On Wednesday, once Endeavour was safely past the 73-second mark of the flight, the moment when Challenger exploded, Mission Control exclaimed that Morgan - McAuliffe's backup for Challenger - was "racing toward space on the wings of a legacy."
Click here to see photos of Endeavour starts mission to space station
Immediately after the shuttle reached orbit, Mission Control announced: "For Barbara Morgan and her crewmates, class is in session."
Morgan and the shuttle crew woke up Thursday to Russell Watson's "Where My Heart Will Take Me" and prepared for a busy day of checking for possible damage from debris shaken loose during the launch.
Shortly after the crew awoke Thursday, Morgan worked inside the shuttle's cockpit alongside other astronauts.
An alarm involving an instrumentation glitch on an oxygen tank briefly awoke the astronauts overnight, but NASA officials did not think it was serious and said they would try to fix it Thursday.
Endeavour was scheduled to dock with the space station on Friday afternoon.
Midway through the flight, Morgan will speak with students in Idaho, where she taught elementary classes before moving to Houston in 1998 to become the first teacher to train as a full-fledged astronaut. If the mission is extended from 11 days to 14 days as planned, thanks to a new station-to-shuttle power converter, she will also have a chance to answer questions from students in Virginia and Massachusetts.
But Morgan's primary responsibility in orbit will involve helping to operate Endeavour's robot arm and overseeing the transfer of cargo from the shuttle to the station.
The rest of the crew will be busy installing a huge square-shaped beam to the exterior of the station and replacing a broken gyroscope. Three spacewalks are planned; a fourth is possible.
Late Wednesday, Morgan, 55, was all-business as she periodically updated Mission Control on the activation of the shuttle's cargo-carrying module.
The remarks from the Pope came as "a very strong step towards degradation," "given the rather massive nature of homosexuality" among the Catholic clergy.