Mikhail S. Gorbachev arrived at the United Nations this week with precisely the message people across the globe most wanted to hear from a man with his finger on the button: it's time to stop using military might to settle political disputes - nobody's omnipotent.

Even in his hurried departure from the United States, Gorbachev was showing a face of Kremlin leadership that stood in stark contrast to the shoe-waving visit of the last Soviet leader to visit the United Nations.Addressing diplomats who know well that he is wrestling with difficult choices between guns and butter, Gorbachev on Wednesday delivered a poignant call for peaceful coexistence punctuated with a theatrical announcement of Red Army troop reductions.

"Our people want to live in peace with the American people," he said at one point. Later, sightseeing in Manhattan, he remarked, "We're very pleased by the fact that thousands of New Yorkers have come out to see us. We saw their faces, we saw their eyes, their friendliness."

All in all, quite different from the 1960 visit of Nikita Khrushchev.

It was Khrushchev who took off his shoe, waved it around and then pounded it on his desk in anger. He was unhappy when a speaker had referred to Eastern Europe as nations which "have been swallowed up, more or less, by the Soviet Union."

Gorbachev was polished and polite, making friends from his arrival on - but never so many as with his declaration on unilateral troop reductions. Even his sudden departure demonstrated a fresh character of Soviet leadership: Gorbachev was returning home to cope with a devastating earthquake had killed thousands in the Soviet Caucasus region.

"Despite the fact that all emergency measures are being taken . . . Mr. Gorbachev believes when the people are suffering he has to be there, he has to lead the efforts," the Soviet foreign minister said late last night.

Gorbachev left behind him a troop-reduction timetable that many experts had expected last spring as a welcome-to-Moscow gesture toward President Reagan. The American view, clearly, was better late than never, and officials applauded Gorbachev's call at the United Nations for less reliance on military force.

The commander of armaments as ferocious as any in history told the United Nations that the days were over when military force "can or must be an instrument of foreign policy."

It may well come as a surprise to students of history - students of Chile's humiliation of Bolivia and Peru in the War of the Pacific, for example, or of Genghis Khan's mastery of the "feigned retreat" in establishing the Mongol empire - that force is not the only way to settle disputes.

In a world besot with thermonuclear arms, where the next war could be the last, the world thirsts for another way.

The internal problems of the Soviet Union have apparently prompted the Politburo to seek another way as well.

"It is now quite clear that building up military power makes no country omnipotent," Gorbachev said. Tacitly acknowledging the realities of a sputtering economy at home, he added, "What's more, one-sided reliance on military power ultimately weakens other components of national security."

He said the Soviet Union will reorganize Soviet divisions in Eastern Europe so they are "clearly defensive." He said it plans to cut soldiers and armaments in the European part of his country and in its Asian territory. In Mongolia, for instance, "a major portion of Soviet troops temporarily stationed there will return home" - words that are sure to gain favor with Khan's ancestors and the communist leaders of China.