It was the first time anyone had seen the orbiting observatory up close in seven years.
"Hubble has arrived on board Atlantis," commander Scott Altman said.
"It's great to be back with the telescope," replied Mission Control.
Robot arm operator Megan McArthur used the 50-foot boom to seize the school bus-sized telescope as the two spacecraft sailed 350 miles above Australia.
Altman fired thrusters onboard Atlantis to gently approach the telescope and crewmate Greg
Johnson used a steady to steer the shuttle for the final few yards - a delicate dance that took place while traveling five miles, or 85 football fields, every second, reports CBS News science and technology correspondent Daniel Sieberg.
"They're using a radar gun to measure the speed and distance between the shuttle and the telescope," said CBS News space analyst Bill Harwood. "It's a remarkable procedure. They make it look easy but it's quite complicated."
With the telescope safely in hand and launch debris concerns put to rest, the astronauts and flight controllers turned their attention to the upcoming repair work.
Late Tuesday, the astronauts learned the ugly stretch of nicks on Atlantis' thermal tiles were not considered serious, and no further inspections were needed. NASA is continuing to prep another shuttle, though, just in case a piece of space junk hits the shuttle during the mission.
Hubble's unusually high orbit is strewn with smashed satellite pieces and other debris that could pierce the shuttle or suit of a spacewalking astronaut.
Going into the mission, Hubble scientists and managers warned that Hubble might look a little ragged; it hasn't had a tuneup since 2002. But initial observations showed nothing major.
"It's an unbelievably beautiful sight," said John Grunsfeld, the telescope's chief repairman. "Amazingly, the exterior of Hubble, an old man of 19 years in space, still looks in fantastic shape."
Beginning Thursday, two teams of spacewalking astronauts - two men per team - will take turns venturing outside to replace the 19-year-old Hubble's batteries and gyroscopes, and an old camera and pointing mechanism. They also will install fresh thermal covers on the telescope and a new science data-control unit - the original conked out last September and, although revived, delayed the shuttle flight by seven months.
Tomorrow's task is to install a new camera about the size of a grand piano and 30 times more powerful than the old one, Sieberg reports. The new camera is so strong that scientists should be able to look back more than 13 billion years ago to when galaxies were just starting to form.
"With the new camera on the telescope, they're hoping to push back the frontier to within a few hundred million years of the big bang that started it all, to find out exactly how those galaxies started," Harwood said.
The space repairmen also will go into the guts of two broken science instruments and attempt to fix the fried electronics. Astronauts have never attempted anything like this before at Hubble.
"Everybody's very excited up here, I can tell you," said Grunsfeld, who's making his third visit to Hubble.
This is the fifth and final flight to Hubble, costing NASA just over $1 billion. The space agency hopes to get another five to 10 years of dazzling views of the cosmos, with all the planned upgrades, which should leave the observatory more powerful than ever.
The mission almost didn't happen.
A year after the 2003 Columbia tragedy, NASA canceled the repair effort, saying it was too dangerous. The astronauts would not have anywhere to seek shelter because the international space station is in a different, inaccessible orbit.
But a new NASA regime reinstated the flight in 2006 after shuttle repair techniques were developed and tested in orbit. A plan also was put in place to have a rescue shuttle on the launch pad to blast off within days for a rescue.
That shuttle, the Endeavour, will remain on standby until Atlantis and its crew of seven head back to Earth late next week.
As for the nicks on Atlantis, they stretch over 21 inches on the right wing, on the forward edge where it joins with the fuselage. The astronauts discovered the damage Tuesday while inspecting their ship.
The nicks are shallow and embedded in thick thermal tiles, in a location that is not particularly vulnerable during re-entry at flight's end. Engineers believe those scrapes were caused by debris that came off the fuel tank 1½ minutes after liftoff Monday.
Sieberg reports that a far more serious debris strike on a very sensitive part of the wing is what crippled Columbia's heat shield in 2003, causing it to break up during re-entry. All seven astronauts onboard were killed.
Columbia's left wing was punctured, along a vulnerable edge and at the time NASA managers ignored an engineer's request for more photos of potential damage. NASA said the nicks on Atlantis are in a less sensitive location.
NASA managers initially said they wanted to spend Tuesday night and Wednesday looking at photos of the damage to see if a more detailed inspection of the tiles would be needed on Friday. But just before astronauts went to sleep, Mission Control told them that the examination with Atlantis' robot arm was not required.
Even before damage was discovered, NASA was preparing shuttle Endeavour to rush to the astronauts' rescue if needed. Nothing so far has been found that would require a rescue.
Unlike other space flights, the astronauts cannot reach the international space station because it is in a different orbit to the telescope.
Earlier Wednesday, the astronauts (and Earth-bound technophiles) celebrated the first Twitter message, or tweet, sent from space.
Astronaut Mike Massimino, checking in as AstroMike, said "Launch was awesome!!" and reported he's feeling great and working hard.
Before Monday's liftoff of space shuttle Atlantis to the Hubble Space Telescope, Massimino posted regular updates on his training to the micro-blogging site.
Now, the 46-year-old from Long Island, New York tweets that he's enjoying the magnificent views from space, adding "the adventure of a lifetime has begun!"
Massimino has said he'll send Twitter updates as time allows during his busy schedule in orbit. He's set to do two of the five spacewalks to repair and upgrade the telescope.
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