The National Aeronautics and Space Administration set in motion today a long, slow and extraordinarily complex search for the cause of the catastrophic explosion that killed seven astronauts and destroyed the space shuttle Challenger in the worst disaster in space-flight history.

Ten ships and 10 aircraft began salvaging what was left of Challenger in a broad swath of ocean off the Florida coast, retrieving several hundred pounds of metal and tiles today from a space vehicle that once weighed more than 715,000 pounds. At the same time, officials at three space centers gathered together hundreds of millions of bits of computer data, pictures from more than 120 NASA cameras and statements from mission controllers, and even the film of remote-control news cameras near the launch pad.

All of it was placed under strict impoundment for analysis by specialized teams and boards assembled today for an investigation that could last six months or longer -- with no guarantee of ever providing a firm answer.

The White House announced that President Reagan, who spent much of the day consoling families over the telephone, will fly to the Johnson Space Center in Houston on Friday to lead the national tribute to crew members Francis R. (Dick) Scobee, Navy Cmdr. Michael J. Smith, Christa McAuliffe, Gregory B. Jarvis, Ellison S. Onizuka, Ronald E. McNair and Judith A. Resnik.

"I think all of us have kind of escaped the numbness of shock that we all felt" Tuesday, the president said today. "But life has to go on, and so does the space program."

Despite two briefings by haggard-looking officials, the day after the Challenger disaster produced not even a hint of its cause from agency experts. However, NASA did provide at least one important new piece of information about events immediately after the explosion.

The two towering solid-fueled rocket engines that help lift the shuttle into orbit were deliberately blown up by the Air Force range safety officer just after the accident. The order to destroy the still-burning rockets was given when one of them headed out of control directly toward the Florida beaches. The rocket was apparently destroyed by radio command when it was less than 30 seconds from the Florida coastline.

"There was an indication that the rocket was headed for a populated area of the beach and the Air Force made the decision to destroy it," Richard G. Smith, director of the Kennedy Space Center in Florida, said. "It was the right decision."

The decision, however, destroyed what may have been the only pieces of evidence that were still intact after the explosion. Both rocket boosters blew up into fragments that fell and sank almost immediately to the bottom of the ocean, only 30 feet deep in the area.

Nevertheless, enough debris had already been picked up today that it filled an 82-foot Coast Guard cutter, which brought it back to Cape Canaveral to be sorted, marked and archived. Debris also floated up on beaches, prompting a plea from NASA to souvenir hunters to notify the agency rather than to pick up the material themselves.

"We want to get what's on the surface before it sinks. That's our main goal today," said Lt. Cdr. James Simpson, the Coast Guard officer supervising the air-and-sea search for Challenger wreckage. "We want to leave no stone unturned."

"We're looking at every possible scenario and every possible piece of evidence to locate a probable cause," Jesse W. Moore, NASA associate administrator for space flight, said at the Kennedy Space Center. "We intend to clearly understand all the circumstances of Challenger's flight by the time this investigation is over."

NASA's acting administrator, William Graham, appointed an interim seven-member investigation board consisting of Moore; Richard G. Smith, director, Kennedy Space Center; William R. Lucas, director, Marshall Space Flight Center; James C. Harrington, Spacelab director; Arnold Aldrich, Space Transportation System manager, Johnson Space Center; Marine Col. Robert F. Overmyer, chief of the astronaut office at the Johnson Space Center, and Walter Williams, a NASA consultant.

Space officials took sworn statements from everybody in the Launch Control Center in Florida and at the Mission Control Center in Houston for their accounts of every second from launch to the explosion, one minute and 14 seconds after liftoff.

There was still no sign of any of the bodies of Challenger's seven crew members.

NASA officials would not comment on widespread speculation that the explosion began in the enormous fuel tank holding almost 1.6 million pounds of explosive liquid hydrogen and oxygen, in the three giant engines that burned these supercold fluids, or in the two rocket engines that burn more than a million pounds of solid propellant for almost two minutes before burning themselves out on the way to space.

"None of this is close to being determined yet," said Graham. "We are concentrating on finding all the available evidence and are going ahead with deliberate speed to get it."

Stray reports reaching the news media in Florida and in Texas range from ice striking the shuttle's fuel tank to mysterious electronic signals sent from the air or the sea that would cause the shuttle to self-destruct.

"We show nothing like that at all," said Jay Greene, flight director in Houston's Mission Control. "We have no evidence that anything abnormal took place."

Greene gave the news media a chilling account of what the 74 seconds were like inside Mission Control -- from launch to disaster. He said that when the explosion was seen on television screens at Mission Control, data pouring off the Challenger and into the more than 50 consoles used by flight controllers suddenly ceased.

"We had a sharp cutoff of all data . . . . One second the screens all had data and suddenly, an 'S' lit up on the side of our screen indicating 'static' [a term indicating that data flow has ceased], but no more data was coming in," Greene said. "Then all we had was radar tracking data which showed multiple pieces all over our screens."

Red-eyed and drawn from lack of sleep, Greene said the explosion stunned everybody in the control room. There was no warning of any problem on ascent.

"We train awfully hard for these flights and we train for what we think is every possible contingency," Greene said. "There was nothing anyone could have done to save this flight."

He said that once the tragedy had sunk in, everybody in Mission Control reacted professionally, adding, "If you'd asked me what the mood was like, I'd say very somber but very professional."

All of the flight controllers, who monitor consoles showing everything from engine and fuel tank pressures to the condition of electrical circuits, volunteered exhaustive tape-recorded accounts of what they saw and remembered about the brief last flight of Challenger. Each flight controller also gave a written statement.

Even though shuttle flights may have begun to look routine to the public, Greene said shuttle liftoffs are still the most dangerous aspects of space flight.

"I've been a flight director for nine years now and I've never stopped watching a launch until it's over," Greene said. "If you get complacent about it, you don't understand it. It's still a very hazardous phase of flight."

Like other NASA officials, Greene refused to be drawn into speculation about what caused the accident, except to say that the explosion seemed to be caused by something that nobody anticipated.

When asked if slow-motion television pictures of the accident hinted at any clues on the origin of the explosion, Greene paused, sighed, stared ahead and said tiredly, "I don't know. I do know it would be nice to have the temperatures on the external tank right now but we have no operational use for those temperatures and so we don't have them." Moments before the explosion, close-up pictures of Challenger appear to show an orange flame starting on the downward side of the bullet-shaped fuel tank and crawling up its side until it disappears in the fireball that consumed the spaceliner.

What Greene seemed to be suggesting was that the investigative team does not have access to the sort of evidence that might link a rupture of the tank to the cause of the accident. Had the fuel tank ruptured, its explosive fuel would surely have leaked out and exploded on contact with the atmosphere. At the time of the explosion, Challenger was moving more than twice the speed of sound and had reached an altitude of 47,000 feet.

Out of the countless number of clues the space agency is examining, one is a report that so much ice had formed on the fuel tank during the countdown that it posed a threat to liftoff. Shuttle managers said that crews of technicians were dispatched twice to the launch pad to check the tank to see if ice formations were sufficient to postpone the launch.

"The primary purpose of the ice team is to go out and see if there is ice that could cause damage to the flight hardware," Kennedy Space Center director Smith said. "We send them out a second time to look at it and we even clean off any ice particles on top of the mobile launcher the structure attached to Challenger until liftoff to assure we had no damage. The consensus by all the experts was that we did not have a problem or at the worst we might ding a tile or two with ice debris."

NASA officials were asked at a morning briefing about reports that Rockwell International, a shuttle contractor, had recommended a delay of the flight just before launch time because of concern about icing conditions. Moore did not respond directly to the question and tonight David Garrett, a NASA spokesman in Washington, said that "nobody at the agency could verify" the report. "I could not confirm from anybody that it happened," he said.

Moore was asked what conditions might have created the sequence of events that triggered the explosion. He replied: "You're asking me to pin down the cause and I can't. I mean, you saw the same films I saw yesterday and that's all I'm prepared to say at this point in time.

"We are not discounting any possibility. What we're trying to do is amass the best data we can and we're going to look through a family tree of failure modes that's going to include a lot of different scenarios."

Moore said he has split up the investigative board into teams and subgroups that will examine every discipline associated with the shuttle's ascent. He said all the telemetry sent back in the 74 seconds of flight will be probed and reexamined exhaustively. A second team will review every beat of the space shuttle's liquid hydrogen engines while another will look at the performance of the solid-fueled rockets.

Still another team will probe everything it can find about the performance of the external fuel tank while a fifth team studies the shuttle's thousands of electrical circuits.

"We're going to go through this with a fine-toothed comb," Moore said.

Flight director Greene seemed to sum up the frustrations and the anguish of everybody on the shuttle team when he was asked today how the flight was going just before disaster struck.

"We were showing nothing anomalous. We had gone through an almost flawless countdown and our weather was almost perfect at liftoff. And I can still remember the last voice transmission that came from Challenger. He [shuttle commander Scobee] sounded great to me."

NASA's speed-up of shuttle launches is likely to be a subject of hearings expected to start in both the Senate and the House by mid-February as key lawmakers questioned whether the space agency had sacrificed safety by shortening the turnaround time between shots.

"There is a lot of pressure in the system and I think we will have to look at it to see if it did have an adverse impact," said Rep. George E. Brown Jr. (D-Calif), a ranking member of the House Science and Technology Committee.

NASA authorities and other lawmakers, however, insisted that safety remained a prime objective of the space agency even with the accelerated launch schedule. In defending the shortened turnaround time, NASA officials told Congress last year that a new launch pad and extra workers gave it the ability to lift off as many as 24 shots a year.

The hearings will be held by the House Science and Technology Committee under Chairman Don Fuqua (D-Fla.) and the Senate Commerce, Science and Transportation Committee under Chairman John C. Danforth (R-Mo.).