audience.

“Chappaquiddick” was directed by John Curran, from a super-sharp original screenplay by Taylor Allen and Andrew Logan (it’s their first), and though the film is about a large event, it’s a gratifyingly compact, restrained, and level-headed drama that doesn’t hype what it shows you; it teases the intrigue out of the facts. It starts the day of the accident, when Kennedy heads to Martha’s Vineyard for an annual regatta. His family has a cottage on the adjoining isle of Chappaquiddick, and there’s a low-key party atmosphere, with Ted spending most of his time talking to Mary Jo Kopechne (Kate Mara), a former secretary for his late brother Robert who was so devastated by his assassination that she left Washington. Ted is trying to convince her to come back.

Around 11:00 p.m., they drive out to the beach. Ted, who’s been guzzling whiskey from a bottle, zooms away from a local cop (he doesn’t want to be caught drunk, or seen with a pretty blonde he may have designs on). He then turns his gaze toward Mary Jo — and that’s the moment he drives off the bridge. It’s a short wooden structure, with no guard rails, and after fighting his way out of the water, he walks, in a daze, back to the cottage. He may be soused, but he’s already in damage-control mode.

At the cottage, when he sees Joe Gargan (Ed Helms), his cousin, friend, and lawyer, the first thing he says is, “We’ve got a problem,” followed by a quick, “I’m not going to be president.” He’s already thinking about himself, and no one but himself. He is thinking, in other words, like a Kennedy. Joe and their other comrade, the Massachusetts Attorney General Paul Markham (Jim Gaffigan), both tell Ted that he needs to report the crime, and he assures them that he will. But what he knows is that reporting the crime means he’ll be tested for alcohol consumption, so he has to wait. And wait.

The film says that what happened at Chappaquiddick was even worse than we think. Kopechne’s body was found in a position that implied that she was struggling to keep her head out of the water. And what the film suggests is that once the car turned upside down, she didn’t die; she was alive and then drowned, after a period of time, as the water seeped in. This makes Edward Kennedy’s decision not to report the crime a clear-cut act of criminal negligence — but in spirit (if not legally), it renders it something closer to an act of killing.

“Chappaquiddick” is a meticulously told chronicle, no more and no less, and at times there’s a slight detachment in watching it, because it’s too tough and smart to milk the situation by turning Edward Kennedy into a “tragic figure.” In certain ways, he may well have been, and there are moments when we see the sad grandeur with which this disaster hangs on his stooped shoulders, but the movie is fundamentally the portrait of a weasel: a man who, from the moment the accident happens, takes as his premise that he will not suffer the consequences, and then does what it takes to twist reality so that it conforms to that scenario.

That twisting consists, mostly, of calling his protectors. It starts with his father, Joseph P. Kennedy, who rasps out one word on the phone: “Alibi!” Joe is an 80-year-old stroke victim who can barely speak; he’s played, sitting in a wheelchair, by Bruce Dern, with a slack leer and a mouth twisted open, but with eyes that still burn with the merciless ferocity of power. Ted, with Joe’s help, is soon face to face with their high-end version of the Deep State: All the Kennedys’ Men, like the brainy speechwriter Ted Sorenson (Taylor Nichols) and the former Secretary of Defense Robert McNamara (a grimly magnetic Clancy Brown), who begin to make their moves.

A local physician is summoned, so that he can decree that Kennedy suffered a concussion (even though Ted is fine, and the doctor never even examines him). Amazingly, the incident on the bridge took place on the very same weekend as the moon landing, and utilizing that fact, and a little more strategic delaying, the news is kept out of the headlines (though not The New York Times). Then a deal gets cut with the local prosecutor — an old friend of Ted’s — to charge Kennedy with leaving the scene of an accident, which results in a suspended sentence.

It’s all a half-truth, a whitewash, yet Kennedy is so frazzled that he keeps screwing up the cover-up. He gives a written statement to the press that’s full of contradictions, and his decision to wear a neck brace to Mary Jo Kopechne’s funeral — where he somehow has no trouble turning his neck around — becomes an iconic advertisement for his guilty conscience. (The neck brace looks just like the prop it is. Therefore: What’s he hiding?)

Clarke’s Kennedy remains a humanly abashed yet strangely unapologetic figure. His call to the Kopechne family results in a rare moment of remorse, at which point he considers resigning from the Senate. But the pang of sanctimony doesn’t last. He’s a survivor, and a good son, and he does what his father tells him to do. He holds on to his power, without regard to the consequences.

Forty-eight years later, let’s be clear on what the meaning of Chappaquiddick is. Ted Kennedy should, by all rights, have stood trial for involuntary manslaughter, which would likely have ended his political career. The fact that the Kennedy family — the original postwar dynasty of the one percent — possessed, and exerted, the influence to squash the case is the essence of what Chappaquiddick means. The Kennedys lived outside the law; the one instance in American history of an illegally stolen presidential election was the election of John F. Kennedy in 1960. He in all likelihood lost the race to Richard Nixon, but his father tried to steal the election for him by manipulating the vote tallies in (among other places) Illinois. That’s the meaning of Chappaquiddick. too.

I don’t say any of this as a right-wing troll. But those are the facts, and they are facts that liberals, too often, have been willing to shove under the carpet. And they have paid the price. Ted Kennedy became known as “the Lion of the Senate,” and did a lot of good, but when you try to build a governing philosophy on top of lies, one way or another those lies will come back to haunt you. (Hello, Donald Trump! He’s an incompetent bully, but his middle name might be “Liberal Karma.”) As a movie, “Chappaquiddick” doesn’t embellish the incidents it shows us, because it doesn’t have to. It simply delivers the truth of what happened: the logistical truth of the accident, and also the squirmy truth of what went on in Ted Kennedy’s soul. The result may play like avid prose rather than investigative cinema poetry, but it still adds up to a movie that achieves what too few American political dramas do: a reckoning.