To the bizarre sound of a cricketlike beeping radio that some Americans said could open remote-controlled garage doors (remember?) and others feared presaged more woundrous and sinister developments, the Soviet Union 20 years ago Tuesday opened the space age with the launch into earth orbit of a 184-pound silvery globe called Sputnik 1.

There were millions of us in America and much of the rest of the world who gathered on chill nights in the weeks after the Oct. 4, 1957, launch to see if we could catch a glimpse of this little harbinger of a new, unsettling era. In doing so, we were helping to fulfil one of the continuing goals of the Kremlin's space program - we were awed by the Soviet Union's achievement.

The Sputnik mission set off a search for nationhood in the United States even as it seemed to confirm it in the Soviet Union. The American search ended, in a symbolic and real sense as well, when an astronaut bearing the Stars and Stripes on his silvery sleeve stepped onto the moon 8 1/2 years ago. For the U.S.S.R. however, the certainty of power and purpose that Sputnik seemed to confer at the expense of the envied West has never quite materialized out of the void on space.

Instead, the Soviet Union has had 20 years of glory and travail that find it now immeasurably more powerful because of its space prowess, but still unfulfilled and with no clear goal, no dreamed-of conquest to fire the national imagination the way the Sputnik did, or later, when a Russian became the first human to orbit the world.

Ask any Soviet citizen above the age of 24 and each can tell you exactly where they were and what they were doing when they heard the news that a Soviet satellite was in orbit.

The next question is: What about Gagarin? and you are met with a hurt look, an old injury. Yuri Gagarin, the photogenic cosmonaut who first orbited the earth, died in a plane crash in 1968. He was a real hero," is the answer.

And what about the moon? That question elicits a shrug of the shoulders.

"What about it?" answered one Muskovite. "You got there first."

The Soviet space program, like the American one, grew out of the military's interest in perfecting long-range rockets to carry explosives far-beyond the front lines of a battlefield - or a nation's frontiers. The Soviets had used small rockets on their Western front during World War II and, like the Americans, had captured some German V-2 scientists and German rockets during the final collapse of the Third Reich. In the mid-1950s, as the military men were gaining both range and accuracy in their successor rockets to the German machines, space beckoned strongly.

The nonmilitary programs, began to be talked about publicly in both countries. The Soviets decided to make one of their early intercontinental ballistics rockets the mainstay launch vehicle for their "civilian" program. This rocket, now know to Western analysts as the A-2, became their prime launch vehicle, and it still is today.

Relatively cheap to produce in quantity, with its test program behind it, this missile seemed ideal. In the early years of the space competition, it was more than enough to startle the world. The list of Soviet space firsts from those years is impressive:

Sputnik I was orbited Oct. 4, 1957, and followed just a month later by Sputnik II, which carried a live dog, Laika. A few months later, while the Americans were scrambling to recover and some of their rockets were fizzling on the launch pads in the glare of embarrassing world interest, the Soviets orbited a true geophysical observatory, capable of sophisticated (for those days) analysis of magnetic fields and other arcane factors. In September, 1958, the Soviets landed the first payload from the earth on the moon and a month later, in a complex feat, photographed the back side of the moon never before seen by humans.

Then, on April 12, 1961, the Soviet Union sent cosmonaut Gagarin around the world for one orbit and recovered him. His flight electrified the world, coming as it did months before the U.S. Mercury manned flights. A few months later, Gherman Titov orbited 17 times, far longer than anything planned for the first few U.S. flights. When President Kennedy proclaimed a race to the moon against the Soviets the outcome seemed nearly preordained: The U.S.S.R. had already made impressive headway.

At the same time, there were flaws. While the Americans moved to successively bigger and more sophisticated rocket launchers for their vehicles, the Soviets stuck with their tried and true rockets. As the U.S. computer capacity grew, it far outstripped that of the Soviets, who soon were having trouble achieving the complex maneuvers in deep space required to send payloads to Venus or Mars. According to one reference work, the Soviets failed six times in 1965 and 1966 to get a payload to Venus.

In 1967, just after a catastrophic fire in an Apollo spacecraft killed three American astronauts during a ground test, the Soviets lost their first cosmonaut, who died when the parachute of a new manned vehicle, the Soyuz, failed to open on reentry. The Soyuz had been intended as the Soviet mooncraft.

The Soviet program to build a big moon rocket to power their mission began to fall behind. While the United States was perfecting the giant Saturn V booster to send three men to the moon, the Soviet program was bogging down. In a report to the Senate two years ago, American space experts suggested that the failure of the Soviets' big booster was a major factor in their losing the race to the moon.

When the Eagle lunar lander settled on the moon in July, 1969, the Soviets still were sending unmanned Soyuz spacecraft around the moon then retrieving them in a series of complex automatic re-entry maneuvers.

With the moon race over, the United States and Soviet Union began cooperating in space in several areas. The most spectacular project was the 1975 Soyuz-Apollo space rendezvous and linkup when an American and Soviet joint mission docked and orbited together for two days. That mission is still hailed here as an important event, and a fullscale reproduction of the docked spacecraft is about to open at the Moscow exhibition grounds.

U.S. experts who participated in the Soyuz-Apollo project came away dismayed by the crudeness of Soviet space hardware. One American expert, discussing the Soyuz craft in a recent interview, compared it unceremoniouly to a "hot water radiator in your home. It works, but that's about all you can say for it." The authoritative aviation weekly, Aerospace Weekly, after interviewing many Americans in the Soyuz-Apollo project, rated the Soviet spacecraft as technically on a level with the Mercury capsule, the first U.S. manned spacecraft.

"Their scientists man for man are every bit as good as ours," an American physicist visiting here this week said, "but the technical gap is still huge." And yet, the United States has found it useful and rewarding to cooperate with the Soviets in space.

In the early 1970s, the United States abandoned its space medicine research program. The Soviets have continued and broadened theirs. Recently, the Soviets launched and recovered a "biosatellite" containing rats, fruit flies and other living organisms after subjecting them to many days in space. Scientists of the U.S. National Aeronautics and Space Administration flew to Moscow and retrieved their portion of the cargo for study: the vital organs of half the rat crew.

There is also cooperation in calibration of space instruments and exchanging samples of lunar material. So far the United States has given the Soviets nine samples to the Soviets' six. The two countries also collaborate on reaching agreement on exchange of information regarding earth resources satellites, and on a possibly revolutionary system of satellites that could locate with pinpoint accuracy the positions of ships or aircraft in trouble.

One U.S. source admitted that the Soviets had things to teach their American counterparts.

"We discovered that their Soyuz space suits were less flammable than ours," he said.

The Soyuz spacecraft suffered one more catastrophe in 1971, when three crew members returning from 22 days in a space station were killed in an accidental venting of the cabin atmosphere just as the craft started its descent. The three were wearing overalls, because there is not room for three fully spacesuited men in the Soyuz. Since then, the Soyuz has taken only two-member crews, who have worn their full pressure space suits during takeoff and re-entry.

Soviet space stations, 20-ton cylindrical craft with huge solar panel "wings" to turn sunlight into electrical power, have been in use since 1971. The Soviet Union last week launched No. 6 in its series, and it seems likely that the station soon will be visited by a crew.

Customarily, the Soviets have sent several missions to the Salyuts for up to 48 days at a time. One Soviet team stayed aboard for 63 days, but apparently cut the visit short when they became emotionally fatigued. The Salyuts are left in space for months at a time, visited occasionally and then destroyed by a fiery re-entry in the atmosphere.

There have been various failures to dock between some Soyuz and Salyut stations, and Western observers believe that at least two endurance missions were cut short when the crews began to have psychological problems. The space endurance record so far is an American one: 84 days by the crew of a Skylab.

Unlike the American space program, which has been marked by shifts and changes of direction and only now is beginning to revive with the first few flights tests of a space shuttle, the Soviet program has continued doggedly onward. This is partly because of the closed nature of the system here. There are no citizens groups of congressional critics to question the need for a manned space program. While there is competition within the bureaucracy for limited resources not unlike the competition that exists within the U.S. bureaucracy, the lack of public debate allows managers luxuries of continuity not available to their counterparts in a democracy.

"Look, these guys are in space for good," one Western source said recently. "They've had problems, but so have we. And eventually, they may solve their technical difficulties and be able to fulfill all the promises they make and the hopes they have. I admire them for that."

The Russians trace their impulse to explore beyond the atmosphere to a bewhiskered inventor and theorist named Konstantin Tsiolkovsky, who was born and lived here in Kaluga. During the last years of the Czars, Tsiolkovsky began to cast his intellect away from the earth toward the solar system and beyond. Like Jules Verne, his inspiration, Tsiolkovsky foresaw an era of space travel with rockets, space colonies and interplanetary travel. There is a museum of the space age here, and his home is preserved as a National monument. He was admired by Lenin who granted him a pension in 1921 after he had labored in obscurity under the Czar.

Here in the quiet of a midweek afternoon, a traveler can look long at the strange shapes and bizarre creations of the scientists and technicians that mark the movement of man into space - from the tracings in notebooks of visionaries like Tsiolkovsky to such machines as a Mars lander or a capsule burnt black that once carried a frail human safely from the void back to earth.

There is no hint here, nor is there much hint in the much bigger space museum on the Mall in Washington, of the sinister side to this age that dawned 20 years ago. Men rode into space on the broad backs of military rockets. Military spy satellites of both superpowers observe each other's defenses and, peculiarly, arms limitation efforts rest largely on what those space spies report of the development and deployment of intercontinental ballistics missiles, their technological cousins.

Statistics are available that define this relationship more precisely. These numbers tell us that of 99 Soviet space missions in 1976, at least 81 were military in nature. One U.S. defense industry publication asserts that of 1,042 Soviet space missions logged from 1957 to 1975, 613 were military and 429 civilian. The United States, which has launched about 800 missions in the same period, shows a similar breakdown.

The exploration of space and the mastery of the technology to do so have brought increased might to this already mighty nation, just as it has for the United States. Space exploration is firmly woven into the popular culture by the controlled media, and you can find squares or streets named after cosmonauts, plaques, monuments, and books of all sorts about these stirring conquests.

Gagarin was truly a great hero, a man universally admired and respected as being a good person, a non-controversial man who brought glory to his motherland. His broad smile graces thousands of publications and he is spoken of in tones of longing by many.

Something he said from space still echoes in my head with a wistful simplicity that explains why I and some others of my generation were fascinated and even moved by the early years of the space age. Gagarin, the first man to stare down from the empty void outside the earth's protective envelope of air, contemplated the blues and greens moving beneath his rudimentary capsule and couldn't restrain his delight: "how beautiful is our earth."