History of Planetary Motion

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The Greek philosopher Aristotle provided two more reasons why the Earth was round. First, he noted that Earth’s shadow always took a circular bite out of the moon during a lunar eclipse, which would only be possible with a spherical Earth. If the Earth were a disk, its shadow would appear as an elongated ellipse at least during part of the
eclipse. Second, Aristotle knew that people who journeyed north saw the North Star ascend higher in the sky, while those heading south saw the North Star sink. On a flat Earth, the positions of the stars wouldn’t vary with a person’s location. Despite these arguments, which won over most of the world’s educated citizens, belief in a flat Earth persisted among many others. Not until explorers first circumnavigated the globe in the 16th century did those beliefs begin to die out.

The man who first measured the world, the Greek astronomer Eratosthenes (c. 276-196 B.C.), lived in Alexandria during the 3rd century B.C. He noticed that on the first day of summer in Syene (now Aswan), Egypt, the Sun appeared directly overhead at noon. At the same time in Alexandria, however, the Sun appeared slightly south (about 7 degrees) of the zenith. Knowing the distance between Syene and Alexandria and assuming that the Sun’s rays were parallel when they struck the curved Earth, he calculated the size of our planet using simple geometry. His result, about 25,000 miles for the circumference, proved remarkably accurate.

Eratosthenes wasn’t the only Greek who tried to measure the Earth. About a century later, Posidonius copied this feat, using the star Canopus as his light source and the cities of Rhodes and Alexandria as his baseline. Although his technique was sound, he had the wrong value for the distance between Rhodes and Alexandria, so his circumference came out too small. Ptolemy recorded this smaller figure in his geography treatise, where it was seized upon by Renaissance explorers looking for a quicker way to the Indies. Had Ptolemy used Eratosthenes’ larger figure instead, Columbus might never have sailed west.

The Greeks also originated the idea that the Sun, and not Earth, lies at the center of the universe. In the 3rd century B.C., Aristarchus of Samos hypothesized that the observed motions of the stars and planets could be explained if Earth revolved around the Sun. No one knows why he made this conceptual leap, although he had made a crude calculation showing the Sun to be much larger than Earth, and perhaps he felt it made more sense for the bigger object to lie at the center

For most ancient astronomers, accurately predicting the positions of the planets was tantamount to understanding the workings of the universe. The far more distant stars were simply the backdrop against which planetary action took place. Ptolemy (c. 100-170) who wrote a 13-volume treatise on astronomy, THE ALMAGEST compiling the achievements of his predecessors, was the last of the great Greek astronomers of antiquity. He developed an effective system for mapping the universe. Basing much of his theory on the work of his predecessor, Hipparchus. Ptolemy designed a geocentric, or Earth-centered, model that held sway for 1400 years. That Ptolemy could place Earth at the center of the universe and still predict the planets’ (7) positions adequately was a testament to his ability as a mathematician. That he could do so while maintaining the Greek belief that the heavens were perfect—and thus that each planet moved along a circular orbit at a constant speed—is nothing short of remarkable. The greatest difficulties he had to overcome were explaining the changing speeds and the occasional east-to-west, or retrograde, motion of the planets. He accomplished this by having each planet move along a small circle, called an epicycle, whose center travelled along a larger circle, called a deferent, with Earth at its center.

Although this scheme came close to accomplishing what he wanted, it still came up a little short. So Ptolemy made a couple of refinements. First, he placed Earth slightly away from the center of the deferent. (A slightly off-center circle comes very close to mimicking an ellipse.) And second, he had the center of the epicycle move at a constant angular speed around a third point, called the equant, which lay on the opposite side of the deferent’s center from Earth. These modifications allowed Ptolemy to predict the positions of the planets with reasonable—though far from perfect—accuracy.

Although trained in the law and medicine, Nicolas Copernicus (1473-1543) was more interested in astronomy and math. By the early 1500s, he realized that Ptolemy’s system for calculating the positions of the planets was much too cumbersome. He decided that the computations would be far simpler if the Sun were placed at the center of the universe instead of Earth, and he worked out the details. Although he shared his ideas with many European intellectuals, he bided his time before publishing—probably a smart idea because he was a canon in a cathedral, where his explosive ideas would not have been popular.

His book detailing the heliocentric model—DE REVOLUTIONIBUS ORBIUM COELESTIUM,  or THE REVOLUTION OF THE HEAVENLY ORBS—finally appeared in print in 1543, the year he died. He dedicated it to Pope Paul III, and a preface was added (without the knowledge of Copernicus) saying that the theory was intended only for making the calculations of planetary positions easier and not meant to be a statement of reality. It must have worked—it didn’t make the list of banned books until 1616. The title also helped give a new meaning to the word “revolution,” which previously referred only to the motion of celestial bodies but has since taken on political overtones made a great leap forward by realizing that the motions of the planets could be explained by placing the Sun at the center of the universe instead of Earth. In his view, Earth was simply one of many planets orbiting the Sun, and the daily motion of the stars and planets were just a reflection of Earth spinning on its axis. Although the Greek astronomer Aristarchus developed the same hypothesis more than 1500 years earlier, Copernicus was the first person to argue its merits in modern times.

In Copernicus’ Sun-centered (heliocentric) view of the cosmos, the planets’ occasional backward, or retrograde, motion comes about naturally through the combined motions of Earth and the planets. As Earth speeds around the Sun in its faster orbit, it periodically overtakes the outer planets. Like a slower runner in an outside lane at a track meet, the more distant planet appears to move backward relative to the background scenery.

Copernicus’ model also explains why the two planets closest to the sun, Mercury and Venus, never stray far from the Sun in our sky. And it allowed Copernicus to calculate the approximate scale of the solar system for the first time. That’s not to say Copernicus’ model was without problems: He still clung to the classical idea that the planets should move in circular orbits at constant speeds, so like Ptolemy, he had to jury-rig a system of circles within circles to predict the planets’ positions with reasonable accuracy.

Johannes Kepler (1571-1630) took the basic heliocentric idea of Copernicus and turned it into a system that worked. Using the extremely accurate positions measured by the Danish astronomer Tycho Brahe, Kepler formulated three laws of planetary motion. First, the orbits of the planets are ellipses with the Sun at one focus. (An ellipse is a closed curve that can vary from a perfect circle to a very long, very thin oval.) The second law describes how a planet travels faster along its elliptical path when it gets closer to the Sun. And the third law gives a precise relation between the size of a planet’s orbit and the length of time that planet takes to orbit the Sun. By abandoning the classical concept that motions had to be circular and at constant speeds, Kepler showed that the universe behaves by its own laws and doesn’t necessarily follow our arbitrary preconceptions.

Kepler took Copernicus’ heliocentric view of the universe and removed the requirement that the planets move in circular orbits at constant speeds. But that was only after he exhausted every combination of circular motions he could conceive. Basing his work on the meticulous and exceedingly accurate naked-eye observations of the Danish astronomer Tycho Brahe, Kepler tried for more than a decade to match the positions of Mars to some sort of circular motion. Only after he ran out of possibilities did he try to fit the observations with another type of curve called an ellipse, the next-simplest form after the circle. He found that the positions of Mars matched almost perfectly with an elliptical path, and that the other planets followed suit.

Many scholars trace the birth of modern science back to Galileo Galilei (1564-1642), who used instruments to observe nature and experiments to understand it. Like Copernicus, he began training for a career in medicine, but later switched to a subject more to his liking, mathematics. Galileo long accepted Copernicus’ idea that Earth and the other planets orbited the sun, but he was the first able to prove it based on his observations with a telescope.

Many people think Galileo invented the telescope, but that’s not true. Spectacle makers in Europe had probably discovered how to make distant objects appear closer well before Galileo. The first telescope to arouse interest, however, was made in 1608 by the Dutch optician Hans Lippershey. When Galileo heard of it, he quickly made his own and turned it on the heavens.

Within a few months he had discovered four moons orbiting Jupiter—destroying the Greek idea that Earth was the center of all motion—and the phases of Venus— overturning Ptolemy’s concept that the Sun and planets all orbited Earth. He wrote of his sensational discoveries in Italian rather than academic Latin so the general public could read about them. His observations improved our knowledge of the universe we live in and helped turn science into an experimental endeavor. For his efforts, and their devastating effect on the religious dogma of the time, he was forced to recant his findings before the Inquisition and spent the last decade of his life under house arrest.

Certainly one of the greatest scientists who ever lived, Isaac Newton (1642-1727) had a profound impact on astronomy, physics, and mathematics. Born prematurely and after his father’s death, Newton had a difficult childhood. His mother remarried when he was just three, and he was then sent to live with his grandparents. After his stepfather died, his mother brought him home to Woolsthorpe in Lincolnshire, where she wanted him to become a farmer. An uncle recognized his scholarly talents, however, and he eventually made it to Trinity College in Cambridge.

Many of his great ideas came in 1665-66, when he spent time back at Woolsthorpe while Cambridge was closed because of the plague. Among his many achievements were the invention of the reflecting telescope—the basic design behind all large telescopes used today; the invention of a branch of mathematics known as calculus, a critical tool throughout science; the elucidation of the three laws of motion; and the development of the law of universal gravitation. Until the coming of general relativity in the 20th century, Newton’s theories were the basis for all cosmological models. When still in his mid-twenties, he was named Lucasian Professor of Mathematics at Cambridge—the post now held by Stephen Hawking.

Copernicus did not prove that Earth moved around the Sun. The first direct evidence came from Newton’s laws of motion, which say that when objects orbit one another, the lighter object moves more than the heavier one. Because the Sun has about 330,000 times more mass than Earth, our planet must be doing almost all the moving. A direct observation of Earth’s motion came in 1838 when the German astronomer Friedrich Bessel measured the tiny displacement, or parallax, of a nearby star relative to the more distant stars. This minuscule displacement reflects our planet’s changing vantage point as we orbit the Sun during the year

Perhaps more than any other person, Edwin Hubble (1884-1953) expanded our view of the universe. At the dawn of the 20th century, most astronomers thought that the Milky Way Galaxy was the universe, and it measured only a few thousand light-years across. In the 1910s, Harlow Shapley showed that the galaxy actually stretches about 100,000 light-years, and Henrietta Leavitt determined that the Large and Small Magellanic Clouds (two companion galaxies to our own, visible from the Southern Hemisphere) lay slightly outside the Milky Way’s border. But one big question that remained was the nature of the fuzzy patches of light known as nebulae.

In 1923 and 1924, Hubble used the largest telescope in the world, the 100-inch Hooker Telescope at Mt. Wilson, to examine the Andromeda Nebula. The Oxford-trained lawyer-turned-astronomer detected for the first time stars similar to those in our own galaxy. By comparing how bright the stars appeared with how much light they actually gave off, he estimated the distance to the nebula as nearly a million light-years, clearly making it a huge galaxy in its own right. Hubble went on to find the distances to many other galaxies, eventually pushing the frontiers of the universe out to hundreds of millions of light-years.

By the late 1920s, Edwin Hubble had been taking spectra and measuring distances to a large number of galaxies. From each spectrum he learned the galaxy’s redshift, which told him how fast it was moving away from Earth, then he compared that with the object’s distance. What he found set the stage for much of 20th-century cosmology: the farther away the galaxy, the faster it receded. The relationship that a galaxy’s speed is directly proportional to its distance became known as Hubble’s Law. It was observational proof that we live in an expanding universe, and it helped lay the foundation for the big-bang theory of the universe’s origin.

The picture of the Sun lying at the center of the universe held sway until early this century, though by then astronomers were beginning to realize that the universe was bigger than they had presumed. Back in the 18th century, they started to suspect that the Sun was part of a large system of stars, called a galaxy, but the general consensus was that the Sun lay at the center. Then, in the 1910s, the American astronomer Harlow Shapley showed that we actually reside in the galaxy’s backwaters, some 30,000 light-years from the center of a system that itself measures about 100,000 light-years across. The heliocentric view was dead, replaced by the new “galactocentric” idea.

Our view of the universe was just beginning to grow larger. One big question remained: What was the nature of the fuzzy patches of light known as nebulae? The 18th-century French comet hunter Charles Messier had catalogued more than 100 such objects, some of which appeared to have a spiral shape. By the 1920s, literally thousands of these objects were known. Although the 18th-century philosopher Immanuel Kant had speculated that they were large star systems like our own, it fell to Edwin Hubble to prove it. Using the 100-inch telescope at Mt. Wilson in California in the 1920s, Hubble observed individual stars in some of these fuzzy patches and, based on their apparent brightness, calculated them to be far outside our own galaxy. The universe suddenly became filled with thousands, if not millions, of galaxies.

It was only a matter of time, and just a few short years at that, before the galaxies themselves were found to be moving. Hubble proved that the universe is expanding, with every galaxy flying away from every other galaxy in response to a prodigious “Big Bang” that occurred some 10 to 15 billion years ago.

We’ve come a long way in the last few millennia, from a small, quiet universe existing above a flat Earth to a vast, dynamic one with Earth out in the boondocks. Despite our sophisticated theories and in-depth knowledge, we still have a way to go before we know everything about our universe. As Newton once said: “To explain all nature is too difficult a task for any one man or even for any one age. ’Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things.”