Jupiter's Moons and the Longitude Problem
May-June 2002, Mercury Magazine, pp. 34-39
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.
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.
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
A Heavenly Clock
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
Problems at Sea
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.
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
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 (firstname.lastname@example.org) 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
-----Chronometers were delicate scientific
instruments; if you gave them a licking they
Determine Your Longitude with Jupiter's Moons
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.
|PASS v7 Article|