The U.S. Supreme Court reconvenes for its 2009-10 term on Oct. 5, with most of the attention going to the court’s freshest face, newly confirmed Justice Sonia Sotomayor. But Sotomayor and her eight colleagues won’t have a lot of time for orientation: the court will start immediately on a docket of controversial cases that will call on Justices to consider new facets of the Establishment Clause, gun ownership and prison terms for minors, among other issues. In total, the Justices have already agreed to hear 55 cases in the new term. Here are five to keep an eye on.

Salazar v. Buono
At issue: Whether the government can permit the display of a crucifix on public land as per the Establishment Clause.

An 8-ft.-tall crucifix has stood on an outcrop called Sunrise Rock on the Mojave National Preserve since 1934, but in one of the court’s earliest arguments of the term, the Justices will be asked to consider whether it should be removed. The battle has been brewing for a while — the cross, erected without government approval, was slated for removal by the U.S. National Park Service after a request from Buddhists to create their own memorial near the site was denied. But in 2000, Congress hastily passed a law prohibiting the use of public funds to remove the cross, in essence tying the National Park Service’s hands. Congress declared the cross a National Memorial in 2002, and in 2003 it gave the small parcel of land to the Veterans of Foreign Wars (VFW) — the group that constructed the original cross. (See TIME’s photo-essay “Sonia Sotomayor, the Making of a Judge.”)

The removal of the cross brings up the Establishment Clause, that long-debated line separating church and state that takes its name from the First Amendment (which begins, “Congress shall make no law respecting an establishment of religion”). This case has been in the court system since early 2000, before Congress’s involvement. The National Park Service’s attempt to transfer the land to the VFW, per the 2003 congressional order, has been viewed by the lower courts as an illegal way of circumventing repeated rulings compelling it to remove the cross. (Once the land is considered private property, the Establishment Clause no longer applies.) The Supreme Court will be asked to sort out the issue — and ownership of Sunrise Rock — once and for all.

Maryland v. Shatzer
At issue: The scope of the rights of police suspects, as given in the court’s landmark 1966 decision, Miranda v. Arizona.

In Maryland v. Shatzer, Michael Shatzer was questioned by police about sexual abuse of his 3-year-old child, and after being told he had the right to counsel as part of his Miranda rights, declined to answer any questions without an attorney present. The officer never pursued Shatzer further, but nearly three years later, a different detective questioned Shatzer, at which point he admitted abuse. Shatzer now argues this confession is inadmissible because the second police officer, who was unaware of Shatzer’s original Miranda request, questioned him without an attorney present. (Read “Four Enduring Myths About Supreme Court Nominees.”)

The court has already considered a similar case in 1981’s Edwards v. Arizona, in which the court found admissions made by a suspect without the presence of an attorney, which he had requested, inadmissible. But in Edwards, these admissions were made only a day after the suspect had been given his rights — not nearly three years later. The court will be asked to decide whether to treat their decision in Edwards as a so-called “bright-line” rule — that is, one that would create an absolute standard of police conduct in regard to the Miranda rights, regardless of how much time has passed.

Graham v. Florida / Sullivan v. Florida
At issue: Whether life imprisonment for juveniles on nonhomicide charges constitutes cruel and unusual punishment.

The Eighth Amendment precludes cruel and unusual punishment, but it has long been left to the Supreme Court to define exactly what that term means. This court will be asked to consider it again in a pair of cases on the docket. In Sullivan, the petitioner was 13 years old when he was indicted as an adult and sentenced to life in prison without parole in Florida for sexual assault of an elderly woman. In Graham, a 19-year-old violated his parole by committing attempted armed robbery while on parole for two previous robbery attempts he had committed while he was a minor. He too was subsequently sentenced to life in prison without the possibility of parole.

In making their decision, the court will review its logic in 2005’s Roper v. Simmons, which held that individuals could not be sentenced to death for crimes committed under the age of 18, as the court found that minors had a “lack of maturity.” The petitioners in Graham and Sullivan are arguing for a similar standard for their noncapital offenses.

National Rifle Association v. Chicago / McDonald v. Chicago
At issue: Second Amendment rights to gun ownership.

A pair of cases challenge Chicago’s 27-year-old ban on handgun sales within the city limits. Originally designed to curb violence in the city, the ban has long irked Second Amendment advocates, who take an expansive view of the amendment’s wording that the “right of the people to keep and bear arms shall not be infringed.” But the Supreme Court had long held that the Second Amendment pertained only to federal laws, until a 2008 decision in District of Columbia v. Heller struck down a ban on handguns in Washington, D.C. The ruling marked the first time the Supreme Court acknowledged an individual right to bear arms, and it opened the door for these challenges to the Chicago regulation.

American Needle v. National Football League
At issue: Whether sporting leagues should be exempt from antitrust regulations.

Experts say American Needle may turn out to be the most important legal decision in sporting history. The sportswear manufacturer contracted with NFL teams to produce hats and headgear with official team logos. But the NFL decided to give an exclusive leaguewide license to Reebok in 2000, leading American Needle to sue, claiming the NFL’s action violated the Sherman Antitrust Act by limiting the market for who could produce team-branded merchandise.

The fundamental question for the court to decide is whether the NFL should be considered a single entity or a collection of 32 individual businesses. The answer to this question has repercussions beyond the production of licensed merchandise. If the NFL is considered a single entity, it would largely be exempt from antitrust laws, giving the league not only continued right to grant exclusive licenses for team apparel but also the ability to make decisions on a leaguewide basis. This opens the door to the NFL — rather than individual teams — determining things like ticket prices and player salaries. Indeed, the bargaining power of the NFL Players Union is based on antitrust legislation that the league would largely be immune to if it receives a favorable ruling from the Supreme Court. Other sporting leagues are watching the American Needle case closely; many have filed briefs in favor of the NFL’s position.