In the late 1960s celestial mechanicians—scientists who study the motions of planets and spacecraft—began to solve problems posed by the immensity of the outer solar system. If a spacecraft is aimed to fly close to a planet in just the right way, it can be accelerated by the gravity of the planet to higher speeds than could ever be obtained by direct launch from Earth. If a second, more distant planet is in the correct alignment, the gravity boost given by the first encounter can speed the craft on to the second. Jupiter, with its huge size and strong gravitational pull, could be used as the fulcrum for a series of missions to Saturn, Uranus, Neptune, and even distant Pluto. In addition, the early 1980s would offer an exceptional opportunity, one repeated only about once every two centuries. At that time, all four giant planets would be in approximate alignment, so that gravity-assist maneuvers could be done sequentially. A single spacecraft, after being boosted from Jupiter to Saturn, could use the acceleration of Saturn to continue to Uranus, and in turn could be accelerated all the way out to Neptune. Such an ambitious, multiplanet mission was named the Grand Tour. The first essential step in the Grand Tour was a flyby of Jupiter. However, this planet is ten times farther away from Earth than Venus or Mars. In addition, there were two potentially lethal hazards that had not been faced before in interplanetary flights: the asteroid belt and the Jovian magnetosphere. The first danger was presented by the many thousands of asteroids that occupy a belt between the orbits of Mars and Jupiter. The largest asteroid, Ceres, was discovered in 1801 and was initially thought to be the “missing planet” sometimes hypothesized as lying between Jupiter and Mars. However, Ceres is only 1000 kilometers in diameter, too small to deserve the title of planet. Hundreds more of these minor planets were discovered during the nineteenth century, and by the 1960s more than 3000 had well-determined orbits. Most were only a few tens of kilometers in diameter, and astronomers estimated that 50 000 existed that were 1 kilometer or more in diameter. Any spacecraft to Jupiter would have to cross this congested region of space. Even 50 000 minor bodies spread through the volume of space occupied by the asteroid belt would present little direct danger, although a chance collision with an uncatalogued object was always possible. Much more serious was the possibility that these larger objects were accompanied by large amounts of debris, from the size of boulders down to microscopic dust, that were undetectable from Earth. Collisions with pebble-sized stones could easily destroy a spacecraft. The only way to evaluate this danger was to go there and find out how much small debris was present.