With 4,546 manmade pieces of machinery and debris whizzing through space in every direction, it was probably inevitable that one would go astray and become what Zbigniew Brzezinski yesterday called a little "Space Age difficulty" - an unguided craft headed home to Earth.

And it was probably just as inevitable, in this day and age, that first to spot the problem was a computer.

That discovery was made in early December deep inside Cheyenne Mountain in the Colorado Rocky Mountains where the North American Air Defense Command maintains a computerized watch on every item floating in space.

Cosmos 954. NORAD's name for the errant Soviet satellite - one of 939 working, satellites now in space - began losing speed and altitude faster than expected. The change triggered a warning in the NORAD computer and the military alerted the Central Intelligence Agency and other intelligence agencies.

Exactly when NORAD learned something was wrong is a classified intelligence secret, military officials maintained yesterday, although schoolboy ham radio operators in Europe who were tracking the Soviet satellite's radio emissions apparently were in on the secret almost from the start.

"It's been quite well known among ham radio operators for some time," Leonard David, head of the Forum for the Advancement of Students in Science and Technology said yesterday. David said his Washington-based group got a telegram from the European ham operators about the satellite's problems last week - before the United States formally notified members of the North Atlantic Treaty Organization, Japan, Australia and New Zealand.

In military jargon, Cosmos 954 was "de-orbiting": spinning closer and closer to earth with a potentially lethal nuclear cargo.

The problem, military officials said yesterday, was that despite the computer's ability to forecast a possible reentry route for the satellite, no one could tell pricesly where it would go once it struck the relative density of the Earth's atmosphere.

The officials compared the situation to that of a stone hurled into a calm lake. Sometimes the stone skips across the water and sometimes it follows its original trajectory and goes straight down.

"We knew where it was going to land at 6:53 a.m. a when it hit the atmosphere," said a Pentagon spokesman. "Before that it could have gone anywhere in the world."

The Canadian Ministry of Defense, which is part of NORAD, was offered two choices spelling out the dimensions of the problem. The renegade satellite, the Cauadians were told, might hit in the far north of their country - or it might come down in the South Atlantic.

Brzezinski said yesterday that the White House was notified of the problem by U.S. intelligence officials in late December. Other senior officials said, however, that at the time U.S. intelligence specialists were still hoping that the Russians had a fail-safe device on board Cosmos 954 that would hurl it off into space if the problem couldn't be corrected.

That hope was dashed Jan. 6 when the satellite became "sharply depresurized." U.S. experts, by then tracking the craft closely saw the inevitable fate of Cosmos 954.

"What they (the Russians) were saying was that it had stopped working and they were no longer in control," a U.S. official said.

Brzezinski and a small committee of top administration officials began meeting almost daily after that in the Executive Office Building office of Benjamin Huberman, a National Security Council staff member designated to head the group. Analysts told them the risk to life from the satellite crashing to earth was "negligible."

Brzezinski, meanwhile, began communicating with Soviet Ambassador Anatolly Dobrynin. On Jan. 12, he said, he sent Dobrynin a message expressing the President's concern that "if the debris fell near a populated area there could be a serious hazard to the public."

The Soviets responded through Dobrynin two days later in a reply that Brzezinski described as "somewhat reassuring but not fully satisfactory."

Brzezinski sent another message asking for reassurance that if the satellite came down it would not cause a nuclear explosion. That information, he said, was conveyed by Dobrynin Jan. 19.

With that, U.S. and Canadian officials began to count down to the satellite's re-entry and prepare for possible nuclear contamination problems. White HOuse officials notified a number of friendly nations of the problem and briefed several congressional leaders.

"The real wonder is that it never leaked," said a White House official yesterday.

Just before the sun came up yesterday seven U.S. planes loaded with radiation decontamination equipment were standing by at air bases around the country - including one C-141 at Andrews Air Force Base. The Canadians had additional 22-man "nuclear accident standby crews" waiting as the satellite came streaking closer.

By 6:57 it was all over.The "Space Age difficulty" ended up as a spectacular celestial show for the handful of those around to watch. In Yellowknife, 850 miles north of the U.S. border, Canadians unaware of what was happening gaped at the rain of fireballs sweeping across the sky as the satellite disintegrated.

"All of the pieces were bigger than shooting stars," said Marie Runman, on her way to work in the predawn darkness. "As it was disappearing the main piece turned bright red," she marveled. "It was just fantastic."