Devlin's Angle

September 2003


On September 21, the spacecraft Galileo will crash land on the surface of Jupiter, bringing to an end one of the most successful space voyages of all time. Launched from the Space Shuttle Atlantis back in 1989, Galileo has been exploring Jupiter and its moons (now known to number at least 61, thanks largely to Galileo's own findings) since December 1995.

Since the successful end of the primary mission (orbiting Jupiter and its moons for two years, taking photographs and making scientific measurements), NASA has redirected the spacecraft three times to carry out scientific explorations not in the original schedule.

With its fuel almost all gone now, however, the time has come to bring this incredibly productive voyage of discovery to an end. Although NASA will obtain one final burst of photographs and data as the spacecraft plunges towards Jupiter's surface and is crushed by the huge gravitational forces of this massive planet, the main reason for this spectacular end is to eliminate even the slightest chance that the craft would crash instead on Jupiter's moon Europa. Ever since Galileo discovered what seems to be a subsurface ocean on Europa, in the course of its second mission, scientists have wondered if there could be life there. Given that possibility, however remote, the last thing anyone wants is for an earthly spacecraft to crash there, possibly carrying tiny microbes from home and as a result maybe ruining a future exploration of the planet.

Part of the reason NASA was able to coax so much life out of Galileo is the use of clever mathematics to work out orbits that minimized the use of fuel, by relying on the gravitational forces of Jupiter itself and its many moons to provide most of the propulsive forces. A similar approach was adopted for the original six year flight out to the Jupiter system.

NASA had planned to launch Galileo from the Shuttle in May of 1986, but the loss of the Challenger in January of that year put everything on hold. Even worse, the original plan called for a Shuttle to carry the spacecraft into low-Earth orbit, from where it would be boosted to Jupiter using the powerful Centaur rocket as an upper stage. After the Columbia disaster, it was clear that when Shuttle flights were resumed, the Shuttle would not be allowed to carry another highly volatile rocket as cargo in its payload compartment. Not for the first time in its history, NASA had to come up with an ingeneous workaround.

When released from the Space Shuttle in October 1989, Galileo's tiny rocket engine put it on a course around the Sun where it first headed for Venus, and then made two further Sun orbits bringing it past Earth each time. On each of these three fly-bys, the spacecraft picked up additional speed from the planet in a sort of slingshot fashion, so that by the end of this initial maneuver it had enough speed to make it to Jupiter in free flight. Known as Gravity Assist, this method has been used by NASA on a number of missions. It depends on our ability to perform delicate computations that predict the spacecraft's orbit with incredible accuracy. The reason that is possible is that the planets, like all other inanimate objects in our universe, move according to the precise laws of mathematics. The first person who fully realized that and made significant use of the fact was the spacecraft's namesake, Galileo Galilei of Italy.

Contemplating the Galileo mission prompted me to think back to this 16th century genius to whom those of us who benefit from the products of today's science and technology owe so much.

Galileo was born in Pisa on 15 February 1564. He grew up in Pisa and Florence. At his father's wish, in 1581 he enrolled at the University of Pisa to study medicine, but his first love was mathematics and natural philosophy. (The latter was what passed for science in those days. When he was older, Galileo was one of a handful of revolutionary thinkers who invented what we now think of as science.) In 1585, Galilei senior finally accepted the inevitable and allowed his son to drop out of university, without a degree.

Galileo made a living for a while giving private lessons in mathematics in Florence, then obtained a regular teaching position in Siena. It was while in Siena that he wrote his first book, La balancitte (The little balance), describing Archimedes' method for determining centers of gravity. The book contained some original ideas, and those in the know started to take notice of this young newcomer. In 1589, Galileo was appointed to the chair in mathematics in Pisa.

During his three year tenure at Pisa, Galileo wrote a series of essays on motion titled De motu. It is in those unpublished notes that we first see definite expression of the idea that theories can be tested by performing experiments. In particular, Galileo suggested how his own theory of falling bodies could be tested by rolling a ball down an inclined plane.

Galileo left Pisa in 1592 to take up a much more prestigious professorship at the University of Padua, near Venice, where he would remain for the next eighteen, highly productive years. It was in his lectures at Padua that he first began to put forward his agreement with Copernicus' heliocentric theory of the universe, setting himself on what would later become a collision course with the Roman Catholic Church.

In 1609, Galileo learned that a Dutchman had invented a device enabling detailed visual examination of distant objects such as planets -- called then a spyglass but known nowadays as a telescope. Galileo used his knowledge of optics to design such an instrument for himself, and his technical skill was such that his own telescope was far better than that of the Dutchman Fleming. The following year, Galileo published his pamphlet Sidereus Nuncius (The Starry Messenger), in which he described what he had seen through his new instrument. Among the wonders he had observed were mountains on the Moon and -- a foretaste of the spacecraft that would be named after him almost four hundred years later -- four moons of Jupiter, whose orbital periods he was able to estimate.

The Starry Messenger made Galileo famous, and soon after its appearance he resigned his position at Padua to become Chief Mathematician at the University of Pisa -- a highly prestigious position with no teaching duties. With his new found fame, Galileo soon found his work coming under even greater scrutiny by the Catholic church. In a 1616 essay titled Letter to the Grand Duchess (Christina of Lorraine) he argued explicitly in favor of the Copernican theory of the universe in print, not just as a mathematical simplification, as some suggested in order to stay clear of the Inquisition, but as an accurate description of what actually was. Although Rome did not contact him directly, the Church's displeasure at his essay was conveyed to him indirectly. He must have known that, from now on he was a marked man.

In 1623, Galileo published his book Il saggiatore (The Assayer), describing in considerable detail what we would today call the scientific method. It was in this book that we find his famous quotation "In order to understand the universe, it is necessary to understand the language in which its laws are written, and that language is mathematics."

Well, no, actually we don't find those words there, or anywhere else in Galileo's writings as far as I know. The sentence above is one of those irrepressible misquotes, like "Play it again, Sam" (which neither Humphrey Bogart nor Ingrid Bergman actually say in the movie Casablanca) or "Come up and see me sometime" (which Mae West never said in any movie) which seem to live on in the face of any number of protestations to the contrary. Here is the full quote, translated from Galileo's Italian original:

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
Believing that his fame, his advancing years, and his declining health would make him immune from serious Papal repercussions, Galileo spent the remaining years of his professional life writing a book on the Copernican theory of the universe. He couched the book in the form of a dialogue between two protagonists arguing for and against the heliocentric theory, calling his work Dialogue Concerning the Two Chief Systems of the World -- Ptolemaic and Copernican, but the moment it came out in 1632 it was clear to everyone which side Galileo was on. In particular, it was clear to the Church authorities. They immediately banned publication of the book, tried Galileo in his absence when he was too ill to travel to Rome, convicted him of heresy, and sentenced him to house arrest for the remainder of his life. The book itself had to be smuggled out of Italy and be published in Holland in order to see the light of day.

In 1992, Pope John Paul II finally admitted in public that the Catholic Church had acted unfairly toward Galileo. By then, of course, Galileo had been dead for 350 years (he died on 8 January, 1642) and the spacecraft Galileo had been whizzing round the inner planets of the heliocentric solar system for three years prior to heading off toward Jupiter at the start of 1993. What goes around, comes around -- but sometimes very slowly.

For details of the Galileo mission, see
Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin ( is the Executive Director of the Center for the Study of Language and Information at Stanford University and "The Math Guy" on NPR's Weekend Edition. His most recent book is The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, published last fall by Basic Books.

Devlin's Angle is updated at the beginning of each month.