An unmanned Delta rocket carrying a $57.5 million weather satellite swerved out of control, burst apart and was destroyed over the Atlantic by command from the ground tonight, the third consecutive disaster for the U.S. space program.

The Delta rocket -- considered the most reliable in NASA's inventory -- veered off course about 71 seconds after lifting off at 6:18 p.m. EDT from Pad 17A at Cape Canaveral Air Force Station. National Aeronautics and Space Administration officials said the rocket's main engine shut down abruptly when the Delta was 11.3 miles high and 49.2 miles downrange.

As the 116-foot rocket lost thrust, its nose broke off and burst into pieces. Ninety-one seconds into the flight, as the rocket was veering out of control 15 miles high, Air Force officials destroyed it with onboard explosives and debris rained into the ocean about 30 miles east of the Florida coast.

Shocked NASA officials and others watching from the ground could see the rocket, traveling at 1,400 mph, blow up in a burst of orange flame.

"It devastates me," William Russell, NASA's Delta project manager, said at a news conference. "It's quite a setback for all of us. We were counting on getting back on track with this, and in the past the Delta was a reliable vehicle. We're very disappointed."

NASA spokesman Hugh Harris said the Delta will be grounded pending an investigation. "You don't launch a Delta again until you know what went wrong," he said.

President Reagan was informed of the accident Sunday morning in Tokyo. White House spokesman Larry Speakes said Reagan is determined to proceed with the U.S. space program. "Clearly we have had specific problems," Speakes said. "They are being looked at very thoroughly."

It was NASA's first launch since the Jan. 28 Challenger disaster that killed the space shuttle's crew of seven, and came barely two weeks after the explosion of an Air Force Titan 34D rocket carrying a classified payload.

Russell and other NASA officials said they had no explanation for the sudden engine failure. The flight initially appeared normal, Russell said, with the first group of solid-rocket boosters being jettisoned on schedule about 64 seconds after liftoff. Then the main engine shut down abruptly, "as though it were a commanded shutdown. Once you lose that . . . the rocket has no stability control," Russell said.

"I don't have any idea what happened," said Charles Gay, NASA launch director. "We went into this thing with everything in good shape. We had a virtually trouble-free countdown. We followed the book all the way."

Within minutes of the failure, NASA officials impounded the launch data, ordered the area off-limits and put all records "under lock and key," officials said.

The launch, originally scheduled for Thursday night, was put off when technicians found that less than a cup of rocket fuel had leaked from a valve.

The flight was delayed for two days, giving technicians time to dry all the fuel lines and perform five extra checks for leaks before they certified that it was ready to go.

Gay said there is no connection between the fuel leak, which officials had described as minor, and the shutdown of the engine.

The failure stunned NASA officials watching inside the green blockhouse that served as operations center for the mission. One could be heard crying out "Oh, no" over the public address system when the rocket began to falter.

"It was hard to believe what had happened," said Gay, who was in the blockhouse. "It got pretty quiet in there. It was shock."

NASA officials tonight estimated that the accident would cost the government more than $100 million. NASA estimated launch costs at about $42 million, including $30 million for the three-stage Delta rocket.

The Delta's engine is manufactured by the Rocketdyne division of Rockwell International. The rocket is made by McDonnell Douglas Corp. A McDonnell spokesman said company officials were reviewing flight data.

The rocket also is powered by nine solid-fuel boosters strapped around its bottom stage. The boosters, made by Morton Thiokol Inc., are similar to those on the space shuttle, but are much smaller and are in one section, rather than in parts.

The weather satellite, owned by the National Oceanic and Atmospheric Administration, was a Geostationary Operational Environmental Satellite (GOES) that was to be used to detect hurricanes and other Atlantic storms. The flight was supposed to restore the nation's two-satellite system for weather detection. Another GOES malfunctioned in July 1984. Only one is operating.

The accident also hurt NASA because it happened with a rocket that agency officials have long touted as their most reliable "workhorse." The Delta had a 95 percent success rate over 177 missions dating to 1961, when it launched the experimental Echo balloon satellite.

Its last 43 flights were successful; a Delta had not failed since Sept. 13, 1977. But the rocket had not been launched since Nov. 13, 1984, and some McDonnell Douglas officials acknowledged before the flight that they were concerned about the relatively long 18-month "down time" for the launch crew.

In preparation for today's countdown, NASA officials had introduced a host of new safety precautions, including requiring contractors to sign written statements certifying the flight readiness of parts of the rocket.

They also revised preflight reviews to prevent the communications breakdowns that apparently marked the ill-fated decision to launch the Challenger.

"We've tried to be squeaky clean," Russell said before the countdown started. "We did a lot of additional inspections . . . and if there was any doubt, we redid it."