As Washington and Moscow pirouette over the possibility of talks on space weaponry, attention focuses on the man who will have a key voice in what the Soviet Politburo does next. The man is Andrei A. Gromyko.
Because the Soviet foreign minister of more than 25 years is the most knowledgeable and experienced of the present Soviet leaders in the foreign policy field, diplomatic experts here believe his input will weigh heavily as the Soviets decide how to respond to President Reagan's position on starting space-weapon talks.
Reagan has accepted the Soviet offer to begin such talks but insists the United States will also raise the sensitive issue of nuclear arms, whether the Soviet negotiators listen or not. Soviet Ambassador Anatoly F. Dobrynin returned to Moscow this week bearing a message from Mr. Reagan and Secretary of State George P. Shultz. At this writing, the ball is in Moscow's court.
''Gromyko is obviously the most authoritative in the leadership in foreign policy,'' says Mark Garrison, a former US diplomat who served in Moscow. ''He must be playing an important role simply by process of elimination. He is suddenly important because other people have left the scene.''
''He is the dominant figure,'' says former national-security adviser Zbigniew Brzezinski. ''He has established authority in foreign policy and is asserting it. I'm struck by the extent to which he does the talking in meetings between (Konstantin U.) Chernenko and foreign leaders.''
But experts agree that the dour-faced Mr. Gromyko cannot and does not run the show in Moscow. He has no political base in the party, the military, or the KGB. His authority stems from the fact that none of the senior Politburo leaders have been outside Eastern Europe. Gromyko alone knows the territory and the details of decades of diplomatic history.
''He's the vicar but not the pope,'' says a senior administration official. ''He's a member of a collective leadership with the portfolio of foreign policy. He has to clear any general policy with the others because such a policy cuts across jurisdictional lines - defense, resource allocation, the economy, internal security. He is required to have the clearance of others.''
''There's no question his is the major voice inside the inner councils,'' comments Malcolm Toon, a former US ambassador to Moscow. ''But I wouldn't attribute Moscow's present hard-line policy to his ascendancy. He speaks for the collective.''
American officials say the Politburo has more vitality than generally thought following the death of Yuri P. Andropov. While Chernenko is said to have a number of health problems, he is nonetheless involved in Politburo business. ''They're not taking new initiatives, but they are taking decisions,'' says an administration expert. Since Chernenko came in, he adds, the Politburo has reversed Andropov's decisions on economic reform and the dismissal of party and government officials. It has also continued to increase defense expenditures.
Nor is it thought that Mr. Gromyko, for all his vast experience, has an entirely successful track record in steering Soviet foreign policy. Soviet pressuring of the West Germans to oppose NATO deployment of medium-range nuclear missiles, for instance, is widely seen as a miscalculation. It merely heightened the determination of most European governments to go ahead with the move.
''Gromyko is not all that smart,'' Dr. Brzezinski says. ''He was tempered in the past. Now he has overplayed his hand. He has screwed up Soviet relations with China, the Europeans, Japan, and the US. Soviet relations are bad with all, so he is not an example of diplomatic skill.''
Even Moscow's handling of the space weapons issue is viewed as clumsy. By not responding quickly and favorably to the President's acceptance of space-arms talks, some experts say, the Soviets have given back to Reagan the propaganda advantage.
Mr. Gromyko and his colleagues are in a bind, experts say. If they have any concern about the long-term future of US-Soviet relations, they have to give the impression that they are not totally unreasonable and are prepared to negotiate. On the other hand, they do not want to give the impression that Reagan can be safely elected for another four years.
The Soviet offer to negotiate on space weapons is thus an effort to cope with the long-term need to deal with the US (including the need to know what its intentions are) and the short-term desire not to help Reagan politically. Many observers here believe that Moscow was surprised by the President's acceptance of its offer.
Some experts say that the Soviet leadership is still trying to puzzle out a US President who early on harshly castigated the Russians and later reversed course, adopting a more conciliatory posture - a tactical change dictated by pressures from Congress and European allies and the need to deprive the Democrats of a peace issue in the November.
Whatever Foreign Minister Gromyko counsels his fellow Politburo members, experts say, he will be guided principally by Moscow's long-term goal of maximizing its security and its influence and standing in the world.
''Gromyko has seen a lot of American policy changes,'' says Mr. Garrison, director of Brown University's Center for Foreign Policy Development. ''He figures that in the long run a consistent Soviet policy will achieve its purpose while US policy swings back and forth. But he is concerned that such swings will lead to confrontation. He probably figures that the way to avoid this is to be strong and tough rather than respond to the swings.''