NASA’s post-shuttle plans for ferrying cargo — and eventually crew — to the International Space Station rely on private industry to not only design and build the spaceships, but also to foot a substantial share of the costs.

The first company to successfully emerge from the process was California-based Space Exploration Technologies, or SpaceX, which so far has made a test fight and two supply runs to the station. SpaceX also is among three firms developing space taxis to fly station crew members under a related NASA program.

PHOTOS: Dragon’s Bounty: SpaceX Mission Complete

On Wednesday, a second firm, Orbital Sciences Corp., will attempt to follow SpaceX to the station’s door. Launch of Orbital Sciences’ Antares rocket and Cygnus cargo capsule is scheduled for 10:50 a.m. EDT from a commercial spaceport on Wallops Island, Va.

If the launch goes as planned, the Cygnus would reach the station on Sunday and remain attached to the outpost for about a month. Unlike SpaceX’s Dragon capsules, which return to Earth intact, Cygnus spacecraft are designed to burn up in the atmosphere during re-entry.

The mission marks the final milestone of a NASA program that began seven years ago and so far has cost the government $681.5 million. Orbital Sciences stands to collect another $2.5 million under the development program, and then turn its attention to regular resupply flights as part of a follow-on, $1.9 billion contract.

PHOTO: When Antares Delivered its Payload to Orbit

Like SpaceX, which has more than 40 other launches on its manifest for customers besides NASA, Orbital Sciences is looking to market its Antares rocket beyond the U.S. space agency. It also sees a future for Cygnus flying cargo to destinations beyond the space station, which flies about 250 miles above Earth.

“We know that there’s not 10 customers coming forward right now asking for cargo delivery to low-Earth orbit,” Orbital Sciences executive vice president Frank Culbertson told reporters during a prelaunch press conference.

“Right now there’s only one customer, but developing this capability for both us and SpaceX shows that you can have a commercial service that can keep something as complicated and as important as the space station going,” Culbertson said.

Image credit: NASA/Bill Ingalls