But in 1959, Dr. Leonard Schiff of Stanford (and independently Dr. George Pugh of the Defense Department), suggested that gyroscopes in space could do the trick. Shortly afterward, at the swimming pool, Dr. Schiff and Dr. William Fairbank, also of Stanford, recruited a colleague, Dr. Robert Cannon, an aeronautics professor who was also a gyroscope expert. They were joined in 1962 by Dr. Everitt, a young British postdoctor.
In 1964 NASA gave the Stanford group a contract to study the idea. While Stanford built the gyroscopes, Lockheed Martin constructed the spacecraft that would carry them. As the probe progressed, NASA sent men to the Moon and landed probes on Mars. The Vietnam War started and ended. The World Trade Center rose and fell. Gravity Probe A, which showed how gravity affects the rate of clock, flew in 1976.
Dr. Schiff died in 1971; Dr. Fairbank, in 1989. After stints as an assistant secretary of transportation and at Caltech, Dr. Cannon returned to Stanford in 1979. Dr. Everitt, born in England, is now 69. His long hair is gray. He admits that he didn't know what he was getting into when he joined Stanford and the gyroscope team at age 28.
''I knew I was getting into something that might waste two or three years and get nowhere,'' he recalled. But he was young. ''It's good to spend a couple years on a far-out idea and then move on,'' he said.
Gyros and Squids
By all accounts the experiment now at Vandenberg is a technical tour de force. At its heart, isolated as much as possible from the universe, are the gyroscopes: four quartz spheres slightly larger than golf balls. They are said to be the most perfectly spherical objects ever made by humans -- out of round by only 40 layers of atoms. If the Earth were this perfect, the tallest mountain would rise just six and a half feet.
In space, they will be suspended by electrical fields and spin at 10,000 revolutions per minute inside a quartz telescope trained assiduously at the star IM Pegasi.
To make sure that no outside influence imparts a stray wobble to the spinning balls, the telescope floats freely inside an external spacecraft equipped with jets to sense and counter any drag from stray wisps of atmosphere. It is also surrounded by a superconducting lead bag that shields it from magnetic fields. And the whole assembly is cooled by liquid helium to less than 2 degrees above absolute zero, or about minus 456 degrees Fahrenheit.
But that's only the beginning. After having isolated the gyroscopes from the rest of the universe and aligned them with IM Pegasi, the scientists have to monitor which way they are spinning.
To this end, the quartz balls are coated with niobium, which loses all resistance to electrical current at these temperatures. As a result, when the balls rotate, some of the electrons in the niobium slip behind their atoms. Their relative motion creates a small current that generates a tiny magnetic field, located by detectors known as squids -- superconducting quantum interference devices -- built into the gyroscope.
The squids have two missions. One is to measure the frame dragging, which would cause the gyros to turn in the direction of the Earth's rotation. The other is to measure a parameter called gamma, or how much matter causes the geometry of space to deviate from the ''flat'' Euclidean geometry familiar from high school. Because the Earth makes space-time sag, a circular orbit around the Earth should turn out to have a circumference ever so slightly less than pi times the orbit's diameter.
This ''missing inch,'' as Dr. Everitt calls it, should cause the gyros to turn in a direction perpendicular to the Earth's rotational axis. Some physicists regard gamma as a more interesting measurement than frame dragging, because many of their more exotic speculations, like hidden extra dimensions and undiscovered forces permeating space, could cause its value to deviate from the Einsteinian prediction of exactly 1.0.
Up and Away, at Last
The gravity probe's technological legacy is already secure. Many of its advances have been incorporated into other projects. Its scheme for cooling by liquid helium, for example, was used on the Iras infrared astronomy satellite back in 1983.
But its scientific legacy is less clear.
Although frame dragging has not been detected directly, astronomers say it has been measured indirectly. Last year a group of Italian physicists claimed to have measured it within a margin of error of about 20 percent by analyzing data from the two Lageos satellites, spherical objects pocked with reflectors that were launched to serve as sort of geodetic markers in the sky. More satellites in coming years could reduce the margin of error to 1 percent, the precision that Gravity Probe B is aimed at.
Meanwhile, last September, astronomers claimed that they had measured the parameter gamma by timing radio signals on their way to Earth from the Cassini spacecraft, which is approaching Saturn. The signals were delayed as they passed the Sun, dipping into its gravitational warp. The scientists found that gamma was equal to the Einsteinian value of 1.0 to a precision of about one part in 40,000.
That is better than the designed precision of the gravity probe, said Dr. Nordtvedt, though Dr. Everitt replied in an interview that final tests indicated that the experiment could exceed that level.
Dr. Nordtvedt said that Dr. Everitt was a good friend and that he would be at the launching on Monday. Nevertheless, he said, ''I'm critical of the fact that the program has been allowed to drag on for 40 years and to consume so much money.''
Such doubts came to a climax a year ago when the spacecraft failed an important test, portending yet another postponement and more expense. NASA convened panels of engineers and physicists to determine whether to go on with the mission.
The panelists concluded that there had indeed been ''erosion'' in the gravity probe's mission, particularly in regard to the measurement of gamma. Nevertheless, they wrote, Gravity Probe B ''is still a precedent-breaking mission for the space program in that it will perform a precision physics experiment in space.''
In November, a month before the probe was to be launched, electrical problems sent it back to the clean room for four months. After all that time and money, NASA was playing it safe.
Dr. Michael Turner, a cosmologist at the University of Chicago and chairman of the review panel, said, ''I think all of us -- Francis included -- just want to see this remarkable experiment in space get done.''
Dr. Everitt agreed. ''We could have done it better and quicker, but not enormously quicker,'' he said, adding:
''The medieval cathedral builders took longer.''
Photo: Gravity Probe B is to be launched next Monday on an 18-month mission, after 45 years of planning. Nearly 100 doctorates have been awarded for work on the project. (Photo by Stanford University)(pg. F4) Chart/Diagram: ''Putting Einstein to the Test'' Gravity Probe B is to gauge the subtle twisting and warping effects of the Earth on surrounding space and time. DETECTING SPACE-TIME WARP The satellite has a telescope and four gyroscopes that are are precisely aligned and spin on the same axis. They are pointed toward a distant star. As the satellite orbits, the telescopes aim remains fixed on the star. But the gyroscopes, floating in a vacuum and protected from interactions with other bodies, can drift with changes in the space-time frame. Einstein's theory of relativity predicts that the gyroscopes should detect these distortions: 1. FRAME DRAGGING The mass of Earth dragging space-time in the direction of Earth's rotation. 2. GEODETIC EFFECT (GAMMA) The mass of Earth sagging the otherwise flat geometry of space-time. MINUTE DIFFERENCES Changes found by the gyroscopes should amount to less than one hundred-thousandth of a degree over a year. This is the width a human hair would appear when viewed from one-quarter mile away, or across the length of Times Square. (Bill Marsh/The New York Times; Earth image by NASA) (Sources by Stanford University, NASA)