The mission, known as Near (Near-Earth Asteroid Rendezvous) is also a first in another respect for Nasa. Until now, the agency has had a reputation for doing things in the grand style, bigger and more expensive than anyone else. But Near is, in space terms, a cut-price mission - one of the new "Discovery" series, whose budgets have a ceiling of $150m (pounds 100m).
Near's objective is to map an asteroid known as Eros, whose large diameter and apparently varied surface make it an attractive target for planetary scientists. They believe that such bodies are remnants of the building blocks from which the planets were made 4.6 billion years ago.
Until Eros was discovered in 1898, all asteroids were thought to orbit the Sun in a broad belt between Mars and Jupiter. Now scientists reckon that many thousands of asteroids less than a kilometre in diameter pass close by our planet, most of them undetected. In addition, there are probably more than 1,000 objects that are larger than a kilometre across. Eros is one of them; and its path around the Sun occasionally crosses Earth's - though not, yet, at the same time.
But scientists worry that one day Earth's gravity might capture one of these extraterrestrial wanderers - bringing it crashing to the ground, where its effects could be catastrophic. This potential threat is driving astronomers to learn more about their numbers, orbits and composition, in preparation for the day when one of them is found to be on a collision course with Earth.
Our only knowledge of asteroids that approach Earth or cross its orbit comes from ground-based telescopic and radar observations. A great deal remains to be learned, and even the few "main belt" asteroids so far studied in any detail have yielded surprises. One of them, Ida, was found to have a tiny satellite. Several others seem to be peanut shaped, or possibly even consist of two asteroids that have somehow joined together and now orbit in unison.
Ground-based studies suggest that Eros rotates once every five and one quarter hours and is potato shaped, measuring 40km across at its widest point. Its "stony" composition seems to resemble most of the asteroids in the inner part of the main belt. At some time in the distant past, Eros must have been ejected from the main asteroid belt, possibly after passing too close to Jupiter, or colliding with another asteroid.
Reaching Eros will not be easy, since Near will be launched from Cape Canaveral by a relatively cheap, low-energy, Delta 2 rocket. The spacecraft will have to take a roundabout route that will carry it one and a half times around the Sun and bring it back to within 500km of Earth in January 1998. This will change the spacecraft's orbit and inclination to put it on course for a rendezvous with Eros, after a trip of 2 billion kilometres.
There will also be a close flyby of another asteroid en route to Eros. While studying Near's flight path, mission planners noticed there would be a rare opportunity to observe Mathilde, an unusual main belt asteroid that seems to be rich in carbon.
"It has only been seen a few times," says Dr Robert Farquhar, the mission manager, from Johns Hopkins University in Baltimore, Maryland. "It has a diameter of about 61km and is twice the size of any asteroid seen so far and 10 times more massive." Although Near should pass within 1,200km of Mathilde, observations will be difficult since the spacecraft has no movable scan platform.
After three years in flight, Near will begin its approach to Eros in January 1999. By firing the onboard motor, the spacecraft's speed relative to the asteroid should be reduced to about five metres per second. The first close pass will come on 6 February 1999, when Near will fly past the asteroid's sunlit side at a height of around 500km, enabling the first accurate determinations of its mass, rotation and surface features.
Over the next five weeks, the orbiter's altitude will gradually be lowered until it is skimming only 15km above the surface. At that height, there is the constant danger that local fluctuations in the gravity field will send Near spiralling down to oblivion on the asteroid's barren surface.
Scientists hope that the orbiter will spend at least nine months revealing Eros's secrets, using what Dr Farquhar refers to as "state-of-the-art instruments". These include an advanced camera system for mapping the entire surface at spatial resolutions of three to five metres, a laser altimeter for measuring surface relief, and instruments to measure the elemental and mineral composition of the asteroid. In addition, a magnetometer will search for the presence of even the weakest magnetic field.
By the end of the mission, we should know whether Eros is a pile of unconsolidated rubble or a solid, rigid body, perhaps with a metallic core. Many astronomers believe that its composition will resemble that of numerous meteorites which periodically fall to Earth. The US Air Force will be particularly interested in such details, since they could well determine the feasibility of using nuclear missiles to blow apart any asteroid that is found to be heading our way.
But the end of the Near mission will not be the end of such low-price missions. It will just be the first of the "faster, better, cheaper" planetary missions advocated by Nasa chief Dan Goldin after his appointment in 1992. Aware of the acute funding squeeze facing future exploration missions, Goldin has instructed his cohorts to find cost-effective ways of probing the planets.
The Discovery projects' $150m budget limit includes spacecraft development and launch costs. Furthermore, the spacecraft has to be ready for launch within three years of passing the selection panel. Near comes well within these criteria with a budget of $112m and a development time of just 26 months.
It will also be the first Nasa-funded mission in the Solar System in which the agency has surrendered responsibility to an outside organisation.
However, this is less risky than it sounds: Johns Hopkins University Applied Physics Laboratory, which designed the mission and built the Near spacecraft, has a long history of involvement in Earth-orbiting satellites.
Three more Discovery missions have already been accepted by Nasa. Next November, the Mars Pathfinder spacecraft will land and send back the first surface observations from Mars for 20 years. In 1997, the Lunar Observer will map the Moon and search for water ice. Then, before the decade is out, the Stardust mission will set off to take close-up pictures and capture dust samples from Comet Wild-2.
For Dr Farquhar, formerly Nasa's first programme manager for Discovery, these missions are the outcome of a long, hard campaign of argument and persuasion. "I like low-cost missions," he said, "but we had to convert people." Future missions are likely to use even more advanced, miniaturised components, which means smaller launch vehicles are required and costs plummet. Nasa is already looking at sending spacecraft weighing just a few kilograms to the far reaches of our Solar System - in a programme appropriately dubbed the New Millennium.