Updated 9:58 a.m., May 25

Space is just a click away Friday morning.

The next step in that historic private space mission that began this week has just occured. The space capsule Dragon successfully docked with the International Space Station just before 10 a.m. Friday. This is part of the SpaceX private exploration launch, as media reports have detailed.

And you can watch the completion of the docking, courtesy of live streaming from space relayed by Mashable.com.

Docking manuevers have already started, and the ISS’ robotic arm is expected to grab hold of Dragon at 9 a.m. EDT. Full berthing is expected two hours later, according to Mashable.com.

Following a successful docking, the astronauts aboard the ISS will open the Dragon’s hatch the next day and unload the supplies the spacecraft is carrying.

Early Tuesday, a commercial rocket blasted off from Cape Canaveral, Fla., and was bound for a rendezvous with the International Space Station, as several media outlets noted.

It's the first time a private company -- in this case, SpaceX -- has launched a vessel to the space station. That's something only major governments have done — until the present test flight, USA Today noted.

Already Friday, live streaming has captured the capsule approaching the ISS, as well as shots from the mission control center.

At 6 a.m. Friday, the capsule was about 240 miles above earth, and west of Portugal, according to the live stream narration.