Burt Rutan, the aerospace pioneer, and Paul Allen, Microsoft's co-founder, hope that SpaceShipOne will fly 100km up to where the blackness of space meets the blue line of the atmosphere.
In doing so they hope to take the first steps to breaking a government monopoly on space travel and introducing trips into space for the masses.
The pilot of the rocket will be named on Sunday. The journey will begin at about 6:30am (13:30 GMT) at Edwards Air Force Base, California, in the middle of the Mojave Desert.
The White Knight
A jet mothership, known as The White Knight, will be launched and initially carry the rocket underneath its belly for an hour, soaring up to 15,450m.
White Knight will then release SpaceShipOne, which weighs less than three tonnes.
The hybrid liquid and combustible solid-powered engine will then fire for 80 seconds taking the rocket up to about 50km at a speed of more than 3500km an hour.
SpaceShipOne will glide up to about 103km, where it is likely to lose momentum and fall back to Earth.
During this time, the pilot will feel weightlessness as do astronauts in space. The zero gravity effect, lasting three minutes, will continue until SpaceShipOne returns to about 60km from Earth.
The pilot will gradually retake control and from 25km altitude, the craft will glide for 17 minutes back to a landing at the base at between 10:30am and 11:30am (17:30-18:30 GMT).
The design of this prototype, decorated with blue stars, will make re-entry easier because the aircraft will be able to fold its wings, reducing resistance and allowing the air to propel it down like a badminton shuttle, says Rutan, whose company, Scaled Composites, designed the spaceship.
The characteristics of this suborbital flight reduce the risks at takeoff and reentry, as illustrated in both the 1986 Challenger and 2003 Columbia catastrophes.
If the SpaceShipOne flight is
successful, a repeat is likely
In 1986 Rutan engineered the US Voyager, the first aircraft to travel around the world without refuelling.
For this ambitious challenge, Rutan charmed Allen, who was smitten with space, astronomy and science fiction, and has spent about $20 million on the project.
If SpaceShipOne is successful, its organisers predict that they will do launch again in 15 days with three people aboard.
Scaled Composites is one of 20 teams convinced that there is a future in space tourism, and who are vying to win a $10million competition to be the first to privately finance and carry three people 100km into the sky, safely return and then do it again within two weeks.
But profit is not one of the immediate objectives of Rutan and Allen. They say their main aim is to end the government's monopoly on space exploration and put it within the reach of all those who can pay.
Plans so far are to charge $100 a flight in the first years of business and then eventually lower the fare to $10 with the arrival of other spaceships planned for 2010.
"Our programme involves a few, dedicated individuals who are focused entirely on making spaceflight affordable"
"Since Yuri Gagarin and Al Shepard's epic flights in 1961, all space missions have been flown only under large, expensive government efforts," Rutan said.
"By contrast, our programme involves a few, dedicated individuals who are focused entirely on making spaceflight affordable."
Rutan said that without an entrepreneurial approach "space access would continue to be out of reach for ordinary citizens. The SpaceShipOne flights will change all that and encourage others to usher in a new, low-cost era in space travel."