When the 113 cardinals file into Michelangelo's Sistine Chapel two weeks from now to elect the 262d successor to the Apostle Peter, they will apply nearly eight centuries of papal electoral rites to global social law and political problems as new and complex as the Roman Catholic Church has ever known.

More so, perhaps, than in any other time in recent history, the Sacred College of Cardinals is not nominated by a few forceful personalities and will be to focus on the basic question of where the Vatican is headed in a troubled and rapidly changing world.

Preferences for certain individuals will surface over the next two weeks as the cardinals hobnob together in seminaries scattered through Rome and lobby one another for various papabili , or leading candidates to succeed Pope Paul VI, who died Aug. 6 following a heart attack.

As in lay politics from Chicago's South Side wards to the backrooms of Parisian party local headquarters, factions will be tested again and again, until a choice is made.

Yet Vatican experts of various ideological presuasions agree that as the conclave approaches, speculation about names and personalities is less relevant than larger questions such as decentralization of the church, ecumenism, world poverty and over-population, human rights and the church's controversial policy of reaching out to Eastern Europe's Communist governments.

Having resolved those formidable - almost cosmic - questions, the cardinals can then assess the field of papabili and decide who can move the church in that direction for the last quarter of the 20th century.

Pope Paul's 15-year papacy was, in effect, an extension of the reign of Pope John XXIII, and was characterized by his attempts to implement the changes devised by Pope John and the Vatican II ecumenical council.

What the Sacred College has to decide behind the locked doors of the Sistine Chapel - as thousands wait in St. Peter's Square for the traditional signal of white smoke proclaiming a new Pope - is whether the Vatican will lead the world's 600 million Catholics in the same philosophical direction as Pope John and Pope Paul, or whether it will return to the more rigid, conservative ideology of Pope Pius XII.

Because of the gravity of that question, and because the Sacred College swelled under paul's papacy to a record 130 members, most Vatican experts predict a longer than usuall conclave of the 130 cardinals, 15 are ineligible to vote because they are over 80 years old, and two will not come to the Vatican because of illness.

Were it not for the larger number of cardinals and the ideological crossroads at which the church finds itself, modern history would suggest that the conclave will not last long. There has been no papal election this century that lasted longer than four days with Pope Pius XII being elected in 1939 in one day, and Pope John and Pope Paul in two days.

The longest conclave occured in the 13th century, when they nearly three years of waiting for the cardinals to pick a pope, angry townspeople in Viterbo tore off the roof of their meeting place and subjected the electors to cold rains. After two cardinals died and the rest faced starvation, the Sacred College finally elected Gregory X.

One obstacle they did not have which the 87th conclave must face is whether - for the first time since Pope Adrian VI of Holland was elected in 1522 - the church should have a non-Italian pope.

The most frequently mentioned papabili include three foreigners, Franz Koenig, archbishop of Vienna; Johann Cardinal Willebrands of Holland; Eduardo Cardinal Pironio of Argentina and Jean Cardinal Villot of France, the Vatican secretary of State under Pope Paul and chamberlain of the church. The leading Italians are Cardinals Sergio Pignedoli, Giovanni Benelli and Sebastiano Baggio.

As head of an international church - and, in a sense, a wider pluralism that includes all Christians - the pope has concerns larger than the ties that link Italy and the Vatican, and the election of an Italian is not expected to be a dominant consideration in the conclave.

Nonetheless, the Vatican has been attempting to maintain some temporal privileges for the Catholic Church in Italy in the face of an increasingly secular - and even anticlerical - shift by Italians as the nation has moved steadily to the left and close to communism.

During Pope Paul's papacy, Italy pulled further away from Vatican influence, passing and then upholding by referendum a divorce law and now pressing for major revisions in the Holy See's nearly 50-year-old concordat with the government, which created Vatican City as an independent sovereign state but limited the Papancy's once-vast territory to [WORD ILLEGIBLE] acres plus some extraterritorial buildings.

In exchange, Roman Catholicism was established as the state religion, Rome designated a "sacred city" and the government agreed to pay parish priests' salaries, as well as grant the church other special privileges.

With the Communist Party as Italy's second largest political movement, and a Marxist installed as Rome's mayor, the Vatican agreed informally to water down many of the concordat's provisions and further diminish its tem-

The Sacred College, therefore, will have to decide whether it wants a pope who will fight to retain church-state-ties, or accept the reality of an isolated Vatican in an increasingly secular Italy.

The cardinals will also have to decide how the church, should regard Eurocommunism, and whether it wants to follow the policies toward Eastern Europe purpsued by Pope John and dis diplomatic troubleshooter, Archbishop Agostino Casaroli.

"That's a controversial matter that will very much be in the hands of the new pope. Not everyone in the Vatican and outside thinks it is a good policy. It will be very difficult for many of them [the cardinals] to accept," said a Vatican official.

Under Pope John, the Vatican made numerous overtures to Eastern European countries to establish the viability of the church behind the Iron Curtain, and the pontiff angered many in the church by receiving Communist leaders.

Ostpolitik was Montini's [Pope Paul's] speciality. None of the cardinals has really had that much experience in it, except, perhaps, for Koenig. It will be interesting to see whether the new pope pulls back on a policy that has been established for a long time," said a Vatican official.

An even larger question confronting the cardinals is the Third World, and the role it will play in Vatican affairs.

In 1960, more than half the world's Catholics were in Europe and North America, with only scant representation in the emerging nations. By the end of this century, according to estimates, 70 percent of the world's Catholics will live in the Third World, and bishops from those countries are convinced that the next pope must be sensitive to particular problems of emerging nations, such as poverty, overpopulation, birth control, human rights and emerging socialism.

One Vatican official estimated that by the year 2000, more than half the world's Catholics will live in Latin America alone.

"They would be looking for someone who shows an awareness of what these people are talking about," he said.

Said Joseph Cardinal Cordeiro of Pakistan, "In this conclave the Third World will have substantial, if not decisive, weight."

Nevertheless, in spite of the growing claims of Third World Catholics, the Sacred College still has a majority of conservative cardinals, according to most Vatican analysts, one estimate offered here is that of the 115 eligible electors, 44 are conservatively oriented, 44 are classified as "moderates" and 27 are felt to be liberal or radical. poral power in Italy.

Yet, a Vatican source cautioned against putting too much stock in those breakdowns, saying. "You are dealing with people whose primary responsibility is pastoral affairs, and their ideology is not always known on every issue.

"You get many men who is some social questions can be fairly liberal, but on communism, say, they are staunchly conservative. Or some may be progressive on theological change, but resistive to social reform."

Moreover, he said, some cardinals live in relatively quiet areas of the world and rarely take public positions on controversial social issues.

"There are men there that I can't say if I know he has a deep liberal streak or deep conservative streak or not. It may be their own mothers don't know," he said.

But there is a growing feeling here among Vatican observors that the next pope will be a moderate upon whom both conservatives and liberals can agree, and who essentially will be similar to Pope Paul.

That choice will be made by the 113 members of the Sacred College during their deliberations in the Sistine Chapel, but not before many of the broader philosophical questions are thrashed out among the electors.