Houston, Febuary 12,2000 (UPI) -- When NASA's asteroid probe arrives at the asteroid Eros on Valentine's Day, it will be due to one of the most complex and difficult flight plans ever followed by any space vehicle. The incredible difficulty of matching orbits with the asteroid was matched only by the human imagination that solved it.

Classic "cook book" solutions of "aim and shoot" had been good enough to send probes to the Moon, Mars, Venus and to Jupiter and beyond. But they weren"t efficient enough to make this mission possible. New routes through space had to be invented.

If one man can be credited with inventing them, it's Robert Farquhar, 67. He's now the program manager for the NEAR mission, the "Near Earth Asteroid Rendezvous" craft that reaches Eros on Monday. But for decades at work on other projects, he invented unique flight plans that made earlier interplanetary missions possible.

"The man is a genius with celestial pinball," his colleague Don Yeomans told a writer for "Wired" magazine last year. "And he^Òd be the first to admit it."

Almost all previous interplanetary targets have been objects which circle the Sun in the same orbital plane as Earth. Experts compare this to being limited to only reach goals on one floor of a multi-storied building.

Asteroids and comets, however, usually follow orbits that are strongly tilted to this plane of the planets. They only intersect this plane at two points, and then with very high crossing speeds. In the analogy of the multi-story building, such objects are like elevators passing through the floor. If you need to reach one, you have to be at the elevator shaft at exactly the right moment.

This is how a fleet of Earth space probes intercepted Halley's Comet in 1986. The comet was the first object on a different plane that probes had been aimed at. Two Russian probes, one European probe, and a Japanese probe maneuvered through the inner Solar system to the spot where the comet would "fall through" the level of the other planets.

But Farquhar had beaten them to it. He had originally designed on orbit for a small solar storm lookout probe, hanging in space between the Earth and the Sun. When NASA decided to "pass" on a Halley"s Comet mission, Farquhar dreamed up a new flight plan for this solar probe. This permitted it to reach another comet a few months before the other Earth probes reached Halley's.

This success, and NASA's new interest in low-cost missions, led to the approval of a new proposal from Farquhar to actually put a probe into orbit around an asteroid. Compared to just flying past an object as it quickly passes through the planetary plane, an orbiter would have to actually chase down its target. "It's a lot harder to match orbits," Farquhar told UPI.

The first target was an asteroid called Anteros, but when schedule problems made that goal impossible, they switched their aim to another small asteroid named Nereus. "That was a pretty lame mission," Farquhar admitted to UPI. Both Anteros and Nereus were tiny bodies, about 1 kilometer (about half a mile) in diameter. "We were going to get pretty bored after a few months at that little pebble" he said.

Farquhar then turned his attention to the larger and more famous asteroid, Eros. Its vaguely brick-like shape was known from radar and telescopic measurements. It was a much more interesting target. But Eros was in a different orbital plane than Earth, like a target in that multi-story building that was on a different floor. There was a ten degree tilt between the orbits of Earth and Eros. Because of that tilt, an object departing from Earth into the asteroid's orbital plane would need a very powerful sharp turn from Earth's normal motion.

In practical terms, this meant launching a small probe on a giant Titan rocket from California, instead of a more affordable Delta rocket from Cape Canaveral. It would have to head nearly due south and to achieve speeds normally needed only for missions headed for Jupiter or beyond. The asteroid mission did not have the budget for such an expensive rocket.

Farquhar conceived of a different method to obtain such speeds at such a great tilt to Earth's orbit. He would still launch the probe on a small rocket from Cape Canaveral. But then he would guide it out into space and back to Earth, where Earth's gravity would twist and push the probe onto the path that would take it to Eros.

Using this so-called "gravity assist" technique has been a tool for interplanetary navigation since the early 1970s. Probes have been directed past Venus to reach Mercury, and past Jupiter to reach Saturn. They have even looped around the Sun to return to Earth to generate an even more powerful slingshot effect towards their ultimate goal.

Space navigators explain that a space probe's speed is just the sum of the target planet's speed around the sun, plus the speed of the probe relative to the target planet. It's like drawing a line on a watch dial from the tip of the hour hand to the tip of the minute hand, to represent the sum of the two speeds.

The gravity assist technique works because flying past a planet bends the probe's motion through space. It^Òs like moving the minute hand on the watch, while keeping the hour hand the same. Even though neither hand changes length, the length of the line between their two ends can get longer or shorter, depending on the angle between the two hands.

In the same way, a probe passing a planet can have its direction and speed changed by passing through the planet's gravity field. If it picks up some speed, the encounter will slow down the planet by a proportional amount. The difference in size of the probe and the planet is so large that the effect on the planet is too small to notice.

Farquhar sent the NEAR probe far out into the asteroid belt, where it then turned back towards Earth. But instead of allowing it to swing back and overtake Earth on a parallel path, Farquhar planned a strong rocket maneuver to slow down the probe. On this new path, it fell inwards towards Earth and would have crossed its orbit heading even closer to the Sun. That crossing would have been at a fairly sharp angle.

Farquhar timed the probe's crossing of Earth's orbit to occur just as Earth was at that point. As a result, Earth's gravity could twist the probe's orbit into an entirely new shape. And by design, after passing Earth, the probe wound up right on the path that would have required the large rocket to launch due south.

"That's an old trick", he told UPI. But his combination of such old tricks made the mission possible. The probe's mating dance through space was made even more complicated when it missed its first date with Eros in December 1998 due to a rocket misfiring. Farquhar and his staff had designed many emergency alternate plans to swing around for a second pass at Eros, and after that first problem, they implemented one of them.

This long-awaiting tryst in space is the probe's last opportunity, and so far everything has been working properly. "It's a very historic mission," Farquhar points out. "It's only the sixth time that a probe has orbited a celestial body for the first time. "With this success," Farquhar added, "it evens the score at three 'firsts' for the Russians and three for the US."

As with most unimaginably difficult space missions, this one was made possible first in somebody's imagination. If it becomes real, it will be first and foremost a tribute to Robert Farquhar's imagination.