Two astronauts are stuck in space. Here’s how they’re passing the time.

“This time we might have…too little time to be able to do a marathon," she said at a press briefing in March.

As it turned out, Williams may have time after all. Williams and her fellow astronaut, Barry Wilmore, are caught in the middle of a debate within the National Aeronautics and Space Administration over whether Boeing’s Starliner vehicle, which took them to the ISS, is safe enough to bring them back.

What was expected to be a roughly one-week mission has turned into a summer in space, with their stay possibly lasting until early next year. Boeing has said it is confident Starliner is up to the task of transporting the astronauts home.

Williams and Wilmore arrived at the space station in early June with limited luggage and duties. Since then, the two have immersed themselves in day-to-day routines and research 250 miles above the Earth’s surface: studying microbes, microgravity jogs, tinkering with equipment and taking in some of the 16 sunrises and sunsets visible each 24-hour period.

“We’ve been thoroughly busy up here," Williams said during a short news conference in July, the last time she and Wilmore have spoken publicly. Tasks she highlighted included gene-sequencing work, an experiment involving a “moon microscope" and replacing a pump for a system that converts astronaut urine into water.

Last week Wilmore spent time inspecting plumbing hardware and more recently installed a light meter in “Veggie," a planting project where astronauts have grown radishes and other crops. Williams set up high-definition video gear.

Other activities have ranged from taking microbe samples collected from ISS water systems to deep-cleaning a station module and studying optical-fiber manufacturing, NASA said.

The Starliner astronauts are used to curveballs, and risk-taking is on their résumés. Before blasting into orbit this year, Wilmore and Williams had flown test missions of military jets and helicopters, deployed overseas for the Navy and launched to the ISS on both U.S. and Russian spacecraft.

‘Her happy place’

Williams, 58 years old, was born near Cleveland and got her start flying for the Navy. She was selected to join the Naval Test Pilot School and has flown more than 30 aircraft. Known as Suni, she was picked for NASA’s astronaut corps more than two decades ago.

Wilmore, who goes by Butch, grew up in Tennessee, where he still lives with his family. Before joining NASA he was a Navy test pilot, logging thousands of flight hours. Now 61, he became a NASA astronaut in 2000, and first flew to the space station nine years later.

The astronauts’ test-pilot tenures made them naturals for June’s Starliner mission, aimed at demonstrating the Boeing-built vehicle was ready to start regularly transporting astronauts. For Boeing, which had struggled for years with technical setbacks and cost overruns on the program, the mission was a long-in-the-making moment.

But Starliner’s propulsion system hit snags before it docked with the facility. A handful of thrusters that maneuver the spacecraft temporarily failed, and several helium leaks emerged. Since then, NASA and Boeing have been debating whether Starliner can safely bring Williams and Wilmore back home.

This week, NASA said the pair might wind up staying in space until 2025, though no decision has been made. An even-longer posting would happen if the agency taps SpaceX to bring them back, on a return trip the Elon Musk-led company is scheduled to conduct for NASA in February.

Officials at the agency and company have said that the astronauts aren’t stranded or stuck onboard the space station, and in the event of an emergency, could head back to Earth on Starliner.

“This is just the life that we live," Wilmore said in an interview in March, when asked about preparing for moments during the flight when something might go wrong. An effort to reach Wilmore and Williams for comment over email wasn’t successful.

Williams’s husband, Michael, said Thursday that he didn’t think she was disappointed to wind up spending more time at the space station.

“That’s her happy place," he said.

Clothes left behind

Upon arriving at what Wilmore called the “big city in the sky," the astronauts delivered a pump for the system that converts urine into potable water. To make space for the part, Williams and Wilmore had to leave behind some clothing and personal-hygiene items.

“They’ll just use our generic supplies that we have," Dana Weigel, the NASA space station program manager, said before the launch. “We keep a certain contingency supply on board."

The more than 20-year-old space station—which travels about 17,500 miles an hour—consists of a series of connected modules that stretch about the length of a football field. It is run by an international consortium that includes Russia and Europe, and besides Williams and Wilmore, there are seven other crew members on board.

Astronauts typically rotate on and off over six-month periods. In addition to scientific investigations and maintenance, they conduct public outreach, such as live video question-and-answer sessions with students.

To stave off bone and muscle loss, astronauts exercise at least a couple of hours a day. Doctors on the ground have also taken readings of both Williams and Wilmore’s veins, with the pair taking turns scanning each other’s necks, shoulders and legs.

Rest and sleep periods usually run about eight hours, though everyone is always on call. Crew members can talk with family members and send email.

Food arrives during regular cargo trips to the facility. In April, NASA officials said the station also keeps at least four months of food and other items stowed on board for contingencies. Most of what astronauts eat comes out of dehydrated packets, but some fresh items make their way onto ISS, too.

An uncrewed Northrop Grumman cargo ship connected with the station Tuesday, carrying 8,200 pounds of supplies, including coffee, grapefruit and blueberries, as well as scientific devices. Wilmore spent time Friday helping unpack some of the recent haul.

“It’s a great place to be, a great place to live, a great place to work," he said during last month’s news conference.

Write to Micah Maidenberg at micah.maidenberg@wsj.com