An Introduction to Solar System Astronomy
Prof. Richard Pogge, MTWThF 9:30
The Copernican system provides a straightforward geometric means to measure planetary distances in terms of the size of the Earth's orbit, or in units of Astronomical Units (AU).
Nothing could be simpler, except for one, minor detail...
From antiquity up until the 1700s, estimates of the distance to the Sun differed widely from each other. Aristarchus of Samos working in the 3rd Century BC estimated that the Sun was about 20x further from the Earth than the Moon, or about 8 million km in modern units. This is about 20 times too small. Ptolemy, Copernicus, and Tycho Brahe all adopted a comparable value of 1210 Earth radii (also ~8 million km). Johannes Kepler realized that if the AU were that small, Tycho should have been able to detect the geocentric parallax of Mars but did not, which suggested that the AU had to be at least 3 times larger, or at least 24 million km. All of these estimates were based on naked-eye observations. With the invention and application of the telescope, much finer observations were possible, and sizes for the AU up to 111 million km, estimated by Edmund Halley in 1716, were proposed. Taken together, by the time of Halley's influential paper in 1716, the various estimates of the distance of the Sun had an experimental precision of only about 1 part in 5. This is like saying you are 6-feet tall, give or take a foot or so. It was an unacceptable state of affairs and had to be improved.
Every now and then, Mercury and Venus pass across the face of the Sun. Because Venus is closer to the Earth, and its orbit tilted slightly (~3-degrees), these events are very rare, occuring every century or so. Mercury, being closer to the sun, transits more frequently, at intervals of 7, 13, and 33 years in May and November, when Earth and Mercury are in the same plane. Mercury, however, is so tiny that it is hard to observe the exact timing of the transit with any accuracy. It was one of these transits of Mercury in 1677 that got Halley to thinking. He was sent to observe a Mercury transit from the island of St. Helena (even then, well before it became the final home of Napoleon, a by-word for the middle of nowhere). Halley was able to accurately measure the amount of time it took Mercury to cross the sun's disk using a 24-foot [long] refracting telescope. This experience led him to realize that that a transit of Venus, because Venus was closer to the Earth and therefore had a greater parallax than Mercury, could be use to estimate the parallax to the Sun. In fact, they would be much better than Mercury transits, despite their considerable rarity. He calculated that if a Venus transit were observed not from one place but from many widely-separated locations on the Earth, the combined data would provide an excellent way to measure the parallax of the Sun, and hence its geometric distance from the Earth with unprecedented precision.
The key is "precise timing" of the length of the transit from limb-to-limb of the Sun. A transit of Venus across the Sun takes about 7 hours, but you need to measure this time to a precision of a few seconds to be of any use. Halley calculated that if you can get the timing precision down to 2 seconds, then it should be possible to measure the sun's parallax to a precision of 1/40-th of an arcsecond, which would provide a distance to the sun with an unprecedented precision of 1 part in 500! (This number was based on his assumption that the solar parallax would be 12.5 arcsec). Observing from more than 2 locations on the Earth not only improves the precision, it also gives you a hedge against bad weather and other mishaps. Only by combining many observations from different locations, from both transits, do you have a hope of getting a precise measurement of the AU.
Transits of Venus are even more rare than transits of Mercury. In order for a transit to occur, Venus and Earth have to be in the same plane on the same side of the solar system. The tilt of Venus' orbit (about 3.3 degrees) means that the Earth only crosses the plane of Venus' orbit twice a year, within a few days of December 8th and June 7th. But, there is no guarantee Venus will also be between the Earth and the Sun at that precise time. However, because the period of Venus' orbit around the Sun is almost 8/13-ths that of Earth's orbit (more precisely, the ratio of Venus' orbital period to that of the Earth is a fraction more like 243/395), such lineups can occur, but rarely: in cycles of 121.5, 8, 105.5, and 8 years (note that 121.5+8+105.5+8=243, that's no accident). This means, in round numbers, that Venus transits occur in pairs separated by 8 years roughly every 120 to 105 years apart.
Halley knew that the last pair of Venus transits was in December of 1631 and 1639. The first transit was predicted by Johannes Kepler, using calculations based on the then heretical idea that the Earth went around the Sun. Kepler knew it wouldn't be observable from Europe, but suggested that mariners at sea might keep an eye out for it. Nobody succeeded in observing it. The second transit in the 8-year pair was predicted by British astronomer Jeremiah Horrocks, who discovered the 8-year pairing of transits that Kepler had missed because he (Kepler) had failed to account for the size of the Earth in his calculations. Horrocks predicted that a Venus transit would occur on Dec 4 1639. Horrocks was called away before the first transit began, but he observed as much as he could before sunset. His friend William Crabtree observed 30 minutes of the transit before the sun set below trees. There were no other known observers. Neither Horrocks nor Crabtree made the kinds of measurements that would be needed to compute the solar parallax, nor were they separated enough in longitude or latitude to make such measurments very precise. But, both proved that the phenomenon existed, and that it was accurately predictable.
Now that Halley had determined what data were needed to convert Venus transit timings into the distance to the Sun, he needed a transit to observe. The problem was that the next pair of transits would not be until June of 1761 and 1769, 121.5 years after the transit seen by Horrocks and Crabtree, by which time he knew he would be long dead.
Undeterred, in 1716 Halley formulated a detailed plan for how the transits of 1761 and 1769 should be observed in order to best measure the distance of the Sun from the Earth. It would require considerable planning, as the farther apart the observers were on the Earth, the better, and that really does mean that the observers must literally travel to the "ends of the Earth". Further, since the transit lasts only 7 hours or so, you have be in the right place at the right time. If the opportunity presented by the 1761/1769 transits was missed, the next chance would not be until the transits of December 1874 and 1882, and after that the next pair would not occur until June of 2004 and 2012.
For astronomers in the 18th century, it would be literally the observations of a lifetime.
The other detail was that in order for the data to be of any use, the observers needed to measure the latitude and longitude of their observing stations with great accuracy. The problem, of course, was that finding longitude on land while not impossible, still required extremely careful observations. The astronomers sent out had to be the best in their profession and very well equipped to make the necessary observations. The observer was required to get the observing station well in advance of the transit, prepare the observing site, setup their equipment, and work hard to measure their precise position both before and after the 7 hours of the Venus transit. Since travel times were measured in months and years in this age, this meant observing runs that were to last years in many cases.
Despite these difficulties, the importance of measuring the distance from the Earth to the Sun was such that for the first time in recorded history astronomers from all over the world collaborated in an international project to measure an astronomical event. By modern standards, the scale of the enterprise can be compared to the space program: it required capital outlays from governments, the cooperation of civilian and military authorities, and a few, brave adventurers willing to travel far and risk life and limb for a common scientific goal.
In addition to all of the problems of long-distance travel, packing clocks, telescopes, instruments and other baggage needed to make the measurements, politics intervened to make the travel more exciting.
Most of the astronomers were English and French, and the first transit was occurring during the height of the Seven Year's War between England and France (here in the US we know the North American campaigns as the French and Indian War). The Seven Year's War was the first true "world war" and was fought in nearly every hemisphere. Its outcome was to essentially decide much of the subsequent course of European history.
Despite bitter the hostilities between their homelands, astronomers from each warring nation were given letters of transit and cooperation to pass the enemy lines and shipping lanes unmolested. Many observations had to be attempted, as weather, illness and the fortunes of war might made the odds difficult at best.
The astronomers of the first transit and their adventures are as follows:
Maskelyne was sent to St. Helena in the mid-Atlantic, then as now a bye-word for the middle of nowhere, where the food was bad and the weather stank. He got clouded out and missed the end of the transit, making his data mostly useless.
Dixon and Mason were originally dispatched to Bencoolen (modern Bengkulu) in Sumatra, but their ship (HMS Seahorse) was attacked by the 34-gun French frigate le Grande only a few hours after sailing from Portsmouth England, forcing them to limp back into port with 11 dead and 37 wounded. After much delay repairing and refitting they reluctantly set sail again (after threats from the Society if they decided to bale out), but only made it as far as Cape Town South Africa before the transit. Undeterred, they changed their plans, setup their observing station in time, and got excellent data.
They worked so well together that in 1763 the British Government dispatched them to the American colonies to survey the disputed border between the colonies of Pennsylvania and Maryland. The border they surveyed is now the border between those two states, and is better known as the "Mason-Dixon Line".
Winthrop was a professor of mathematics and natural philosophy at Harvard College in the Massachusetts Bay Colony. He successfully petitioned the Province to provide a ship to take him to St. Johns, Newfoundland, which was about the only place in North America during this transit where one could observe the transit. He and his three assistants got good observations of the last part of the transit despite a plague of biting insects.
Pingré was sent to the French island of Roderigue, off the coast of Madagascar in the Indian Ocean. Pingre got rained out on transit-day, but saw at least part of the transit, so it wasn't a total loss. During his post-transit work on the island a British Man-O-War shelled and sacked Roderigue. This was to happen two more times while Pingré was in residence. Finally, he managed to catch a ship back to France and almost made it before they were beset by a British warship (again!). Pingré's ship, after a fierce battle, was captured and Pingré was transported to Lisbon as a prisoner of war for exchange. Having had enough of ships, he finished his trip overland. Among his comforts aboard the British warship was the company of the ship's doctor and his stock of "medicinal alcohol", or in Pingré's words:
"Liquor gives us the necessary strength for determining the distance of the Earth from the Sun."
Chappe d'Auteroche was sent to Tobolsk in Siberia, traveling first by horse-drawn sled, on which conveyance he barely made it across the frozen Volga river before the ice pack broke up. He of course arrived during the famous Russian "rasputitsa", when the steppes turn into a sea of gooey mud (as later discovered by the armies of both Napoleon and Hitler in their turns - nobody ever learns). Chappe arrived in Tobolsk with only 6 days to spare before transit day. While setting up his equipment, he had to be physically protected by a cordon of armed Cossack guards because the local peasantry was convinced that the unusually severe spring floods were being caused by this strange foreigner using his bizarre instrument to mess with the Sun.
Despite this, he managed to obtain very good timings of the transit.
Who we shall call "Le Gentil" for short. Mssr. Le Gentil was an educated French nobleman (if you didn't guess from the name) dispatched from France on March 26, 1760 to Pondicherry, a French possession in eastern India. After 3 months at sea, he arrived at the island of Mauritius, a French colony in the Indian Ocean. On arrival, he learned that the Indian Ocean was swarming with British warships, and that Pondicherry was under siege by the British land forces. Despite all his papers giving him free passage, the problem with presenting papers at sea was that you had to get closer than cannon range to an enemy vessel to present them, and this was a major shooting naval war going on, so their possession was next to useless.
Le Gentil was not to be deterred. He talked his way onto a troop ship bound for Pondicherry to try to raise the siege. Off the Indian coast, they learned from passing ships that Pondicherry had fallen 4 months before, so the captain turned around and sailed back to Mauritius.
The transit occurred while Le Gentil was at sea. From the pitching deck of a French troop ship, it was impossible to make any useful observations.
Undaunted, Le Gentil decided to stay in Mauritius and wait until the 1769 transit 8 years later. He set about computing what the best location would be, and made a series of scientific studies of Mauritius and nearby Madagascar (botany, zoology, geology, and anthropology - Le Gentil was very versatile). He finally determined that the best site for 1769 would be Manila in the Philippines, and set about planning his next expedition.
With data in hand from the first transit, astronomers once more set out to observe the second transit. By this time the Seven Year's War had ended, and travel was as safe as it always was, at least insofar as naval gunnery was removed from the long list of things that could kill you at sea.
(Don't laugh, the good Jesuit father was Austrian, and in German "Hell" means "Light" or "Bright"). Accompanied by assistant and fellow Jesuit Janos Sajnovics, Father Hell went to Vardø, Norway, which is located at latitude 70° north, a few degrees above the Arctic Circle. Even in June it is cold as, well, anyway, he got good data on the transit, that was later (unfairly) disputed. It was not until the 19th century that Fr. Hell and his observations got their due. Fr. Hell was also an early exponent of "magnetic healing" and apparently coined the term "animal magnetism", a term later lifted by fellow Austrian and infamous crank Franz Anton Mesmer (from whom we get the word "Mesmerize").
Wales was sent to Fort Churchill on Hudson's Bay, then as now pretty much in the middle of nowhere, and also then as now the Polar Bear capital of the world. He left a year early and decided to winter over. Not a good idea as it turned out. His journals record how in boredom during the long, harsh winter he observed how it took only about 5 minutes for a pint of brandy to go from liquid to mushy to frozen solid. The brief summer helped him thaw out, just in time for the season of black flies, mosquitoes, horseflies and other carnivorous flying insects which tried their best to eat him alive while setting up his equipment.
He did manage, however, get good transit timings despite the bugs, and then disappears from astronomy, apparently having had enough.
This time Chappe d'Auteroche was sent to Mission San Jose del Cabo on the tip of Baja California, then Spanish territory. The trip down and setup was uneventful (unlike his Siberian adventure), and he got excellent timings on transit day. Shortly after the transit, however, an epidemic of fever swept through the region. Chappe, also trained as an physician, nursed the sick as well as he could, but soon took ill himself and died a few days later. In all, roughly three-quarters of the inhabitants of the tiny mission village and all of the French Academe expedition members save three died. These set out with the precious data, two dying en route. The sole survivor, a man named Pauly, made it back to Paris with Chappe's notebooks, in 1770. Chappe's data were to prove the best made of either transit.
Captain Cook set sail from Plymouth in 1768 on the H.M.S. Endeavor. The Endeavor's mission was to circumnavigate the globe and explore the southern Pacific Ocean. On the way, they were to put in at the South Pacific island of Tahiti to observed the Transit of Venus. On board Endeavor was a team of scientists including the naturalist Joseph Banks and the astronomer Charles Green. After more than 7 months at sea, they dropped anchor in Matavia Bay on the mythic island of Tahiti. Cook and his crew were only the third European ship to visit Otahete, as the locals called their island, and they were warmly welcomed. The expedition astronomers, with help from a detachment of Royal Marines, setup an observatory on a high point of ground above the bay still known to this day as "Point Venus" and settled down to prepare for the transit.
Meanwhile on the beach, the sailors were characteristically bored, but at least the weather was pleasant, the food was fresh, and the local women were friendly. Very friendly. Maybe too friendly. As always, an active trade got going between the sailors and the Tahitians. The Tahitians were particularly fascinated by iron and metal of any kind since they had no natural sources of their own. They especially prized iron nails, which were so useful for so many things. The Tahitians loved iron nails, and would do just about anything for a nail.
Anything at all, in fact...
The situation was simple yet volatile. On the one hand you have friendly Tahitian women willing to trade sex for iron nails, and on the other hand you have lonely, bored British sailors on the beach with nothing to do but figure out how to get their hands on iron nails. And between them you have the good-ship H.M.S. Endeavor riding at anchor in Matavia Bay. A wooden ship held together with iron nails.
Captain Cook was no fool, he came through the ranks so he knew his sailors. And he knew about the H.M.S. Dolphin, the first European vessel to visit Tahiti only 2 years previously (1767) under the command of Capt. Samuel Wallis. The H.M.S. Dolphin nearly fell apart in Matavia Bay because of her sailors' sudden enthusiasm for carpentry. Cook issued strict orders regarding the trade in nails with the Tahitians:
To put some teeth into this order, Cook had Marine guards posted at the carpenter's shop on board (and had provisioned the ship with extra barrels of nails secreted in the hold, just in case). As a result, the H.M.S. Endeavor stayed intact and the men managed to stay happy (although they all slept on deck because the iron hammock rings were put to other uses).
Meanwhile, despite the temporary theft of a couple of the shinier instruments, Green and his companions (including Capt. Cook) got excellent transit timings. It was on this trip that the infamous "black drop" effect received particular attention. Previous observers had noted that when Venus is just inside the limb of the Sun at the start and end of the transit, the silhouetted disk of Venus appears to be connected by a thin "meniscus" between the planet and the limb of the sun, giving it the appearance of a black drop of liquid oozing in from the limb. This effect is an optical illusion caused by the smearing of the image of Venus by turbulence ("seeing") in the Earth's atmosphere. The "black drop" makes it very difficult to judge the exact moments of "interior contact" that are used to time the duration of the transit. It was to prove a most intractable problem, and ultimately limited the precision of the transit timings to about 10 seconds instead of the hoped-for 2 seconds by introducing an irreducible and difficult to measure amount of systematic error in the timings. The Tahiti team was hoping that better instruments would reduce the effect, but the primary cause was the Earth's atmosphere as correctly described by Lalande in his 1770 analysis of the transit data. Still, the data were better than anything else that had gone before it.
Sadly, Charles Green did not live to enjoy the fruits of his labors. He died in Batavia (modern Djakarta) on the return voyage. Cook and his crew completed their circumnavigation of the Earth and reached England safely and in triumph. The expedition was a terrific success, and established Cook's fame as a mariner and explorer.
When last we left him, Le Gentil was having the scientific time of his life on Mauritius, studying the islands and planning his observations of the second transit. With hostilities ended he was free to travel wherever he needed to go.
Armed with letters of introduction from the governor of Mauritius (which stayed in French hands) and the French Academe, Le Gentil set sail aboard a Spanish ship bound for Manila in May of 1766. After a weary 3 month voyage, he arrived in Manila to find that the Spanish governor, one Don Jose Raon, was not especially fond of foreigners. Le Gentil tried to setup to make his preliminary observations, but Don Jose suspected him of being a spy and had him tailed and otherwise harassed. Before he got arrested, Le Gentil packed up and sailed to Macao where he tried to find passage to Pondicherry (recently returned to France by the Treaty of Paris).
In February of 1768 he finally managed to secure passage on an Indian ship bound for Pondicherry. The ship had a motley crew of Portuguese and mixed local sailors, and the only other paying passengers were Armenian merchants. They were nearly shipwrecked in the Malacca Straits when the pilot took offense at some slight and decided to sulk in his cabin while the crew was left to sail one of the most treacherous stretches of water in the world on their own. Le Gentil and the others finally coaxed, wheedled, cajoled, threatened and otherwise talked him into coming out of his cabin and saving their collective hides. After 32-days of this, he reached Pondicherry in one piece.
At Pondicherry he received a grand welcome from the French governor, and was wined and dined and basically given carte blanch to setup an observatory in a ruined pavilion. An architect and a crew of skilled stone masons were put at his disposal (this was more like it!) and they spent a year preparing the building. In the meantime Le Gentil also undertook a study of classical Indian astronomy, particularly their very accurate methods for predicting eclipses which rivaled contemporary European calculations. Meanwhile, the governor took a liking to the stout, waterproof basement of the pavilion that Le Gentil and his crew had fixed up, and decided it was the perfect place for the main gunpowder magazine for the colony.
No, it didn't blow up.
Transit day approached. The weather was perfect, crystal clear. All the years of preparation were about to pay off.
About 2am on transit-eve, Le Gentil was awakened by the sound of the wind changing. He arose from his bed to see clouds coming in as a front approached Pondicherry.
On Transit day the sun rose behind clouds and stayed there all day for the transit of Venus. After 9 years abroad, and traveling nearly 70,000 miles, he wrote in his journal:
"I was more than two weeks in a singular dejection and almost did not have the courage to take up my pen to continue my journal; and several times it fell from my hands, when the moment came to report to France the fate of my operations."
It is just as well that he did not know that it was sunny in Manila that day.
Le Gentil had nothing left to do but wait in Pondicherry for a ship back home. And wait, and wait, and wait some more. When he got tired of waiting, he came down with severe dysentery and a fever that nearly killed him. Finally he secured passage on a ship bound for Mauritius in 1770. Anything to get out of the scene of his heartbreak. On arriving in Mauritius, he waited around for a ship bound for France. While waiting in Mauritius, a French commissioner arrived who tried to recruit him as the scientist for a trip to Tahiti. We do not know what Le Gentil had to say to the commissioner, but it is clear that he wasn't going anywhere but home.
Le Gentil finally got space on a French ship that left very late in the season. Off the Cape of Good Hope they encountered a hurricane that nearly de-masted the vessel. Leaking and battered, they barely limped back to Mauritius. Le Gentil wasted no time, and managed to talk himself onto a Spanish warship bound for Cadiz. This ship also ran into storms and took nearly 2 weeks to round the Cape.
In August 1771, the ship docked in Cadiz, and Le Gentil, having had quite enough of sea voyages, took off overland bound for Paris. He crossed the Pyrenees on October 8, 1771, after being gone, by his journal, for "11 years, 6 months, and 13 days" from his beloved France.
On arriving in Paris, he found that the caretaker of his home was incompetent and he had been robbed repeatedly. Further, his relatives on hearing a rumor that he had died had proceeded to loot his estate, stripping it bare. The French Academe had also heard the rumor, and had given his chair to somebody else. Le Gentil did the only thing he could do under such circumstances:
He hired lawyers and started suing people.
He got back what he could, but it effectively bankrupted him.
At long last Le Gentil's luck finally took a turn for the better. The Academe created a special chair for him, and best of all, he met, courted, and married a wealthy heiress named Mme. Potier. They lived together in great happiness and had a daughter on whom Le Gentil doted. His memoirs of his journey and his scientific studies of Mauritius, Madagascar, and India met with great critical and commercial acclaim and established his fame.
Guillaume Le Gentil died quietly, at home, on the 22nd of October 1792. After all he went through, his hard-earned good fortune stayed with him to the last. Had he lived another year, his position as a prominent member of the French nobility would have undoubtedly made him another victim of the infamous Reign of Terror that was to claim so many lives.
The analysis of the transit data proved to be worth the great price paid by the astronomers who traveled the world to observe it. While the infamous "black drop" proved the limiting factor in the precision of the timing, Halley's plan paid off handsomely. The combined transit data permitted measurement of the astronomical unit to within 1% of the modern value. In 1771, the French astronomer Lalande used the combined 1761/1769 transit data to derive a distance of 153 ±1 million kilometers. The precision was less than Halley's hoped-for 1 part in 500 or so because of the black drop effect, but still vastly better than previous estimates. In 1891, the American astronomer Simon Newcomb using the same data but better analysis techniques derived a distance of 149.7±0.9 million kilometers.
Subsequent transit observations in the 19th century were to further refine this measurement. When Newcomb combined the 18th century data with those from the 1874/1882 Venus transits, he derived a refined solar distance of 149.59±0.31 million kilometers (a precision of 1 part in 480). This precision was only rivaled by an alternative technique, the parallax of Mars, this time measured in 1877 using then-new photographic techniques. All yielded roughly similar distances.
By the mid-20th century, Venus Transits and Mars Parallaxes were supplanted by radar echolocation and spacecraft Doppler-telemetry techniques. During the late 20th century, direct radar measurements of the distances of Venus accumulated over 40 years helped to refine the estimate of the Astronomical Unit to its modern value of 149,597,870.691±0.030 kilometers. Yes, that is not a typographical error: the AU really is known to a precision of ±30 meters (roughly the width of an American football field).
The next pair of transits of Venus will occur on 2004 June 8 and 2012 June 6 (UT time). The 2004 transit will be visible from Europe, E. Africa, Middle East, and Asia (except W. Asia). From Columbus we'll see the last parts of the transit just after sunrise.
The 2012 transit will be visible from Hawaii, Alaska, the W. Pacific, E. Asia, E. Australia and New Zealand. From Columbus we'll see transit still in progress at sunset.
For more information, see Fred Espenak's excellent 2004 and 2012 Transits of Venus page.