The Quest for the Solar Parallax, World-Wide Adventures
Parallax?
What is parallax? Hold your finger up at arm's length and, without moving it, view it with one eye, then the other. It will appear to shift against the background. That shift is parallax. Webster's Dictionary, 1913, defines parallax as The apparent displacement, or difference of position, of an object, as seen from two different stations, or points of view.Just what is solar parallax?
What is the solar parallax? The solar parallax in general is the difference in direction to the sun as seen by an observer and from the Earth's center. 1 If the sun is at the zenith (directly overhead) its parallax is 0. The parallax is maximum when the sun is seen on the horizon and is called the Horizontal Parallax, or just parallax. Solar parallax is very important since it indicates the sun's distance from Earth. That is more important than it sounds at first, as will be discussed. Parallax is normally measured as a shift against a more distance background. For astronomical objects that is almost always the background stars, at least for solar system objects. The parallax shift is smaller when the object is more distant as may be easily seen from the shifting finger example. Parallax is a common tool in astronomy. The closest astronomical example is for meteors. The same meteor is photographed at the same time by two cameras separated by a few miles. Measuring the streaks on the photos against the background stars allows the path through the atmosphere to be determined and from that the orbit the meteoroid had around the sun before it entered the atmosphere. The moon's distance can be measured by observing its shift against the background stars when viewed from two widely separated places on the earth.Why is it hard to measure?
More distant objects in the solar system have much smaller shifts, even with viewpoints spaced by the earth's diameter, the maximum available to early astronomers. And for the sun a new, and seemingly impossible obstacle arises -- it is too bright to see the background stars. You might think that the parallax could be measured during a total solar eclipse. This won't work, the moon hides the entire sun, including the edge. When the edge reappears, the eclipse is over (totality anyway). Astronomers don't give up easily on hard problems, indirect techniques were found to determine the sun's distance. As far fetched as it may sound, the asteroid Eros was a big hero in the quest for the solar parallax. Soon after its discovery, the importance of this 21 mile long chunk of rock (as measured by NEAR) was realized. But that is jumping far ahead of the story.Motions in the sky
At first there was no such concept as the solar system. Things were a bit more simple, it was either earthly, terrestial, or up there, celestial (with perhaps the atmosphere being somewhat of a gray area). It takes no effort at all to see that there are three distinctly different types of celestial objects: the sun, the moon, and the stars. A bit more observing reveals a fourth type, planets, which look much like stars but move around differently than stars. Comets nearly complete the ancient types of known celestial objects. These celestial objects had one property in common, they all seemed to rotate around earth in about 24 hours. If this rotation is ignored, the stars would appear fixed in the sky. In fact they are known as the fixed stars. Even over a lifetime they show no movement relative to each other when observed by the unaided eye alone. The sun, moon, planets, and comets move against this background of fixed stars, often visibly from night to night. These motions are not random, the sun, moon, and planets all stay within a fairly narrow band in the sky (the Zodiac). Ignoring comets, these objects all tend to drift toward the east in the sky, sometimes reversing direction for awhile, but generally drifting east. Each drifts at a different speed, the moon is by far the fastest, completing a circuit around the sky in a month. The sun takes a year to do the circuit, the planets each take their own time, with Saturn taking almost 30 years.
Venus and Jupiter in conjunction
January 30, 1868Models
Patterns in the movement of the planets are seen with enough observations. The motions are found to be periodic, as if the planets were following some fixed path in space and repeating it over and over. It becomes possible to make models that allow the motions of celestial objects to be predicted. One simple model that very accurately predicts the motion of the fixed stars is that they are attached to a large sphere with earth at the center. This sphere of the fixed stars rotates once every 24 hours, or more closely, 23 hours and 56 minutes. The axis of this rotating sphere passes very close to the North Star, explaining why all the other stars appear to revolve about it. Every star on this sphere rotates about earth with uniform circular motion. Such a model works very well for the stars. But clearly the sun, moon, and planets need additions to this model. The sun travels around the sphere of the fixed stars in a great circle inclined to the equator of the sphere, taking a year to do this. This motion can be modeled by using a smaller sphere, crystal clear, with the sun attached. The sun's sphere rotates once per year, having its axis offset from the fixed star sphere axis. This closely, but not exactly, models the sun's path through the sky. The motions of the planets are even more complex, some move in obvious loops in the sky. Each planet can be modeled with its own crystal sphere that give the basic motion against the background of fixed stars, but to model the loops requires another, smaller, crystal sphere centered on the surface of the planet's main sphere. The planet is attached to the surface of the smaller sphere which rotates to cause the loops in the motion. With the proper orientions and rotation rates the planet motions can be approximated fairly well, but additional smaller spheres are needed to get close. Such a model is a geocentric model, earth centered.Actual spheres are a problem since the planet's paths due to multiple spheres would have to penetrate through some of the spheres. Ways around this can be imagined, like cutouts around each new sphere, but the only real contribution of such spheres is to provide circular motions and this can be done with simple circles instead. If the main purpose is to predict motions then the question of what holds the circles in place need not be answered. The geocentric model of the universe reached its peak in Claudius Ptolemy of Alexandria, Egypt, around A.D. 140. A smaller circle attached to the planet's main circular path is known as an epicycle and is used to model the looping track planets show as they move through the sky. How this works can be seen from the section Ptolemy's geocentric universe of Nick Strobel's Astronomy Notes web pages. 2 Ptolemy's model grew more complicated as smaller circles and other details were added to refine the accuracy. In such a geocentric view the actual ordering of the planetary orbits or their scale are not really all that important.
The basic layout of the solar system
Copernicus
The ordering of the planetary orbits and their relative scale was first made definite by Copernicus in the early 1500s. Copernicus had the sun in the center of his system with the planets in orbit about it. The earth was just another planet orbiting the sun and rotating on its axis. Such a model is a heliocentric model, sun centered.Copernicus, however, original thinker that he was, did not work completely ab initio, in a vacuum as it were. He had Ptolemy's analysis as a guide. The Ptolemaic system is often looked upon, in books on the history of astronomy, as a great obstacle to progress, something which had to be overthrown before the real explanation could be approached. Far from this being the case it would appear that it was an essential step in the approach to a more satisfactory theory. According to Ptolemy's theory of epicycles, each body in the solar system has a significant annual component in its motion. The step taken by Copernicus, of transferring all the annual components in the motion of the five planets to the earth, becomes a natural and obvious simplification. 3The heliocentric system was not new. Aristarchus of Samos, who worked around 280 B.C. had such an idea. He also thought the earth rotated on its axis in 24 hours. But that idea had not caught on and was not seriously considered again until Copernicus brought it back. Other than the sun, solar system objects show no obvious annual component to their motion. However, the Ptolemaic system provides such a component for the period of their epicycles. Copernicus took the multiple epicycles, sharing only their period, and replaced them all by a definite orbit of the earth. Planetary retrograde motions no longer needed epicycles as an explanation, but were seen to be due to the motion of the earth. How this works can be seen from the section Copernicus' heliocentric universe of Nick Strobel's Astronomy Notes web pages. 4
It is interesting to note that Copernicus got quite a bit from the Ptolemaic system. Besides the fact that each planet has an annual component to its motion, the relative sizes of the orbits can be derived from Ptolemy's values once the heliocentric point of view is taken. In the Ptolemaic system the relative sizes of the orbits of the planets is arbitrary, but the relative size of an orbit to its epicycle is not. The table on the right gives the relative sizes of the epicycles and eccentrics (main, off-center circle) that Copernicus had available from Ptolemy. The numbers are from a footnote in Copernicus' book 5, but are from Ptolemy. The numbers in the colored areas correspond to the earth's orbit in the Copernican system, the other numbers correspond to the planets orbit. (The Copernican interpretation, not the Ptolemaic view).
Planet Epicycle Eccentric Mercury 22 1/2 60 Venus 43 1/6 60 Mars 39 1/2 60 Jupiter 11 1/2 60 Saturn 6 1/2 60
The table on the left shows the ratio obtained from Ptolemy's Epicycles and Eccentrics along with the modern orbit radii in Astronomical Units (mean distance between earth and the sun, so earth's orbit has a radius of 1.00).
Planet Ratio Orbit Radius Mercury 0.38 (= 22 1/2 / 60) 0.39 Venus 0.72 (= 43 1/6 / 60) 0.72 Mars 1.52 (= 60 / 39 1/2) 1.52 Jupiter 5.22 (= 60 / 11 1/2) 5.20 Saturn 9.23 (= 60 / 6 1/2) 9.54
A more precise picture
So Copernicus had a fair idea of the relative layout of the solar system. His planetary orbits were in the right order and close to the right relative size. However, he kept circular orbits, so the simple model was not very accurate and required the addition of numerous epicycles and offsets to make it fit observations. And observations were improving. Tycho Brahe became the world's best pre-telescope observer, measuring the positions of planets at least ten times more accurately than ever before.
Tycho BraheUsing Tycho's position measurements, Johaness Kepler was able to work out quite an accurate plan of the solar system. It didn't come easy. All calculations had to be done manually and it took years to explore various possible models to see if they fit observations. Some came close but were off a bit. Kepler trusted Tycho's observations and kept at it. In the end Kepler discovered not only the paths of the planets, but the nature of their motions.
The first problem is to allow for the moving earth, from which all the observations are made. To do this the earth's path around the sun is needed. This may be found in a number of ways, perhaps the easiest to understand is the method described by Tricker 6, where the changing apparent size of the sun is used to estimate the earth's changing distance from the sun. The earth's position throughout the year can be drawn on a chart. The paths of the other planets can then be added as they become known. Kepler used a different method to find the earth's orbit. Besides Tycho's observations, Kepler had available quite accurate periods for each planet. These were known from observations over many centuries. One major assumption needed is that each planet follows a repeatable path through space, so after a whole number of orbital periods it is back to the same place. Using this assumption, and the known period of Mars, Kepler could use Mars as one fixed point in space, the sun as a second and obtain two lines that intersected at earth's position in space. One Mars period later (or earlier) Mars would be at the same place in space but the earth would be somewhere else in its orbit so another point could be found. Doing this many times gives enough points on the earth's orbit to allow its shape and motion to be determined. It is convenient to let the earth's average distance from the sun be 1 unit, called an Astronomical Unit. This is used as a distance unit for the solar system. Planetary positions can be found in terms of Astronomical Units, or AUs. Once the earth's orbit and motion are known its position in that orbit can be computed at any time. That means observations are from a known position in space.
Johaness KeplerNow the layout of the solar system can fall rapidly into place. By reversing the procedure used to find earth's orbit, the orbits of the other planets may be found. For example, to find the orbit of Mars, pick a time when its position has been measured. The earth's position may be computed for that time and from the known direction of Mars a line in space may be defined. Now find the measured direction of Mars exactly one Mars period later. The earth's position can again be computed and second line toward Mars defined. Where these lines intersect is the position of Mars in space. This can be repeated as Mars moves around its orbit, so the orbit can be mapped out in space relative to the earth's orbit. The same method can be used for the other planets, so the layout of the solar system can be obtained from observation, without forcing the orbits to be circular, or any other specified shape. The planetary orbits determined in this way can be quite accurate and very good predications can be made. However, notice that all the distances are in AUs, not miles or kms. The actual scale of the solar system is not given by these techniques, it is all relative. That means that the actual sizes of the sun and planets are not known (only in AU). Also, the tiny shift in the positions of the stars as earth moves in its orbit only give distances to those objects in AU. So even the scale of the universe is relative, not absolute.
The solar parallax as a source of adventure, danger, even death
If any one distance in the solar system could be found in an absolute sense (miles or kms) then the actual size of an Astronomical Unit would be known. The quest for the solar parallax is the quest for this value. Since the relative layout is known quite well it doesn't matter which distance is measured, whichever can be determined most accurately is the one to use.Actually the first attempt at measuring the size of the solar system, or at least the distance to the sun, was by Aristarchus using a more indirect method. He tried to estimate the angular separation between the sun and moon at the moment the moon appears exactly quarter phase (see Michael Fowler's Measuring the Solar System). If the sun were infinitely far away this angle would be 90°. Aristarchus estimated the angle to be 87° which puts the sun about 20 times too close. The equivalent value for the solar parallax is about 3´ which is 180". Much later Kepler set an upper limit of 1´ or 60" from Tycho's observations of Mars and in 1630 Vendelinus repeated Aristarchus' method using a telescope and got about 15". 7
Venus and Mars come closer to the earth than any of the other planets, so they are obvious candidates for parallax measurement attempts. In 1671 the French astronomer Jean Richer was sent to Cayenne, French Guyana, to measure the parallax of Mars. 8 In the fall of 1672 Mars approached earth at a distance of 0.37 AU, just over one third the sun's distance, so its parallax was nearly three times that of the sun. Richer measured Mars' position from Cayenne while Cassini measured it from Paris at the same time. Although near the limits of measurement, Cassini deduced a solar parallax of about 9½" with an error of around 25 to 30%. This was the first reasonable estimate of the actual scale of the solar system. 9
Lacaille went to the Cape of Good Hope, South Africa, in 1751 and spent two years observing. Among his observations were measurements of Mars and Venus but northern observers did not make corresponding measurements so his parallax values were not very good. 10 Halley's observations of a transit of Mercury across the disk of the sun led him to the idea of using a transit of Venus to measure the solar parallax. He felt that by timing the moments of ingress and egress of the disk of Venus the parallax could be computed without doing highly precise positional measurements. The idea was clever, the difference in transit times was a measure of the difference in path lengths across the sun, which was related to the parallax shift. In 1716 Halley again made an appeal for observations of the transits of Venus coming up in 1761 and 1769, and although he was gone long before they occurred the response was large. 11 A quote from Pannekoek will give an idea of the level of activity:
When the time came near, his appeal met with a large response. A number of French and English astronomers journeyed to far-distant and little-known places. In 1761 the phenomenon could be seen in its entirety over Asia and the north polar regions; on the Australian islands the beginning only was visible; in western Europe and the Atlantic the end only. Pingré went to the island of Rodrigues in the Indian Ocean; Chappe d'Auteroche to Tobolsk in Siberia; Maskelyne to St Helena; Mason and Dixon to the Cape of Good Hope; Father Hell from Vienna to Vardö in Norway near the North Cape; Le Gentil to India. And in still greater number astronomers set out in 1769, when the complete phenomenon was visible over the Pacific, western America, and, of course, the North Pole; the end in eastern Asia; and the beginning in eastern America and western Europe. Chappe went to California where he died from pestilence contracted in fulfilling his task. Pingré went to San Domingo, Wales to Hudson Bay, Captian Cook with some astronomers to Tahiti; several Russian observers spread over Siberia; Hell went again to Vardö to see Venus pass over the midnight sun, whereas many European and American astronomers, as well as Mohr at Batavia, observed the phenomenon at their home observatories. 12Such long journeys, as might be expected, were often major adventures in those days, especially since the Seven Years' War (1756-63) was in progress during the first Venus transit. That created great hardships, one case will illustrate. The astronomer Le Gentil left Brest on 26 March, 1760, allowing plenty of time to reach his destination and get ready for the transit of Venus the next year. His destination had been selected by the French Academy to be Pondicherry on the southeast coast of India. Though his ship was pursued by a British fleet he arrived safely at the Isle de France. Pondicherry was now blockaded by the British, but a powerful rescue fleet was prepared and le Gentil decided to go with them. The fleet was struck by a hurricane, causing great damage and the loss of many men. Le Gentil was saved and wrote the Academy for permission to go to Batavia instead, but he caught severe dysentery and decided to try for Pondicherry once again by troop ship. But on approach he learned that it had been overcome, and by now he would be stuck on the high seas during the transit. June 6 was clear and le Gentil could easily see the black spot of Venus crossing the sun, but no useful observations could be made from the ship. The transit had been missed. While waiting at the Isle de France for a ship home le Gentil studied the local geography, geology, and astronomical folklore. He stayed so long he decided to stay in the area to wait for the 1769 Venus transit. From his calculations he thought he should observe from Manila, 4000 miles further east, so wrote for permission from the Academy. Before getting his reply he went there and set up an observatory and started work. But the Academy preferred Pondicherry so he returned there. It was under British control but they were very friendly and helpful and le Gentil set up an observatory and determined an accurate longitude. He stayed up all night before the transit preparing for the first view of Venus. The sun rose clear and everything looked good for obtaining the needed ingress time which was to happen at 7:00 am. But at 6:50 a small cloud floated in front of the sun and didn't leave until 7:20. The needed observation was missed. Manila had been clear. He returned home with further hardships, making a hard overland journey from Lisbon to Paris after an absence of eleven years. During this time he had been legally declared dead and his estate was being liquidated; he recovered his own possessions only with difficulty. He ended on a brighter note, marrying and having a daughter. 13That was only one of many adventure tales. Great effort was put into observing the transits of Venus so the solar parallax could be found. The results were less than expected. The needed ingress and egress times were not so easy to measure. The black disk of Venus seemed to stick to the edge of the sun, connected by a black thread, which, when it broke left Venus well inside the sun's disk. That made timing uncertain, and the derived solar parallax values ranged from 8.55" to 8.88", far more spread than expected. Even so, it was quite an improvement over earlier values. 14 In 1835, Encke reexamined the Venus transit data. Using better computational techniques, and better longitude values, he derived a solar parallax of 8.57" ± 0.04" (although he gave it as 8.57116" ± 0.0371"). 15 This values give the sun a distance of 95 million miles or 153 million km.
After a few decades the solar parallax started to look less certain. The sun's perturbations of the moon's orbit was used by Hanson in 1857 and 1863 to derive a solar parallax of 8.92". Leverrier used the earth's pertubations on Mars and Venus to obtain 8.95". Foucault, after making a more accurate measurement of the velocity of light, determined from the aberration of star light that the solar parallax must be about 8.8". Mars was measured again during 1862, giving results of 8.96" and 8.93", the true value was believed to be about 8.90". The Venus transit of 1769 was revisited in 1864 by Powalky, using newer longitudes, and somewhat different interpretations of some observations he obtained 8.83". Another pair of Venus transits took place in 1874 and 1882. Measurements were taken during the transits, not just ingress and egress, but results were still somewhat scattered: 8.76", 8.88", 8.81". Venus transits were just not a good way to find the solar parallax. Mars in 1877 gave 8.78". An idea first expressed by Galle in 1872 was to use asteroids instead of Mars. Even though they are not as close, so have smaller shifts, their point-like images should be easier to measure as compared to the disk of Mars. Three chosen asteroids were Iris, Victoria, and Sappho. At best they are about 0.83 or 0.84 AU from Earth, compared to Mars at 0.37, so their parallaxes were much smaller. They were observed in 1888 and 1889, giving a solar parallax of 8.802". Michelson and Newcomb, using Foucault's method, found a more accurate velocity of light, which when combined with a better aberration value, gave a solar parallax of 8.80" ± 0.01". 16
In August of 1898 a new discovery would be made that would eventually give the best distance scale estimate obtained for many years.
Back: Too Many Planets Table of Contents Next: Eros comes on stage
References
1 "parallax" Britannica Online.
http://search.eb.com/bol/topic?eu=59856&sctn=1#s_top
[Accessed 29 January 1999]2 "Astronomy Notes: History of Astronomy: Ptolemy's Geocentric Universe" by Nick Strobel
http://www.bc.cc.ca.us/programs/sea/astronomy/history/historya.htm#A2.43 R. A. R. Tricker, The Paths of the Planets (New York: American Elsevier Publishing Company, 1967), p. 50.
4 "Astronomy Notes: History of Astronomy: Copernicus' heliocentric universe" by Nick Strobel
http://www.bc.cc.ca.us/programs/sea/astronomy/history/historyb.htm#A3.35 Copernicus, On the Revolutions of the Heavenly Spheres, in Vol 16 of Great Books of the Western World, ed. Robert Hutchins, Encyclopædia Britannica, Inc. P. 528.
6 Tricker, p. 65.
7 A. Pannekoek, A History of Astronomy (New York: Interscience Publishers, 1961), p. 283,284.
8 "Richer, Jean" Britannica Online.
http://www.eb.com:180/bol/topic?eu=65214&sctn=1#s_top
[Accessed 11 February 1999]9 Pannekoek, p. 284.
10 Ibid., p. 284.
11 Ibid., p. 286.
12 Ibid., p. 286.
13 Gerald S. Hawkins, Splendor in the Sky (New York: Harper & Brothers, Publishers, 1961), p. 92-94.
14 Pannekoek, p. 286, 287.
15 Ibid., p. 341.
16 Ibid., p. 344-346.
Illustrations:
"Venus and Jupiter in conjunction, January 30, 1868" scanned from Fourteen Weeks in Descriptive Astronomy, J. Dorman Steele, A. S. Barnes & Co., New York, 1871
"Copernicus", "Tycho Brahe", and "Johaness Kepler", all scanned from Elements of Descriptive Astronomy, a Text-Book, Herbert A. Howe, Silver Burdett and Company, New York, 1897
