As four T38 jets streaked across the afternoon sky to end a national memorial service for the crew of the space shuttle Challenger, one peeled off with a thunderous whine in the military gesture of mourning. The empty place in the formation captured a nation's sense of loss -- and the three planes that soared on symbolized what President Reagan described as its determination to go forward.

"Today we promise Dick Scobee and his crew . . . that the future they worked so hard to build will become reality," Reagan told their families, National Aeronautics and Space Administration employes and dignitaries at the Lyndon B. Johnson Space Center here today. ". . . Dick, Mike, Judy, El, Ron, Greg and Christa -- your families and your country mourn your passing. We bid you goodbye, but we will never forget you.

"For those who knew you well and loved you, the pain will be deep and enduring. A nation, too, will long feel the loss of her seven sons and daughters . . . . "

The service was held in the memory of spacecraft commander Francis R. (Dick) Scobee, Navy Cmdr. Michael J. Smith, mission specialist Judith A. Resnik, Air Force Lt. Col. Ellison S. Onizuka, mission specialist Ronald E. McNair, payload specialist Gregory B. Jarvis, and Christa McAuliffe, a schoolteacher.

The service was held on a grassy rectangle that has been the traditional site of homecoming ceremonies for returning astronauts. Challenger's seven-member crew died late Tuesday morning when the shuttle exploded 74 seconds after liftoff at Cape Canaveral.

NASA employes and contractual workers poured out of the center's angular concrete-and-glass buildings to mourn what Reagan called their "death in the family." Flags billowed at half-staff in a delicate, spring-like breeze. "The Challenger crew took something of us all aloft on Tuesday," acting NASA Administrator William R. Graham said, struggling to control the grief his voice. The audience of 10,000 included current and former astronauts, military officers, several senators and House members and the children of President John F. Kennedy Jr., who challenged America to go to the moon. Journalists came from as far away as Australia and Japan. But the folding white chairs in front of the blue podium, next to President Reagan, and his wife, Nancy, belonged to those whose losses were greatest.

The Reagans led the crew's relatives to their seats after spending a private half-hour with them in a secluded classroom.

Lorna Onizuka, the widow of Lt. Col. Onizuka, sat for most of the service with her head on a relative's shoulder. Edward and Grace Corrigan, the parents of teacher McAuliffe, held hands, their faces sad but stoic. Erin Smith, who lost her father, pilot Michael Smith, clutched a teddy bear and wept as her older sister, Alison, shut her eyes tightly -- and vainly -- against tears.

Reginald McNair, nearly 4, played with the gold buttons on his navy blue jacket and looked around curiously, too young to comprehend the death of his father, Ronald McNair. Marcia Jarvis, the widow of Hughes Aircraft engineer Gergory Jarvis, aboard Challenger with one of his company's satellites, also attended, as did McAuliffe's husband, Steven.

The family of astronaut Resnik remained in her home town of Akron, Ohio, for a memorial service at Temple Israel. About 1,000 people -- including Gov. Richard F. Celeste (D) and 13 fellow astronauts -- attended the tribute, which ended with four NASA jets flying the "missing-man" formation.

Several thousand mourners joined hands and cried at a community memorial service on the statehouse lawn in Concord, N.H., for McAuliffe, who called herself the first "ordinary citizen" in space. She taught at Concord High School, where students gathered earlier in the day to hear a letter from Reagan.

In his invocation here, the Rev. Bernard R. Hawley of Salina, Kan., father of astronaut Steven Hawley and father-in-law of astronaut Sally Ride, who have flown previous missions and are scheduled to fly again, described the Challenger crew as "seven who embodied in a special way the dream we all possess."

Reagan, his eyes fixed on the families before him, stressed the pioneer spirit of the space shuttle mission.

"We think back to the pioneers of an earlier century," he said, "the sturdy souls who took their families and their belongings and set out into the frontier of the American West. Often, they met with terrible hardship. Along the Oregon Trail you can still see the grave markers of those who fell on the way. But grief only steeled them to the journey ahead.

"Today," he continued, "the frontier is space and the boundaries of human knowledge. Sometimes, when we reach for the stars, we fall short. But we must pick ourselves up again and press on despite the pain."

He said each family member he talked to urged "specifically that we continue the space shuttle program, that that is what their departed loved one would want above all else," he said. "We will not disappoint them."

At the conclusion of the service, some spectators wept anew as they shaded their eyes to see the jets. The 539th Air Force Band played the proud, sad, majestic strains of "Eternal Father," "God Bless America" and "My Country, 'Tis of Thee," as Reagan and his wife, Nancy, spoke again with the Challenger families, lingering with those who seemed most distraught.

The Reagans and the crew's families departed to the stately cadence of the "Battle Hymn of the Republic."

With tears in many eyes, NASA employes slowly began to make their way back to work. Glenn Bunch, an airline employe working for NASA, described sadness mixed with "a strange feeling of exhilaration . . . . I'd go on the space shuttle tomorrow if they would have me," he said.

Out on busy NASA Road, drivers slowed as they passed the space center, their car headlights blazing to show their respect. Near the entrance, a lone elderly woman sat in a lawn chair by the side of the road. She held high a sign that said, "God Bless the Astronauts."