They'll be testing techniques to repair damaged heat shield tiles in orbit.
Tiles damaged by insulating foam falling from the external fuel tank is what doomed Columbia and brought shuttle flights to a screeching halt.
Astronauts began their day with the song 'I Believe I Can Fly,' sung by high school seniors Brianna Payne and Jeffrey Slater. Payne is the goddaughter of astronaut Stephanie Wilson.
Tuesday aboard Discovery, three words rang out, capturing what a beleaguered space community is finally feeling after the problem-plagued Columbia years:
"We're back, baby!"
Astronaut Scott Kelly, down on Earth, telephoned his twin brother up in space, Discovery pilot Mark Kelly, with that assessment.
Several outside space experts and astronauts agree.
Legendary Apollo era spaceflight chief Gene Kranz gave the highest praise possible in space circles: "They've demonstrated 'the right stuff' in addressing this mission."
NASA's top managers won't take a bow until Discovery is safely on the ground Monday, but day-to-day officials are clearly pleased.
"We're going in the right direction," Discovery lead flight controller Tony Ceccacci said. "It's time to get going and start building the station."
Experts say Discovery's performance allows the shuttle program to return to its old job before Columbia shattered in pieces on its return in 2003, killing seven astronauts. NASA's mission is to finish building the international space station with a flurry of 15 more shuttle flights.
And it has made the chance of a 16th flight, to fix and upgrade the aging Hubble Space Telescope, far more likely, NASA officials have said.
Kranz, whose "failure is not an option" speech during the Apollo 13 crisis was immortalized in books and movies, said, "I look forward toward reopening of this space frontier and getting onto completion of the international space station and then get on to the moon and Mars. I think we're on track."
Two quick facts show how far Discovery has taken the space shuttle program:
But in the current mission, the largest chunk of foam that shed off the tank weighed less than one ounce - about 30 times less the Columbia fatal foam - and was the size of a sheet of legal paper. And that one piece of foam broke into six smaller pieces and came off at a time when it wouldn't have had the speed to cause any damage.
Once a spacewalk on Wednesday morning does further tests on heat shield repair techniques, then NASA will have met all the requirements for continued regular shuttle missions set by the Columbia Accident Investigation Board, Ceccacci said.
"They have incorporated the spirit of our recommendations quite effectively," said accident board member John Logsdon, director of the Space Policy Institute at George Washington University. "The shuttle is a less risky vehicle than we were flying at the time of the Columbia accident. That was our plan... We can go back to where we were before Columbia, where the next mission is a space shuttle assembly mission."
And 220 miles above Earth, Discovery astronaut Piers Sellers had the same feeling.
Sellers said Discovery's mission accomplished two needed priorities: Avoid big problems and get the space station ready for more construction. Sellers, in a Monday interview with USA Today, talked about re-establishing a line of success in the shuttle program:
"The line will be drawn where it was rubbed out before Columbia," said Sellers, who on Wednesday will spacewalk for 6½ hours to test heat shield repair techniques. "We would start again with the next mission and continue assembly. I think we're there now. We repaired equipment that will allow the assembly to continue. Two-for-two."
American University public policy professor Howard McCurdy, who has written several books about NASA, credited the space agency's chief, Michael Griffin, for much of the success.
"The old Apollo culture was really coming through," said McCurdy who has been following the mission.
"They're probably at a better place than they were before Columbia," said W. Henry Lambright, director of the Science and Technology Program at Syracuse University. That's because NASA is far more safety-conscious, and for the first time in decades has a new goal and mission: Send people back to the moon and on to Mars.
That goal makes a big difference in the way NASA works, said Sean O'Keefe, who was NASA administrator when Columbia broke apart and is now chancellor at Louisiana State University: "It's an opportunity to really focus your attention on goals and outcomes rather than endlessly debating what those goals should be.
"This has been a very, very long difficult challenging road," O'Keefe said. The success of the last two flights, he said, forms the "opening chapter of the next saga of what exploration is all about."