The very best sporting photographs do not need captions because they do not require explanation: Willie Mays, capless, his back to the camera (and the batter), hauling in Vic Wertz’s long fly.

Y.A. Tittle, helmet off, kneeling and bloody in the end zone at Pitt Stadium. Muhammad Ali, triumphant and ebullient, lording over a fallen Sonny Liston.

But the best of all these unforgettable images, to me, has always been the one captured through the lens of a photographer named William C. Greene, who, on April 10, 1947, snapped an image for his newspaper, the New York World-Telegram, of Jack Roosevelt Robinson walking into the Brooklyn Dodgers’ clubhouse at Ebbets Field.

In the subject’s left hand is a mitt, held high above his head. On his head is a cap, with “M” on it, and on his chest a jersey with “Montreal” written in script. That day had begun with Robinson playing for the Montreal Royals, the Dodgers’ top farm club, in an exhibition. In the fifth inning a news release had been circulated in the press box.

It said, in full: “The Brooklyn Dodgers today purchased the contract of Jackie Roosevelt Robinson from the Montreal Royals.”

Which is why Robinson was where he was, and why he was doing what he was doing: His right arm in the picture is nudging open the door. Just above it are the words: “DODGERS CLUB HOUSE.” And just below that: “KEEP OUT.”

“This is the door that [Dodgers general manager] Branch Rickey has finally opened,” read a caption in the Pittsburgh Courier, then the nation’s leading African-American newspaper, a week later.

“The ‘keep out’ sign doesn’t mean Jackie, or any other colored player who makes the grade. The great American pastime has really become American at last.”

Jackie Robinson would have turned 100 on Thursday. He was born into abject poverty on Jan. 31, 1919, the grandson of a slave, the son of sharecroppers who worked 60-hour weeks at Sasser Plantation near Cairo, Ga.

His father, Jerry, abandoned the family when Jackie was 6 months old, forcing his mother, Mallie, to make up for his work in the fields until she determined to seek a better life for her and her five children. Before Jackie would turn 1, Mallie and her kids boarded the No. 58 train bound for Pasadena, Calif.

Jackie’s life was such that he barely made 50, let alone 100, because he spent so much of his adult life trying to do symbolically what he did literally in that picture — keep that door open, ever so slightly, in the face of a brand of hostility few people have ever known.

“Jackie was one of the most beloved Americans who ever lived,” his friend and teammate Ralph Branca told me in 2007, on the eve of the 60th anniversary of Robinson’s having officially shattered baseball’s color barrier on April 15, 1947, four days after Greene clicked the shutter on his camera. “But he was also one of the most hated, and people weren’t afraid to let him know how much they hated him, either. That takes a toll on a man.”

By the time he died at his home in North Stamford, Conn., on Oct. 24, 1972, Robinson suffered from diabetes, he was virtually blind and his heart was weary from a quarter-century of fighting to keep that door ajar. It was also broken because his son and namesake, Jackie Jr., who had been wounded in Vietnam and battled addiction upon his return, had died in a car accident 16 months earlier.

In his last public appearance, nine days before his heart gave out, Robinson had been introduced to warm applause before Game 2 of the World Series at Riverfront Stadium in Cincinnati — a city where, 25 years earlier, he’d endured some of the most vile treatment due to its location, a short walk across the Ohio River from Kentucky, a state still beholden to Jim Crow in 1947.

But even in his weakened state, the fighter within Robinson could not be caged that afternoon in the brilliant sunshine as he was lauded by Major League Baseball Commissioner Bowie Kuhn and introduced by Red Barber — the erstwhile Brooklyn announcer and son of Mississippi who admitted that his entire view of the world had changed in watching Jackie play from his “catbird’s seat,” the broadcast booth at Ebbets Field.

Even then, his hand was on the door.

“I’m extremely proud and pleased to be here this afternoon,” Robinson said, “but must admit I’m going to be tremendously more pleased and more proud when I look at that third-base coaching line someday and see a black face managing in baseball.”

Cincinnati had also been the site of one of the great pieces of mythology in baseball history. Legend has long held that on May 13 that first year of baseball integration, the stands at old Crosley Field were filled with an especially pointed level of hostility. Pee Wee Reese — born in Louisville, 100 miles away — heard the ugliness, walked over to Jackie and put his arm around him.

Whether this actually happened is something that will never be known for sure, but what is known is that Reese, a southerner, accepted Robinson immediately (the moment exists eternally in a statue outside MCU Park in Coney Island, home of the Brooklyn Cyclones) and was impacted by Robinson, as so many of his teammates were, from the moment Robinson walked through the door and across the baseball threshold.

“To be able to hit with everybody yelling at him,” Reese said in 1997, “he had to block all that out, block out everything but this ball that is coming in at a hundred miles an hour. To do what he did has got to be the most tremendous thing I’ve ever seen in sports.”

Unknown to most at the time was the gentleman’s agreement Rickey had secured with Robinson in August 1945, when Rickey first hatched his plan to break the color barrier and signed him to play in Montreal for the ’46 season.

Rickey knew that there were a dozen Negro League players whose natural talent far surpassed Jackie’s. Robinson was a terrific athlete (he’d played football and basketball at UCLA), but was still something of an unfinished baseball prospect.

But Rickey was well aware of Robinson’s court-martial almost exactly two years earlier. A second lieutenant assigned to the 761st Tank Battalion at Fort Hood, Texas, Robinson was riding a military bus when the driver ordered him to the back. Robinson refused and the driver backed down, but at the end of the trip, the driver summoned military police. At Robinson’s trial for insubordination, a nine-member jury — all white — acquitted him of the charges.

Rickey knew that was the kind of man who would have to lead the fight he had in mind — who would have the strength of both mind and body to barge through baseball’s locked clubhouse doors.

During a three-hour interview, Rick­ey hailed all manner of invective at Robinson to gauge his reaction and told him that for five years, he would be required to take all insults with a stoic face and his fists pocketed. Robinson was incredulous.

“Are you looking for a Negro who is afraid to fight back?” he asked.

“I need a player with the guts NOT to fight back,” Rickey replied.

It was often left to sportswriters sympathetic to Robinson’s plight to fight battles on his behalf. In The Post, in the spring of 1947, Jimmy Cannon wrote about encountering an angry Florida mob at one game where Robinson was playing.

“When they located where I stood, they would hack at me with their sneering bigotry. If we were alone, they stayed courteous and presented their prejudices as necessary to perpetuate our civilization, which they believe is imperiled by equality among the races.

“But if they had an audience, they would snipe with dirty and pointless jokes and try to catch a laugh with their venomously humorless imagery of a race’s agony. I know there are ways to lynch a man without hanging him from a tree.”

Seventy years later, three days before he would leave office on Jan. 17, 2017, President Barack Obama welcomed the champion Chicago Cubs to the White House for one of his final ceremonies as chief executive. In his remarks, the nation’s first African-American president spoke of baseball’s first black major-leaguer.

“It is worth remembering . . . throughout our history, sports has had this power to bring us together, even when the country is divided,” Obama said. “Sports has changed attitudes and culture in ways that seem subtle but that ultimately made us think differently about ourselves and who we were. It is a game, and it is celebration, but there’s a direct line between Jackie Robinson and me standing here.”

Robinson himself was a Republican, a decision he made because he believed the Democratic Dixiecrats had all but driven his family from Georgia. In truth, he had difficulty finding a home in either political party.

He knew Richard Nixon and supported him in the 1960 presidential election and practically begged him to help free a jailed Martin Luther King Jr., a move he believed would clinch the White House for Nixon since it would rally the minority vote. When Nixon refused, John F. Kennedy placed the call, won the black vote overwhelmingly and won the presidency, but Robinson could never square JFK’s action with the fact that he still courted racist Southern Democrats.

Four years later, as an avid supporter of New York’s Gov. Nelson Rockefeller, he spoke at the Republican Convention in San Francisco but was disillusioned by the party’s decision to back Barry Goldwater, a longtime opponent of civil rights. Robinson stepped away from political life after that and spent his final years in Connecticut waiting to see if the changes he’d helped set in motion would ever bear fruit.

“He knew he’d done a lot,” Branca said, “but always believed he could have done more.”

At his funeral, held at Manhattan’s Riverside Church, the Rev. Jesse Jackson urged 2,500 mourners to remember that Robinson’s earthly journey, halted at age 53, was nevertheless one of the most essential of all American lives.

“He didn’t integrate baseball for himself,” Jackson said. “He infiltrated baseball for all of us, seeking and looking for more oxygen for black survival and looking for new possibility.”

Forty-seven years after his death, 100 years after his birth, we celebrate a man who always believed in those possibilities. And who forever opened the door to so many of them.