Abortion. Physician-assisted suicide. Gay rights. How will the Supreme Court handle those issues without Justice Sandra Day O'Connor, the centrist swing voter who announced her retirement from the court last week after a 24-year tenure?

Actually, it probably won't take long to find out. The abortion rights of teenagers, administration efforts to override a state right-to-die law, and the military's "don't ask, don't tell" policy are all on the docket for the court term that begins Oct. 3.

O'Connor's past opinions show that she would have played a pivotal role in these cases. Now, their outcome may hinge on the views of her successor. Learning those views may prove challenging to senators, if a nominee adheres to the practice of not answering questions about matters that are, or soon will be, before the court.

"One of the fascinating dances in the confirmation process is going to be how much you can get a nominee to answer, even about relatively recent precedents, when the issues are presented in cases that are pending on the docket," said Douglas W. Kmiec, a professor of constitutional law at Pepperdine University.

The retirement of O'Connor, who often cast the deciding vote in the court's cases, could portend great change at the court, especially if President Bush replaces her with a steadfastly conservative nominee, as many expect.

If O'Connor's career teaches anything, it is that a justice's initial votes on the court are not necessarily a reliable guide to what that justice will do in the course of a long, life-tenured career. In her first years, she leaned heavily against abortion and affirmative action, only to tack in the other direction later.

Even if O'Connor were replaced by a conservative opponent of Roe v. Wade, the 1973 ruling recognizing a right to abortion, Roe would still have the support of a five-justice majority. Any challenge to its core holding would take years to bubble up from lower courts.

Still, next term will present O'Connor's successor with a chance to answer important questions about the scope of Roe as well as other precedents.

For example, a 1992 Supreme Court decision, co-written by O'Connor, set forth a test for the constitutionality of state abortion regulations, saying they must not impose an "undue burden" on exercising the right to abortion.

The court defined an undue burden as a law that "in a large fraction of cases" puts a "substantial obstacle" in the way of someone seeking an abortion.

At the same time, the court has said that states may pass laws requiring minors to notify their parents of plans to terminate a pregnancy, as long as they permit minors to seek a court's permission when informing their parents is impossible or dangerous.

The court has never clarified whether O'Connor's "undue burden" test means that parental-notification laws, which are on the books in 33 states, must include an explicit exception for cases in which the pregnant girl's health is at risk.

But in Ayotte v. Planned Parenthood, No. 04-1144, which is to be argued in December and decided by mid-2006, the court will rule on a New Hampshire law that has no health exception. The U.S. Court of Appeals for the 1st Circuit, based in Boston, ruled last year that the New Hampshire law is unconstitutional and cannot go into effect.

In its appeal, however, New Hampshire said the 1st Circuit applied the wrong legal standard. It cited a 1987 Supreme Court ruling that suggests opponents of the law must show that the law would limit abortion rights not just in some or most cases but in all cases.

If the justices affirm the ruling of the 1st Circuit, striking down the law, the effect will be to fortify and entrench Supreme Court precedents on abortion rights. If the court rules in favor of New Hampshire law, it will open the door to other states to adopt similar legislation.

Any elucidation of the court's view of its doctrine of a health exception could also affect the federal ban on the procedure critics call "partial birth" abortion. Enacted by Congress with Bush's support in 2003, it included no exception to protect the woman's health. But three district courts have found it unconstitutional under a 5 to 4 Supreme Court ruling in 2000, joined by O'Connor, that said such bans must include a health exception.

The government's appeals are pending, and conflicting decisions by appeals courts could lead to a Supreme Court case in the early years of O'Connor's successor.

In October, physician-assisted suicide will be before the court in Gonzales v. Oregon, No. 04-623. The administration has appealed a lower court's order barring the Justice Department from taking away the prescribing rights of Oregon doctors who prescribe lethal doses of drugs to terminally ill patients who have chosen to die under that state's 11-year-old Death With Dignity Act.

Assisted suicide is an intensely emotional issue, both for advocates of a "right to die," who see it as many people's only means of a dignified death, and for conservative Christians, who see it as a form of murder.

Opposition to laws such as Oregon's was a favorite cause of former attorney general John D. Ashcroft, who issued a November 2001 directive determining that assisting suicide is not a "legitimate medical purpose" under federal drug-control law -- and that the Drug Enforcement Administration could act against any physician who authorized drugs to help someone die.

The directive overturned a 1998 decision by President Bill Clinton's attorney general, Janet Reno, that permitted Oregon doctors to assist in suicides.

Strictly speaking, the case does not involve any assertion of a constitutionally protected right to die. The court unanimously refused to recognize such a right in 1997, ruling that it should be left to the states to determine whether legalized assisted suicide is wise policy.

Rather, the case is framed by the parties as a clash between federal power to regulate drugs and states' power to regulate the practice of medicine.

But the practical effect of the Ashcroft directive is to make Oregon's law a dead letter -- and O'Connor might have been sympathetic to Oregon. She vigorously dissented from the court's 6 to 3 ruling last month in which it upheld a federal override of California's medical marijuana law. In the 1997 case, Washington v. Glucksberg, the court was ruling on state bans on assisted suicide. O'Connor was one of five justices who wrote or signed concurring opinions implying that they might not strike down a state law such as the Oregon one that permits assisted suicide.

"Death will be different for each of us," she wrote. "For many the last days will be spent in physical pain . . . some will seek medication to alleviate that pain and other symptoms."

In Rumsfeld v. FAIR, No. 04-1152, to be argued in November, the question is whether some law schools may curb military recruiters' access to their students in protest of the U.S. armed forces' ban on openly gay members.

The court is being asked to rule on the constitutionality of the Solomon Amendment, a federal law that requires universities to give military recruiters equal access or risk millions of dollars in federal funding.

Legal analysts generally expect a win for the government, but the case will create a high-profile forum in which both opponents and supporters of the "don't ask, don't tell" policy can fight out this particular battle of the culture wars.

Justice Sandra Day O'Connor probably would have played a key role in three upcoming cases.