When Galileo trained his crude telescope on the planet Jupiter, hanging above the horizon in 1610, and observed moons orbiting a planet other than Earth, it created a quake whose waves have rippled down through the centuries to today. Never had such hard evidence been found that supported the Copernican idea of non-Earth-centric orbits, freeing astronomy and cosmology from a thousand years of error that shaded how people thought.
The Earth, after all, was not the center of the Universe.
Galileo’s moons: the Galilean Moons—Io, Europa, Ganymede, and Callisto—have drawn our eyes skyward now for over 400 years. They have been the crucible for numerous scientific discoveries, serving as a test bed for new ideas and new techniques, from the problem of longitude to the speed of light, from the birth of astronomical interferometry to the beginnings of exobiology. Here is a short history of Galileo’s Moons in the history of physics.
Galileo (1610): Celestial Orbits
In late 1609, Galileo (1564 – 1642) received an unwelcome guest to his home in Padua—his mother. She was not happy with his mistress, and she was not happy with his chosen profession, but she was happy to tell him so. By the time she left in early January 1610, he was yearning for something to take his mind off his aggravations, and he happened to point his new 20x telescope in the direction of the planet Jupiter hanging above the horizon [1]. Jupiter appeared as a bright circular spot, but nearby were three little stars all in line with the planet. The alignment caught his attention, and when he looked again the next night, the position of the stars had shifted. On successive nights he saw them shift again, sometimes disappearing into Jupiter’s bright disk. Several days later he realized that there was a fourth little star that was also behaving the same way. At first confused, he had a flash of insight—the little stars were orbiting the planet. He quickly understood that just as the Moon orbited the Earth, these new “Medicean Planets” were orbiting Jupiter. In March 1610, Galileo published his findings in Siderius Nuncius (The Starry Messenger).
It is rare in the history of science for there not to be a dispute over priority of discovery. Therefore, by an odd chance of fate, on the same nights that Galileo was observing the moons of Jupiter with his telescope from Padua, the German astronomer Simon Marius (1573 – 1625) also was observing them through a telescope of his own from Bavaria. It took Marius four years to publish his observations, long after Galileo’s Siderius had become a “best seller”, but Marius took the opportunity to claim priority. When Galileo first learned of this, he called Marius “a poisonous reptile” and “an enemy of all mankind.” But harsh words don’t settle disputes, and the conflicting claims of both astronomers stood until the early 1900’s when a scientific enquiry looked at the hard evidence. By that same odd chance of fate that had compelled both men to look in the same direction around the same time, the first notes by Marius in his notebooks were dated to a single day after the first notes by Galileo! Galileo’s priority survived, but Marius may have had the last laugh. The eternal names of the “Galilean” moons—Io, Europe, Ganymede and Callisto—were given to them by Marius.
Picard and Cassini (1671): Longitude
The 1600’s were the Age of Commerce for the European nations who relied almost exclusively on ships and navigation. While latitude (North-South) was easily determined by measuring the highest angle of the sun above the southern horizon, longitude (East-West) relied on clocks which were notoriously inaccurate, especially at sea.
The Problem of Determining Longitude at Sea is the subject of Dava Sobel’s thrilling book Longitude (Walker, 1995) [2] where she reintroduced the world to what was once the greatest scientific problem of the day. Because almost all commerce was by ships, the determination of longitude at sea was sometimes the difference between arriving safely in port with a cargo or being shipwrecked. Galileo knew this, and later in his life he made a proposal to the King of Spain to fund a scheme to use the timings of the eclipses of his moons around Jupiter to serve as a “celestial clock” for ships at sea. Galileo’s grant proposal went unfunded, but the possibility of using the timings of Jupiter’s moons for geodesy remained an open possibility, one which the King of France took advantage of fifty years later.
In 1671 the newly founded Academie des Sciences in Paris funded an expedition to the site of Tycho Brahe’s Uranibourg Observatory in Hven, Denmark, to measure the time of the eclipses of the Galilean moons observed there to be compared the time of the eclipses observed in Paris by Giovanni Cassini (1625 – 1712). When the leader of the expedition, Jean Picard (1620 – 1682), arrived in Denmark, he engaged the services of a local astronomer, Ole Rømer (1644 – 1710) to help with the observations of over 100 eclipses of the Galilean moon Io by the planet Jupiter. After the expedition returned to France, Cassini and Rømer calculated the time differences between the observations in Paris and Hven and concluded that Galileo had been correct. Unfortunately, observing eclipses of the tiny moon from the deck of a ship turned out not to be practical, so this was not the long-sought solution to the problem of longitude, but it contributed to the early science of astrometry (the metrical cousin of astronomy). It also had an unexpected side effect that forever changed the science of light.
Ole Rømer (1676): The Speed of Light
Although the differences calculated by Cassini and Rømer between the times of the eclipses of the moon Io between Paris and Hven were small, on top of these differences was superposed a surprisingly large effect that was shared by both observations. This was a systematic shift in the time of eclipse that grew to a maximum value of 22 minutes half a year after the closest approach of the Earth to Jupiter and then decreased back to the original time after a full year had passed and the Earth and Jupiter were again at their closest approach. At first Cassini thought the effect might be caused by a finite speed to light, but he backed away from this conclusion because Galileo had shown that the speed of light was unmeasurably fast, and Cassini did not want to gainsay the old master.
Rømer, on the other hand, was less in awe of Galileo’s shadow, and he persisted in his calculations and concluded that the 22 minute shift was caused by the longer distance light had to travel when the Earth was farthest away from Jupiter relative to when it was closest. He presented his results before the Academie in December 1676 where he announced that the speed of light, though very large, was in fact finite. Unfortnately, Rømer did not have the dimensions of the solar system at his disposal to calculate an actual value for the speed of light, but the Dutch mathematician Huygens did.
When Huygens read the proceedings of the Academie in which Rømer had presented his findings, he took what he knew of the radius of Earth’s orbit and the distance to Jupiter and made the first calculation of the speed of light. He found a value of 220,000 km/second (kilometers did not exist yet, but this is the equivalent of what he calculated). This value is 26 percent smaller than the true value, but it was the first time a number was given to the finite speed of light—based fundamentally on the Galilean moons. For a popular account of the story of Picard and Rømer and Huygens and the speed of light, see Ref. [3].
Michelson (1891): Astronomical Interferometry
Albert Michelson (1852 – 1931) was the first American to win the Nobel Prize in Physics. He received the award in 1907 for his work to replace the standard meter, based on a bar of metal housed in Paris, with the much more fundamental wavelength of red light emitted by Cadmium atoms. His work in Paris came on the heels of a new and surprising demonstration of the use of interferometry to measure the size of astronomical objects.
The wavelength of light (a millionth of a meter) seems ill-matched to measuring the size of astronomical objects (thousands of meters) that are so far from Earth (billions of meters). But this is where optical interferometry becomes so important. Michelson realized that light from a distant object, like a Galilean moon of Jupiter, would retain some partial coherence that could be measured using optical interferometry. Furthermore, by measuring how the interference depended on the separation of slits placed on the front of a telescope, it would be possible to determine the size of the astronomical object.
In 1891, Michelson traveled to California where the Lick Observatory was poised high above the fog and dust of agricultural San Jose (a hundred years before San Jose became the capitol of high-tech Silicon Valley). Working with the observatory staff, he was able to make several key observations of the Galilean moons of Jupiter. These were just close enough that their sizes could be estimated (just barely) from conventional telescopes. Michelson found from his calculations of the interference effects that the sizes of the moons matched the conventional sizes to within reasonable error. This was the first demonstration of astronomical interferometry which has burgeoned into a huge sub-discipline of astronomy today—based originally on the Galilean moons [4].
Pioneer (1973 – 1974): The First Tour
Pioneer 10 was launched on March 3, 1972 and made its closest approach to Jupiter on Dec. 3, 1973. Pioneer 11 was launched on April 5, 1973 and made its closest approach to Jupiter on Dec. 3, 1974 and later was the first spacecraft to fly by Saturn. The Pioneer spacecrafts were the first to leave the solar system (there have now been 5 that have left, or will leave, the solar system). The cameras on the Pioneers were single-pixel instruments that made line-scans as the spacecraft rotated. The point light detector was a Bendix Channeltron photomultiplier detector, which was a vacuum tube device (yes vacuum tube!) operating at a single-photon detection efficiency of around 10%. At the time of the system design, this was a state-of-the-art photon detector. The line scanning was sufficient to produce dramatic photographs (after extensive processing) of the giant planets. The much smaller moons were seen with low resolution, but were still the first close-ups ever to be made of Galileo’s moons.
Voyager (1979): The Grand Tour
Voyager 1 was launched on Sept. 5, 1977 and Voyager 2 was launched on August 20, 1977. Although Voyager 1 was launched second, it was the first to reach Jupiter with closest approach on March 5, 1979. Voyager 2 made its closest approach to Jupiter on July 9, 1979.
In the Fall of 1979, I had the good fortune to be an undergraduate at Cornell University when Carl Sagan gave an evening public lecture on the Voyager fly-bys, revealing for the first time the amazing photographs of not only Jupiter but of the Galilean Moons. Sitting in the audience listening to Sagan, a grand master of scientific story telling, made you feel like you were a part of history. I have never been so convinced of the beauty and power of science and technology as I was sitting in the audience that evening.
The camera technology on the Voyagers was a giant leap forward compared to the Pioneer spacecraft. The Voyagers used cathode ray vidicon cameras, like those used in television cameras of the day, with high-resolution imaging capabilities. The images were spectacular, displaying alien worlds in high-def for the first time in human history: volcanos and lava flows on the moon of Io; planet-long cracks in the ice-covered surface of Europa; Callisto’s pock-marked surface; Ganymede’s eerie colors.
The Voyager’s discoveries concerning the Galilean Moons were literally out of this world. Io was discovered to be a molten planet, its interior liquified by tidal-force heating from its nearness to Jupiter, spewing out sulfur lava onto a yellowed terrain pockmarked by hundreds of volcanoes, sporting mountains higher than Mt. Everest. Europa, by contrast, was discovered to have a vast flat surface of frozen ice, containing no craters nor mountains, yet fractured by planet-scale ruptures stained tan (for unknown reasons) against the white ice. Ganymede, the largest moon in the solar system, is a small planet, larger than Mercury. The Voyagers revealed that it had a blotchy surface with dark cratered patches interspersed with light smoother patches. Callisto, again by contrast, was found to be the most heavily cratered moon in the solar system, with its surface pocked by countless craters.
Galileo (1995): First in Orbit
The first mission to orbit Jupiter was the Galileo spacecraft that was launched, not from the Earth, but from Earth orbit after being delivered there by the Space Shuttle Atlantis on Oct. 18, 1989. Galileo arrived at Jupiter on Dec. 7, 1995 and was inserted into a highly elliptical orbit that became successively less eccentric on each pass. It orbited Jupiter for 8 years before it was purposely crashed into the planet (to prevent it from accidentally contaminating Europa that may support some form of life).
Galileo made many close passes to the Galilean Moons, providing exquisite images of the moon surfaces while its other instruments made scientific measurements of mass and composition. This was the first true extended study of Galileo’s Moons, establishing the likely internal structures, including the liquid water ocean lying below the frozen surface of Europa. As the largest body of liquid water outside the Earth, it has been suggested that some form of life could have evolved there (or possibly been seeded by meteor ejecta from Earth).
Juno (2016): Still Flying
The Juno spacecraft was launched from Cape Canaveral on Aug. 5, 2011 and entered a Jupiter polar orbit on July 5, 2016. The mission has been producing high-resolution studies of the planet. The mission was extended in 2021 to last to 2025 to include several close fly-bys of the Galilean Moons, especially Europa, which will be the object of several upcoming missions because of the possibility for the planet to support evolved life. These future missions include NASA’s Europa Clipper Mission, the ESA’s Jupiter Icy Moons Explorer, and the Io Volcano Observer.
Epilog (2060): Colonization of Callisto
In 2003, NASA identified the moon Callisto as the proposed site of a manned base for the exploration of the outer solar system. It would be the next most distant human base to be established after Mars, with a possible start date by the mid-point of this century. Callisto was chosen because it is has a low radiation level (being the farthest from Jupiter of the large moons) and is geologically stable. It also has a composition that could be mined to manufacture rocket fuel. The base would be a short-term way-station (crews would stay for no longer than a month) for refueling before launching and using a gravity assist from Jupiter to sling-shot spaceships to the outer planets.
[1] See Chapter 2, A New Scientist: Introducing Galileo, in David D. Nolte, Galileo Unbound (Oxford University Press, 2018).
[2] Dava Sobel, Longitude: The True Story of a Lone Genius who Solved the Greatest Scientific Problem of his Time (Walker, 1995)
[3] See Chap. 1, Thomas Young Polymath: The Law of Interference, in David D. Nolte, Interference: The History of Optical Interferometry and the Scientists who Tamed Light (Oxford University Press, 2023)
[4] See Chapter 5, Stellar Interference: Measuring the Stars, in David D. Nolte, Interference: The History of Optical Interferometry and the Scientists who Tamed Light (Oxford University Press, 2023).
Since Galileo launched his trajectory, there have been six broad generations that have traced the continuing development of concepts of motion. These are: 1) Universal Motion; 2) Phase Space; 3) Space-Time; 4) Geometric Dynamics; 5) Quantum Coherence; and 6) Complex Systems. These six generations were not all sequential, many evolving in parallel over the centuries, borrowing from each other, and there surely are other ways one could divide up the story of dynamics. But these six generations capture the grand concepts and the crucial paradigm shifts that are Galileo’s legacy, taking us from Galileo’s trajectory to the broad expanses across which physicists practice physics today.
Universal Motion emerged as a new concept when Isaac Newton proposed his theory of universal gravitation by which the force that causes apples to drop from trees is the same force that keeps the Moon in motion around the Earth, and the Earth in motion around the Sun. This was a bold step because even in Newton’s day, some still believed that celestial objects obeyed different laws. For instance, it was only through the work of Edmund Halley, a contemporary and friend of Newton’s, that comets were understood to travel in elliptical orbits obeying the same laws as the planets. Universal Motion included ideas of momentum from the start, while concepts of energy and potential, which fill out this first generation, took nearly a century to develop in the hands of many others, like Leibniz and Euler and the Bernoullis. This first generation was concluded by the masterwork of the Italian-French mathematician Joseph-Louis Lagrange, who also planted the seed of the second generation.
The second generation, culminating in the powerful and useful Phase Space, also took more than a century to mature. It began when Lagrange divorced dynamics from geometry, establishing generalized coordinates as surrogates to directions in space. Ironically, by discarding geometry, Lagrange laid the foundation for generalized spaces, because generalized coordinates could be anything, coming in any units and in any number, each coordinate having its companion velocity, doubling the dimension for every freedom. The Austrian physicist Ludwig Boltzmann expanded the number of dimensions to the scale of Avogadro’s number of particles, and he discovered the conservation of phase space volume, an invariance of phase space that stays the same even as 1023 atoms (Avogadro’s number) in ideal gases follow their random trajectories. The idea of phase space set the stage for statistical mechanics and for a new probabilistic viewpoint of mechanics that would extend into chaotic motions.
The French mathematician Henri Poincaré got a glimpse of chaotic motion in 1890 as he rushed to correct an embarrassing mistake in his manuscript that had just won a major international prize. The mistake was mathematical, but the consequences were profoundly physical, beginning the long road to a theory of chaos that simmered, without boiling, for nearly seventy years until computers became common lab equipment. Edward Lorenz of MIT, working on models of the atmosphere in the late 1960s, used one of the earliest scientific computers to expose the beauty and the complexity of chaotic systems. He discovered that the computer simulations were exponentially sensitive to the initial conditions, and the joke became that a butterfly flapping its wings in China could cause hurricanes in the Atlantic. In his computer simulations, Lorenz discovered what today is known as the Lorenz butterfly, an example of something called a “strange attractor”. But the term chaos is a bit of a misnomer, because chaos theory is primarily about finding what things are shared in common, or are invariant, among seemingly random-acting systems.
The third generation in concepts of motion, Space-Time, is indelibly linked with Einstein’s special theory of relativity, but Einstein was not its originator. Space-time was the brain child of the gifted but short-lived Prussian mathematician Hermann Minkowski, who had been attracted from Königsberg to the mathematical powerhouse at the University in Göttingen, Germany around the turn of the 20th Century by David Hilbert. Minkowski was an expert in invariant theory, and when Einstein published his special theory of relativity in 1905 to explain the Lorentz transformations, Minkowski recognized a subtle structure buried inside the theory. This structure was related to Riemann’s metric theory of geometry, but it had the radical feature that time appeared as one of the geometric dimensions. This was a drastic departure from all former theories of motion that had always separated space and time: trajectories had been points in space that traced out a continuous curve as a function of time. But in Minkowski’s mind, trajectories were invariant curves, and although their mathematical representation changed with changing point of view (relative motion of observers), the trajectories existed in a separate unchanging reality, not mere functions of time, but eternal. He called these trajectories world lines. They were static structures in a geometry that is today called Minkowski space. Einstein at first was highly antagonistic to this new view, but he relented, and later he so completely adopted space-time in his general theory that today Minkowski is almost forgotten, his echo heard softly in expressions of the Minkowski metric that is the background to Einstein’s warped geometry that bends light and captures errant space craft.
The fourth generation in the development of concepts of motion, Geometric Dynamics, began when an ambitious French physicist with delusions of grandeur, the historically ambiguous Pierre Louis Maupertuis, returned from a scientific boondoggle to Lapland where he measured the flatness of the Earth in defense of Newtonian physics over Cartesian. Skyrocketed to fame by the success of the expedition, he began his second act by proposing the Principle of Least Action, a principle by which all motion seeks to be most efficient by taking a geometric path that minimizes a physical quantity called action. In this principle, Maupertuis saw both a universal law that could explain all of physical motion, as well as a path for himself to gain eternal fame in the company of Galileo and Newton. Unfortunately, his high hopes were dashed through personal conceit and nasty intrigue, and most physicists today don’t even recognize his name. But the idea of least action struck a deep chord that reverberates throughout physics. It is the first and fundamental example of a minimum principle, of which there are many. For instance, minimum potential energy identifies points of system equilibrium, and paths of minimum distances are geodesic paths. In dynamics, minimization of the difference between potential and kinetic energies identifies the dynamical paths of trajectories, and minimization of distance through space-time warped by mass and energy density identifies the paths of falling objects.
Maupertuis’ fundamentally important idea was picked up by Euler and Lagrange, expanding it through the language of differential geometry. This was the language of Bernhard Riemann, a gifted and shy German mathematician whose mathematical language was adopted by physicists to describe motion as a geodesic, the shortest path like a great-circle route on the Earth, in an abstract dynamical space defined by kinetic energy and potentials. In this view, it is the geometry of the abstract dynamical space that imposes Galileo’s simple parabolic form on freely falling objects. Einstein took this viewpoint farther than any before him, showing how mass and energy warped space and how free objects near gravitating bodies move along geodesic curves defined by the shape of space. This brought trajectories to a new level of abstraction, as space itself became the cause of motion. Prior to general relativity, motion occurred in space. Afterwards, motion was caused by space. In this sense, gravity is not a force, but is like a path down which everything falls.
The fifth generation of concepts of motion, Quantum Coherence, increased abstraction yet again in the comprehension of trajectories, ushering in difficult concepts like wave-particle duality and quantum interference. Quantum interference underlies many of the counter-intuitive properties of quantum systems, including the possibility for quantum systems to be in two or more states at the same time, and for quantum computers to crack unbreakable codes. But this new perspective came with a cost, introducing fundamental uncertainties that are locked in a battle of trade-offs as one measurement becomes more certain and others becomes more uncertain.
Einstein distrusted Heisenberg’s uncertainty principle, not that he disagreed with its veracity, but he felt it was more a statement of ignorance than a statement of fundamental unknowability. In support of Einstein, Schrödinger devised a thought experiment that was meant to be a reduction to absurdity in which a cat is placed in a box with a vial of poison that would be broken if a quantum particle decays. The cruel fate of Schrödinger’s cat, who might or might not be poisoned, hinges on whether or not someone opens the lid and looks inside. Once the box is opened, there is one world in which the cat is alive and another world in which the cat is dead. These two worlds spring into existence when the box is opened—a bizarre state of affairs from the point of view of a pragmatist. This is where Richard Feynman jumped into the fray and redefined the idea of a trajectory in a radically new way by showing that a quantum trajectory is not a single path, like Galileo’s parabola, but the combined effect of the quantum particle taking all possible paths simultaneously. Feynman established this new view of quantum trajectories in his thesis dissertation under the direction of John Archibald Wheeler at Princeton. By adapting Maupertuis’ Principle of Least Action to quantum mechanics, Feynman showed how every particle takes every possible path—simultaneously—every path interfering in such as way that only the path with the most constructive interference is observed. In the quantum view, the deterministic trajectory of the cannon ball evaporates into a cloud of probable trajectories.
In our current complex times, the sixth generation in the evolution of concepts of motion explores Complex Systems. Lorenz’s Butterfly has more to it than butterflies, because Life is the greatest complex system of our experience and our existence. We are the end result of a cascade of self-organizing events that began half a billion years after Earth coalesced out of the nebula, leading to the emergence of consciousness only about 100,000 years ago—a fact that lets us sit here now and wonder about it all. That we are conscious is perhaps no accident. Once the first amino acids coagulated in a muddy pool, we have been marching steadily uphill, up a high mountain peak in a fitness landscape. Every advantage a species gained over its environment and over its competitors exerted a type of pressure on all the other species in the ecosystem that caused them to gain their own advantage.
The modern field of evolutionary dynamics spans a wide range of scales across a wide range of abstractions. It treats genes and mutations on DNA in much the same way it treats the slow drift of languages and the emergence of new dialects. It treats games and social interactions the same way it does the evolution of cancer. Evolutionary dynamics is the direct descendant of chaos theory that turned butterflies into hurricanes, but the topics it treats are special to us as evolved species, and as potential victims of disease. The theory has evolved its own visualizations, such as the branches in the tree of life and the high mountain tops in fitness landscapes separated by deep valleys. Evolutionary dynamics draws, in a fundamental way, on dynamic processes in high dimensions, without which it would be impossible to explain how something as complex as human beings could have arisen from random mutations.
These six generations in the development of dynamics are not likely to stop, and future generations may arise as physicists pursue the eternal quest for the truth behind the structure of reality.
Galileo Unbound 