Jupiter's Moons and the Longitude Problem

May-June 2002, Mercury Magazine, pp. 34-39
by Robert Mentzer

For a period lasting over a century, the most effective way to determine longitude was to observe the Galilean moons of Jupiter.

On July 15, 1806, Captain Zebulon Pike led a party of 23 soldiers and 51 Amerindians westward out of St. Louis, Missouri. One of Captain Pike's assignments was to escort the Amerindians back to their villages. He was then to continue on and explore the southwestern part of Thomas Jefferson's new Louisiana Purchase. On this very day, Meriwether Lewis and William Clark were near the Great Falls of the Missouri River (in Montana) on the last leg of their return journey, which would end in September. They had been sent to explore the rich furtrapping areas of the northern part of the purchase. Later in his expedition, Pike traveled to eastern Colorado and described a mountain that now bears his name, Pike's Peak.

On August 23, 1806, Pike camped with the Osage Amerindians in their villages near the Kansas-Missouri border. On that day he wrote in his journal, "Took equal altitudes and a meridional altitude of the Sun, but owing to flying clouds, missed the immersion of Jupiter's satellites." In the middle of what Pike would later call "the great American Desert," surrounded by hostile Amerindians, hundreds of kilometers from civilization, he was looking through a telescope. Isn't this rather strange behavior for a rugged adventurer? Actually no, for Pike was doing what explorers had been doing for more than a century: He was using Jupiter's moons to determine his longitude.
Longing for Longitude

It's easy to find one's latitude by measuring the altitude of the North Star (Polaris). Alternatively, one can measure the peak height of the noon Sun, or of a star after dark, and then find the latitude from a set of tables. Longitude, on the other hand, is much more difficult to determine.

Being at 40° north latitude means you are somewhere on a circle that runs around the world 40° north of the equator. But where on that circle are you? Polaris will appear 40° above the northern horizon on any location on that circle and the Sun's peak altitude will be the same. The only difference will be that the Sun will peak at different times at different points on the circle as Earth rotates. So time is the key to finding longitude. Tables can tell you when the Sun or certain stars will peak over Greenwich, England. It takes Earth 24 hours to complete one 360° rotation, so Earth turns 15° per hour. If you have an accurate clock set to Greenwich time, and the Sun peaks an hour later at your location than the table says it peaks in Greenwich, you are one hour (or 15°) west of Greenwich. Given an accurate clock, you can easily determine longitude.
But prior to about 1770, clocks were not accurate enough to determine longitude. Travelers could only make crude estimates of their longitude. This was a real concern for sailing ships, which were constantly in danger of running aground because of poor longitude estimates. In 1707 a British fleet approaching the southern coast of England (commanded by Sir Clowdisley Shovell) ran aground on the Scilly Islands during a storm, with the loss of 2,000 lives. Those 2,000 deaths in the England of 1707 were equivalent to about 60,000 deaths in today's America. Imagine the shock if 300 commercial jets crashed in one day. Almost every person would know a victim. The public outcry in England forced the Admiralty to offer a prize of 20,000 pounds, a fortune at the time, to anyone who could solve the longitude problem.

To win the Admiralty's prize, one had to determine longitude to within half a degree after a long ocean voyage. At the equator, Earth's circumference is about 40,000 kilometers (24,900 miles) and the Sun takes 24 hours to circle. So the Sun appears to move at 1,670 kilometers (1,040 miles) per hour, or 15° per hour (10 in 4 minutes). To win the prize, the clock had to be within half a degree (or 2 minutes) of the correct time. Any clock that loses one second a day for a year would be off by 365 seconds, or 6 minutes. In 1707, no clock in the world came anywhere near the required accuracy.

A century earlier Galileo had to use crude water clocks for his work on falling objects. But he made two key suggestions that were of tremendous help in solving the longitude problem. The first was his observation that a pendulum could be used as a clock. By 1660 Dutch astronomer Christian Huygens had perfected the pendulum clock. But pendulum clocks that kept excellent time when hanging on a motionless wall were hopelessly inaccurate when carried over rough terrain or on a pitching ship.

[This world map from 1713 is a reproduction of Giovanni Domenico Cassini's 1696 map, which was the first world map created with accurate longitude measurements from the observations of Jupiter's moons. Inscriptions are written in French and Latin. Courtesy of the Serge A. Sauer Map Library, University of Western Ontario.]

A Heavenly Clock
It was Galileo's second idea that led to a successful method of determining longitude. In 1609-1610 Galileo had used his new telescope to discover four moons circling Jupiter (later named lo, Europa, Ganymede, and Callisto). Galileo quickly realized that the steady procession of circling moons was a heavenly clock that could be seen from anywhere on Earth whenever Jupiter was in the night sky.

A good mathematician could take observations of the eclipses of the moons and predict the times of future eclipses. An observer anywhere on Earth would look at tables to see if any eclipses occurred that day or in the next few days. The observer would pick some likely eclipses based on estimates of one's longitude. The observer would look at Jupiter, identify the moons, and watch an eclipse. The observer could then set his or her clock to the listed Greenwich time for that eclipse.

An extremely accurate clock was no longer needed. With the clock now set correctly to Greenwich time, in the next few days one would measure the time when the noon Sun peaked. The observer would then compare this time with the Greenwich time listed in the almanac. If the Sun peaked 5 hours later than the table said it would, the longitude would be 5 hours times 15° per hour, or 75° west of Greenwich. And that is exactly why Zebulon Pike was observing Jupiter's moons from that lonely Kansas prairie in 1806.

Pike didn't use Galileo's tables because Galileo was never able to calculate the eclipses accurately enough. That honor fell to Italian-born astronomer Giovanni Domenico Cassini, who published an improved set of tables in 1668. Cassini had emigrated to France after King Louis XIV had formed the Royal Academy of Science. The king wanted to make France the world leader in science, so he was recruiting the world's best scientists. Cassini's work was perfect for another of the Academy's projects, the accurate mapping of France. This endeavor required the determination of longitude, the very thing that Cassini's work promised to do with unsurpassed accuracy. So the king made Cassini an offer he couldn't refuse.

Cassini's team traveled to the major cities of France and with its telescopes observed an eclipse of one of Jupiter's moons. This enabled the team to set its clocks to the correct reference time. The next day the team members would time when the Sun peaked. If it peaked one-tenth of an hour later than the time the tables listed for Paris, they were one-tenth of 15° (1.5°) west of Paris. With the Sun moving at about 1,600 kilometers (1,000 miles) an hour, this placed the city 160 kilometers (100 miles) west of Paris.

["I pay my astronomers well and they have diminished my kingdom." - King Louis XIV]

The results were revelatory. It was only a few hundred miles from Paris to the coastal cities over roads that had been trodden by Roman engineers and countless Frenchmen. Yet these cities were actually up to 100 kilometers (60 miles) closer to Paris than the old maps had indicated. This was a huge error, which exposed the inaccuracies in the older methods. King Louis is rumored to have said, "I pay my astronomers well and they have diminished my kingdom."

Having mapped France, Cassini and his team moved on to do the world. France was in an expansionist phase and her explorers were everywhere, closely followed by her Jesuit priests. Cassini began to train mathematically minded young priests. When they reached their assigned destinations, they measured the latitude and longitude and sent the results back to Paris.

Meanwhile, Cassini began to lay out a huge circular map on the third floor of the Observatoire de Paris. A circle about 10 meters in diameter was drawn on the floor with the North Pole at the center. As longitude from around the world were reported, thee e crc added to this map. Cities and farflung locales such as Québec, Santiago, Lisbon, Venice, Cairo, Siam, India, Canton, and Peking were added. The first accurate map of the world slowly took shape. In 1696 Cassini published his new map, the first ever to use Jupiter's moons to determine longitude. The era of truly accurate maps had arrived. More than a century later, Zebulon Pike's observations went into improved maps of the American West.

Problems at Sea
But a technique that worked well on land was hopeless at sea. No one standing on the moving deck of a ship could possibly keep a telescope trained on those tiny moons of Jupiter, so the Admiralty continued to search for a suitable method of determining longitude. In 1775 Captain Cook returned from his second voyage singing the praises of an amazing chronometer built by John Harrison, which easily met the requirements for the Longitude Prize.

Harrison was an English clockmaker who devoted his life to perfecting a clock that could win the prize (Dava Sobel describes his trials and tribulations in her excellent book Longitude). One of Harrison's sea trials was a trip to the Caribbean, where the chronometer's prediction of longitude was checked by observations of Jupiter's moons.

After a century of being the only accurate method of determining longitude, Jupiter's moons had a serious rival. In fact, it had two rivals. Britain's Astronomer Royal, Nevil Maskelyne, had introduced a method called "lunar distances," which used the Moon's motion against the backdrop of fixed stars. In principle this was the same as using the motions of Jupiter's moons around Jupiter. But the technique was very complicated, requiring three measurements of angles in the sky as close together in time as possible along with at least 30 minutes of calculations. Its advantage was that the Moon wasn't hidden in the Sun's glare as often as Jupiter was. Eventually, the chronometer method would prevail. It was the simplest and it could he used on days when the Sun or clouds interfered with measurements of the Moon or Jupiter.

Jupiter's moons and their shadows routinely cross the planet's face from our point of view. This is because we're viewing Jupiter and its moons along the Jovian system's orbital plane. Such crossings are called transits. lo transits every 1.77 days, while Europa traverses every 3.55 days. It's 7.15 days between transits for more distant Ganymede and 16.69 days between transits for Callisto, when transits happen at all.

A 6-inch or larger backyard telescope working at 200 power will show transiting moons as disks against Jupiter's face. b's disk appears grayish on Jupiter's cloudtops, while Europa is very light and often difficult to recognize, especially when it lies in front of a bright hand in Jupiter's atmosphere. Ganymede and Callisto appear somewhat darker, so they are usually easy to see. The best time to spot a transiting moon is just as it enters or leaves Jupiter's disk. A moon's disk stands out more visibly against Jupiter's edge (limb), which is darkened because of the effects of our looking through a thicker cross section of the planet's atmosphere.
Transits of moon shadows are even easier to spot. There's no mistaking a black dot-like impression on Jupiter's cloudtops. Before Jupiter reaches opposition, shadows creep onto the planet's disk before the satellite begins its transit. After opposition, the satellite goes first. In the case of Ganymede and Callisto, several hours can elapse between the time when a satellite first transits and when its shadow appears.

Periodically, Jupiter eclipses each of the four large moons as they pass into the planet's mammoth shadow. In a telescope, a moon's brightness takes several minutes to fade to black as it enters the shadow. Reappearances are just as gradual.

When Earth passes directly between Jupiter and the Sun (meaning Jupiter comes to opposition), as it did last December 31, Jupiter's shadow falls directly behind the planet. (Next year's opposition is February 2.) But the viewing geometry changes just a bit during the months leading up to and away from opposition. Our perspective allows us to peer slightly around the left or right side of Jupiter and look down this shaft of darkness.

This May and June, the shadow projects from behind the planet's left, or east, side. After Jupiter passes behind the Sun on July 20 and emerges into the morning sky, we'll be looking in on the shadow emerging from the planet's right, or western, limb.

Io orbits so close to Jupiter that, depending upon our viewing perspective, we see it either entering or exiting Jupiter's shadow. We never see both on the same evening. This is because Jupiter's disk almost entirely obscures our view of the planet's shadow at b's distance from Jupiter. After opposition, we always see lo disappear behind the limb of Jupiter and then reappear from the planet's shadow. Conversely, before opposition we always see lo disappear into the shadow and later reappear from behind the disk.

The same largely holds true for Europa. Ganymede and Callisto, however, are far enough from Jupiter so that we see both entry into and exit out of eclipses, except at times near opposition. Eclipse lengths vary because these moons don't always pass through the middle of Jupiter's shadow: Ganymede averages 3.25 hours, while Callisto takes about 4 hours.

Because of a combination of Sun angles (because of the slight tilt of Jupiter's axis to its orbit) and Callisto's distance from Jupiter, Callisto misses Jupiter's shadow entirely for 3 years at a time. Callisto entered its most recent eclipse season late last year and will regularly pass through Jupiter's shadow on each orbit until about 2004.

To get the lowdown on everything happening with the moons of Jupiter, including their eclipse times, visit http://pds-rings.seti.org/tools/viewer2_jup.html
John Shibley

Jupiter's moons still had some advantages, so this method would not die easily. Zebulon Pike's 1806 expedition couldn't afford a chronometer even if one had been available in St. Louis. In addition, the lunar distance method was so difficult that Pike went with the old but reliable method of observing Jupiter's moons. Three years earlier, Lewis and Clark's well-financed expedition had carried a chronometer purchased in Philadelphia and equipment for using the lunar distance method, which Thomas Jefferson favored. A few months into the trip the chronometer stopped.

Chronometers, which worked fine when kept in a special case in the captain's cabin, could not take the pounding of a long trip on a packhorse or the rocking of a canoe on a wild river. These were delicate scientific instruments; if you gave them a licking they stopped ticking. So the situation had just reversed. Jupiter's moons worked fine on land but not on a ship. Chronometers worked fine on ships, but they couldn't hold up during extended journeys across land.

Clark reset his chronometer with the lunar distance method whenever it stopped, but with only a few weeks of training in the technique, his results were disappointing. Ferdinand Hassler, the West Point mathematician who was given the observations, was reported by Jefferson in 1817 to have "given up the calculations in despair:'

In 1832 Captain Benjamin Bonneville used Jupiter's moons to determine his longitude on his western expedition. John Fremont's western expeditions of 1842-44 carried multiple chronometers, all of which broke or ran erratically. Fremont eventually used Jupiter's moons to determine his longitude. But these were last gasps of a dying system. Chronometers were getting better, and this improvement, along with the ability to send time signals by telegraph, led to the demise of the Jupiter moons system. Thus a method that produced the first accurate maps, a method that was the only accurate way to determine longitude for 100 years, and which played an important role for another 70 years, fell by the wayside of scientific progress.

The moons of Jupiter still endlessly circle the giant planet, and Jupiter still shines down upon us as it has through the ages. So next time you are out on a starry night and look up and see Jupiter, take a moment to think of Galileo, Cassini, the Jesuit priests, Zebulon Pike, John Fremont, and all the others who gazed across 600 million kilometers into the blackness of space in order to determine just where they stood on this green Earth.

Retired physics and astronomy teacher ROBERT MENTZER (robmentzer@comcast.net) is treasurer of the Delaware Astronomical Society. One of his hobbies is reading about the early exploration of the West. When he came across references to Jupiter's moons in both Pike's and Fremont's journals, he had to
find out more. This article is the result.

-----Chronometers were delicate scientific instruments; if you gave them a licking they stopped ticking.-----

Determine Your Longitude with Jupiter's Moons
by Morris Jones

It was MIT physicist Philip Morrison who taught me, in a television documentary, how to use Jupiter's moons as a system for synchronizing clocks. This is the first step in calculating longitude with astronomical observations. With an ephemeris for Jupiter satellite transits and occultations that is accurate for the time at the Royal Greenwich Observatory, you can synchronize your clock to the observatory's by watching the scheduled event. The difference between your local time and Greenwich local time reveals your longitude.

On a clear night in late February, I decided to try this experiment. I set up my 4-inch refractor on my back deck outside my house in San Rafael, California. My favorite Jupiter ephemeris (www.projectpluto.com/ jevent.htm) predicted an occultation of Europa for 0510 Greenwich Mean Time (GMT) the following day, or 9:10 p.m. Pacific Standard Time, my local "standard" clock. This event provided a splendid opportunity to synchronize my own GMT clock.

These days it's easy to set your watch to GMT. My computer stays synchronized to a variety of reference clocks available on the Internet using the network time protocol (NTP). So I already knew that my watch was correct.

At about 8:40 p.m., I had my mount aligned and tracking, and Jupiter was looking big and beautiful. I wanted to test my ability to judge the precise moment when the occultation was complete, so I stopped looking at my watch. I knew it was several minutes before the ephemeris's predicted time when I first saw Europa brushing against Jupiter's limb. It was like watching a very distant sunset as Europa sank farther behind Jupiter's disk, appearing as a tiny lump on the edge. The lump shrank to a smaller dot, but it was still there. Would I be able to tell the exact moment of occultation? I looked again and couldn't see Europa. "But wait' I thought, "there's still a tiny pinpoint on the edge. Or is it just my imagination?"

Finally it was clear that nothing was left. No odd pinpoints appeared even when I used averted vision. It was time. I looked at my watch. It was 9:10:30 - dead center in the designated minute.

Following through with the experiment, now that I had a clock synchronized to GMT, I could calculate the sidereal time at Greenwich. Sidereal time, the right ascension coordinate crossing overhead at any particular moment, is the key to calculating longitude. Longitude is simply the difference between the sidereal time at a reference location (Greenwich) and the local sidereal time, expressed as degrees instead of hours, minutes, and seconds.

But my experiment was missing a crucial piece of equipment that a 19thcentury surveyor would have had: a transit scope. A transit scope points only along the meridian. The mount would be plumbed to vertical, and aligned very carefully with the north celestial pole. I could approximate a transit scope by turning off my mount's clock drive and reorienting the mount so the telescope is constrained to rotate along a line including the zenith and the north celestial pole. Alas, most telescope mounts, mine included, won't twist into such a configuration.

If I had such a device, I could watch for any charted star to cross my local meridian. At that moment, my local sidereal time would match the right ascension of that star. I would consult my recently synchronized GMT clock and convert that time to the Greenwich sidereal time, using published tables. Take the difference between local sidereal time and Greenwich sidereal time, convert it to degrees, and bingo! Longitude.

MORRIS JONES (www.whiteoaks.com) serves as newsletter editor for the San Jose Astronomical Association. He is also an avid member of the San Francisco Sidewalk Astronomers.