Bill Ingalls / NASA

A commemorative wreath adorns a monument to the crew of the shuttle Columbia at Arlington National Cemetery in Virginia on Friday, the 10th anniversary of the shuttle's destruction and the astronauts' deaths.

President Barack Obama and NASA's leaders paid a 10th-anniversary tribute to the space shuttle Columbia's fallen astronauts on Friday — and pledged that the lessons learned would be applied to future space odysseys, including eventual trips to Mars.

"As we undertake the next generation of discovery, today we pause to remember those who paid the ultimate sacrifice on the journey of exploration," Obama said in a statement released by NASA. "Right now we are working to fulfill their highest aspirations by pursuing a path in space never seen before, one that will eventually put Americans on Mars."

The shuttle Columbia's catastrophic breakup on Feb. 1, 2003, killed seven astronauts, forced a two-year grounding of the three remaining space shuttles and led to stepped-up safety measures at the space agency. The disaster also led Obama's predecessor, President George W. Bush, to plan for the retirement of the shuttle fleet once construction of the International Space Station was complete. The last shuttle mission flew eight years later, in 2011.

Bush's space vision called for a new generation of vehicles to be built for trips back to the moon by 2020 — but Obama shifted the focus of exploration to a near-Earth asteroid in the mid-2020s, with trips to Mars and its moons starting in the mid-2030s.

'We will never forget'
In his own 10th-anniversary statement, NASA Administrator Charles Bolden said the sacrifices made by the crew of Columbia's last mission will inspire future explorers.

"We will never forget these astronauts, nor all those who have lost their lives carrying out our missions of exploration — the STS-51L Challenger crew; the Apollo 1 crew; Mike Adams, the first in-flight fatality of the space program as he piloted the X-15 No. 3 on a research flight," Bolden said in an agency statement. "These explorers, and their families, have our deepest respect. We work every day to honor and build on their legacy and create the best space program in the world — to infuse it with the life and vitality that they worked so hard to achieve."

Bill Ingalls / NASA

NASA Administrator Charles Bolden looks on as Apollo 11 moonwalker Buzz Aldrin gives a salute during a wreath-laying ceremony at Arlington National Cemetery on Friday. The ceremony paid tribute to astronauts who died in the Apollo 1 fire of 1967 as well as the 1986 Challenger explosion and the 2003 Columbia tragedy.

Slideshow:

Retrace the final, tragic flight of the space shuttle Columbia, from its launch to its catastrophic end on Feb. 1, 2003.

Launch slideshow

On Friday morning, Bolden laid a wreath in honor of the agency's fallen astronauts at Arlington National Cemetery in Virginia, where monuments to the Columbia and Challenger crews have been erected. Earlier in the week, he attended a spaceflight conference held in Israel to honor Ilan Ramon, that country's first astronaut, who died in the Columbia tragedy. The other victims included Columbia commander Rick Husband, William McCool, Michael Anderson, David Brown, Kalpana Chawla and Laurel Clark.

Memorial ceremonies also were conducted in Texas, where the Columbia wreckage fell to earth, and at Kennedy Space Center's visitor complex in Florida. The focal point of the Florida ceremony was the Space Mirror Memorial, which bears the names of NASA fliers who died in the line of duty.

Roots of the tragedy
At that ceremony, Bill Gerstenmaier, NASA's associate administrator for human exploration and operations, acknowledged that the roots of the Columbia disaster went "all the way back to the first shuttle launch in 1981." Even then, NASA knew that ice and pieces of foam insulation could fly off the shuttle's external fuel tank and strike the orbiter — but the fact that no severe damage was done "reinforced the idea that all was well," Gerstenmaier said.

That view changed dramatically when Columbia was felled. Investigators determined that the leading edge of Columbia's left wing was fatally damaged by a piece of flying foam during launch, setting the stage for the breakup 16 days later during atmospheric re-entry. NASA was reminded that "even small problems can surface as major failures," Gerstenmaier said.

"Ten years ago, it would have been easy to pull back from the frontier of space, and say it was too risky to pursue," he said. "Instead, we dedicated ourselves to improving how we pushed the boundaries of space exploration, and we vowed to continue with our eyes open. We cannot be afraid of risk, and we cannot be ignorant of it, either. Our lasting tribute to those we have lost is to carry on with the cause that they believed was worth the ultimate sacrifice."

Other speakers at the Florida ceremony included Evelyn Husband-Thompson, the widow of Columbia's commander, who has since remarried. She recalled how she and other family members anticipated the return of their loved ones on that fateful Saturday morning 10 years ago, only to be jolted into a nightmare of "fear, uncertainty and horror."

NASA

Evelyn Husband-Thompson, the widow of Columbia commander Rick Husband, speaks at a memorial ceremony conducted Friday at the Space Mirror Memorial at Kennedy Space Center's visitor complex.

"The grief journey has been difficult, complicated and surprising," she said. Over the past decade, she has drawn comfort from her friends, her family and her faith. She noted that the Columbia crew's legacy includes educational initiatives, scholarships, museum exhibits, and even the name of the airport near her home in Texas: Rick Husband Amarillo International Airport.

"Just as a forest fire reduces beautiful foliage to ashes, those ashes ultimately become nourishment for new, healthy growth," Husband-Thompson said. "There are indeed small, green shoots of hope that are springing up in our lives."

More about Columbia:

• 10 years later, Columbia's loss still stings
• Shuttle tragedies serve as warnings to NASA
• 10 myths surrounding the Columbia tragedy
• NASA celebrates its fallen astronauts
• Film finds uplifting story amid Columbia's loss

Alan Boyle is NBCNews.com's science editor. Connect with the Cosmic Log community by "liking" the log's Facebook page, following @b0yle on Twitter and adding the Cosmic Log page to your Google+ presence. To keep up with Cosmic Log as well as NBCNews.com's other stories about science and space, sign up for the Tech & Science newsletter, delivered to your email in-box every weekday. You can also check out "The Case for Pluto," my book about the controversial dwarf planet and the search for new worlds.

"Space Shuttle Columbia: Mission of Hope" puts a fresh spin on the 10-year-old story, turning the tragic loss of Columbia and its crew into an uplifting tale of the human spirit. How does the hourlong TV documentary, premiering Thursday night on PBS stations, pull that off? By focusing on one of the Columbia tragedy's casualties, Israeli astronaut Ilan Ramon — and his connections to an even bigger tragedy, the Nazi Holocaust.

The tale's crucial pivot point is a miniature Jewish Torah scroll that was treasured by a survivor of the Bergen-Belsen concentration camp in Germany: Ramon brought the scroll with him on the ill-fated mission, as a symbol of endurance. Even though the scroll was lost in the Columbia's catastrophic breakup in the skies over Texas on Feb. 1, 2003, its symbolism endures, thanks to "Mission of Hope."

"The film is not about the Columbia accident," director Daniel Cohen told NBC News. "The film is about a journey of hope. When I first started making the film, I thought I was making a documentary about the Holocaust. Then I peeled back the top layers and started to look inside, and I said, 'Wait a minute — there's a lot going on inside the story.'"

Let's start with the sacred scroll: During a death-camp bar mitzvah, the scroll was given to a teenager named Joachim "Yoya" Joseph at Bergen-Belsen by the chief rabbi of Amsterdam, a fellow prisoner at the camp. The rabbi didn't survive, but Joseph did, and the Torah held a place of honor in Joseph's office when he grew up to become an Israeli space scientist.

Ramon, a decorated Israeli combat pilot, also had a Holocaust connection. His mother was a survivor of the Auschwitz concentration camp. But his connection with Joseph came in a different context: After Ramon's selection to be Israel's first astronaut, he worked with Joseph on an experiment to analyze the distribution of airborne dust over the Mediterranean and Middle East regions. Ramon noticed the scroll in Joseph's office, and asked if he could take it with him on his spaceflight. 

Joseph's experiment flew on Columbia — and so did his scroll. During one of the mission's downlinks, Ramon showed off the palm-sized treasure and told Joseph's story. "This Torah scroll was given by a rabbi to a young, scared, thin, 13-year-old boy in Bergen-Belsen," Ramon said. "It represents more than anything the ability of the Jewish people to survive. It represents their ability to go from black days, from periods of darkness, to reach periods of hope and faith in the future."

West Street Productions / Herzog

A scene from "Space Shuttle Columbia: Mission of Hope" shows Israeli astronaut Ilan Ramon walking to Columbia's launch-pad entryway.

NASA via West Street / Herzog

Israeli astronaut Ilan Ramon holds up a miniature Torah scroll during Columbia's final mission in 2003, as fellow astronaut Laurel Clark and mission commander Rick Husband look on.

Unfortunately, Feb. 1, 2003, was a black day. The shuttle broke up into pieces during its descent, killing Ramon and the rest of Columbia's crew: Rick Husband, William McCool, Mike Anderson, Laurel Clark, Kalpana Chawla and David Brown. Investigators determined that a piece of foam insulation that flew off Columbia's fuel tank did undetected damage to the leading edge of Columbia's left wing during launch. Sixteen days after liftoff, as the mission was ending, the hot gases of atmospheric re-entry blasted through the breach and destroyed the shuttle from the inside.

Ramon's remains were recovered and returned to Israel. Searchers even recovered the diary that he kept during the flight. But Joseph's little Torah scroll was never found. Cohen, a self-avowed space nut, said he followed the Columbia coverage closely — and took notice of a news item "buried in the back of the newspaper about this little Torah scroll that Ilan carried with him."

"I thought, wow, what a powerful new way to tell a Holocaust story to a new generation," Cohen said. He got in touch with Joseph, and over the course of several years, the filmmaker pieced together the story.

Joseph appears in the movie, although he passed away during post-production and never saw the finished product. "Mission of Hope" also draws upon interviews with Ramon's widow, Rona, as well as with Israeli investigators and former Prime Minister Shimon Peres. Candid footage of the Columbia crew's training, shot by Brown, adds a personal touch to the work.

"The overriding message of the Columbia crew ... is what they brought to each other because of their diverse background," Cohen said. "They brought the magic of diversity to each other, yet woven through that is this story of the Holocaust and this terrible tragedy."

As he gathered the footage and the interviews, Cohen struggled with a problem: He wanted to focus on the message of hope, but it seemed as if the final chapter of the story was filled with loss and despair. "The dilemma was, how do you end this film?" he said.

Then he heard that another miniature Torah scroll had surfaced, in the possession of Henry Fenichel, another survivor of the Bergen-Belsen death camp who became a physics professor in Cincinnati. Fenichel was willing to have the scroll flown aboard another space shuttle flight, at the request of Rona Ramon and under the care of Canadian astronaut Steve MacLean.

"I thought, you just ended my film for me," Cohen said.

The "Atlantis Torah" flew aboard the shuttle Atlantis in 2006, on the first space station assembly mission planned in the wake of the Columbia tragedy. "It goes from the depths of despair to the heights of hope," MacLean told reporters.

More than six decades earlier, when Joseph received his "Columbia Torah," the rabbi who gave it to him asked the boy to promise he'd tell the story of the scroll if he survived.

"Now our documentary continues the promise," Cohen said. "Woven into that is our mission to tell the story of Columbia's crew and their missions. On the 10th anniversary, we will all pause and remember the horror of the moment, a searing moment in history. But at the same time, we'll remember who these people were, and what they brought to us."

More about the Columbia tragedy:

• Columbia remembered, 10 years after launch
• Special report on the shuttle Columbia's loss
• Flash interactive: NASA's Day of Remembrance

This should be the saddest week of the year for NASA — which is marking the anniversaries of three fatal tragedies, including the 10th anniversary of the shuttle Columbia's catastrophic breakup. But the way NASA Administrator Charles Bolden sees it, this week is not just about mourning 17 dead astronauts.

"I think this is not a memorial. It's a celebration, because of what they made possible," he told NBC News this month during a visit to Seattle. "We're commemorating them, and we're thanking them by continuing to move forward — and not dropping back and dwelling on the pain. They'd be pretty angry, I think, if they saw that."

The week of celebration — and, yes, of commemoration — begins on Sunday with the 46th anniversary of the 1967 Apollo 1 launch-pad fire. The 27th anniversary of the 1986 Challenger explosion follows on Monday. This year, NASA is focusing the most on Friday, the 10th anniversary of the Columbia tragedy, which has been set aside as the agency's "Day of Remembrance" for all of its fallen astronauts.

Ever since the loss of Columbia and its crew of seven, NASA has organized solemn commemorations during the last week of January.

"We honor the memory of all three crews that were lost over the history of human spaceflight," Bolden explained. "We thought it was fitting that it be somewhere around the dates of those three losses. We think about this every day, to be quite honest. But we take these particular times and set them aside, when we can let everyone else around the world join us and help celebrate."

There's that word again.

"I use the term 'celebrate' because we have to remember that, yeah, we lost some valiant people — but what their sacrifice brought is what we should really be thinking about: the fact that they dared to challenge and do things differently," Bolden said. "Because of what they did, we're well on the cusp of going deeper into space than we've ever gone before."

Each tragedy took a terrible toll — and in each case, NASA learned from its mistakes:

Apollo 1's three astronauts were Gus Grissom, one of the Mercury 7 pioneers; Ed White, the first American to do a spacewalk; and rookie spaceflier Roger Chaffee. They died during a pre-launch test at the launch pad when bad wiring sparked a blaze in the pure-oxygen environment inside their sealed capsule. After the fire, engineers overhauled the wiring system, switched over to a less flammable oxygen-nitrogen mix and redesigned the hatch to open outward instead of inward. Years later, Apollo 11 commander Neil Armstrong observed that the accident provided "the gift of time" — a chance to change a lot of things for the better. "We got that added benefit, but we regret the price we had to pay," Armstrong said.

Challenger's crew of seven was led by commander Dick Scobee, but the best-known flier was Christa McAuliffe, who was tapped to be the first teacher in space. The other astronauts were Michael Smith, Ellison Onizuka, Judith Resnik, Ron McNair and Greg Jarvis. Their space shuttle blew up 73 seconds after launch, due to a bad seal on one of the solid rocket boosters. The investigation led to a redesign of the boosters, which worked without fail ever since. It also pointed up the problem of "go fever," which led NASA to give the go-ahead for launch amid dangerously low temperatures. Reforms in management procedures gave astronauts, engineers and contractors more of a role in ensuring launch safety. 

Columbia's crew included Israel's first astronaut, Ilan Ramon, as well as commander Rick Husband, David Brown, Laurel Clark, Michael Anderson, Kalpana Chawla and William McCool. The shuttle broke up over Texas during its descent at the end of a 16-day science mission. Investigators concluded that flying foam insulation from the external fuel tank damaged the left wing during launch, setting the stage for the Feb. 1 tragedy. The fuel tank was redesigned, emergency rescue plans were updated, and an array of cameras was added to the shuttle to watch for damage. The investigators also pointed to lapses in NASA's "safety culture." The George W. Bush administration followed up on the investigative panel's recommendations and decided to close down the space shuttle program once construction of the International Space Station was complete. That day finally came on July 21, 2011, with the landing of the space shuttle Atlantis.

Bolden said the successful operation of the space station and the rise of a new generation of commercial space vehicles would not have been possible if it weren't for the sacrifices made by the fallen astronauts. Rather than shutting down America's space program, political leaders gave the go-ahead for more ambitious plans to go beyond Earth orbit, and ultimately to Mars.

"If we didn't have that coming along, then what would have been the point of losing them?" Bolden said. 

To recognize those sacrifices, Bolden will attend a space conference being conducted in Ramon's honor this week in Israel, and then will return to Washington in time for Friday's wreath-laying ceremony at Arlington National Cemetery. NASA's space centers are planning commemorations as well: Officials at Johnson Space Center will participate in memorial events in Texas on Thursday and Friday. Kennedy Space Center's ceremony is scheduled for 10 a.m. ET Friday at the visitor center's Space Mirror Memorial. That Florida observance is open to the public and will be broadcast on NASA TV.

Stay tuned for more about NASA's week of sad celebration in the days ahead — and feel free to add your own reminiscences and tributes as comments below.

More about NASA's space tragedies:

• Apollo 1's tale retold: 'Fire in the cockpit!'
• The chilling saga of the shuttle Challenger
• Columbia remembered, 10 years after launch
• Flash interactive: NASA's Day of Remembrance

Alan Boyle is NBCNews.com's science editor. Connect with the Cosmic Log community by "liking" the log's Facebook page, following @b0yle on Twitter and adding the Cosmic Log page to your Google+ presence. To keep up with Cosmic Log as well as NBCNews.com's other stories about science and space, sign up for the Tech & Science newsletter, delivered to your email in-box every weekday. You can also check out "The Case for Pluto," my book about the controversial dwarf planet and the search for new worlds.