# Measuring the Sky Astrometry This logo denotes A102 appropriate.

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Measuring the Sky Astrometry This logo denotes A102 appropriate

A Branch of Astronomy  Astrometry concerns itself with counting, observing positions, and measuring trajectories  Naked-eye observations  All they could do before 1600  Motions in the Sky ppt!  Telescopes enhanced this study immensely in the 18 th and 19 th centuries  And the advancement of the science of measuring  Metric system

Speed of Light  Galileo tried with hanging lanterns  Time interval far too short to measure in the day  First calculated by Ole Roemer in 1676  Used the predicted time for Jupiter’s Io to come out of eclipse  Distance to Jupiter ~ 400 million miles  Came up with ~ 140,000 miles/second  Helped by Huygens  2/3 the correct answer

How Far the Stars?  The speed of light hinted at the enormity of the cosmos  Neither Copernicus nor Brahe could measure the parallax of stars relative to the “nearby” planets  Copernicus stated the stars were too far

 Tycho had calculated that the distance to the stars not to show parallax had to be at least 6650 AU  He stated that the stars were fixed, bolstering his theory of the universe  Cassini, using parallax of Mars, increases Tycho’s distance to 200,000 AU (~20 trillion miles: in the ballpark)  Halley looked at 2000 year old star charts and finds some stars had moved relative to others, showing depth

Thumb Fun with Parallax  Hold your thumb at arm’s length and blink each eye in turn  See how the thumb appears to move against the stationary background?  Measure your arm and how far the thumb ‘moves’ and voila! You’ve got parallax

 Galileo suggested that nearby stars would exhibit parallax relative to farther stars if the Earth’s orbit was used as a baseline (as in the previous slide)  But he never tested this theory  It wouldn’t have worked, as the angle would be too small to measure in 1610  On the other hand, Descartes assumed that the stars are just like the sun, so if the sun is a million times brighter that a star, then the star must be a million 2 times further than the sun.  Why?

 Huygens had a similar idea to Descartes:  Use a screen to cover up the sun, but poke a hole in the screen so that the amount of sun that shines through the hole is equal to, say, Sirius  The ratio of the hole to the sun’s disk would be the same as the ratio of the distance to Sirius to the sun’s distance  He calculated 27,644 AU  More like 570,000AU  Newton more wisely just compared a planet’s brightness to that of Sirius, since planet distances were well known  He calculated 1 million AU, a little more than twice the value  The universe was astoundingly huge!

Parsec  By the 19 th C, instruments were precise enough to measure tiny parallax  Parallax Second  3.08568025 × 10 16 meters  3.26 LY  Friedrich Bessel 1838 measured the distance to 61 Cygni using a 14- inch refractor Joseph von Fraunhoffer had built for him  1/3“ = 11.4 LY

Huh?  The Kessel run in 12 parsecs? What are you smoking Han?  Do you see the flaw?

Well into the 19 th C. it is all about observing and measuring  Telescopy advanced greatly in the 16 th and 17 th centuries  At right is Christian Huygen’s 123 ft aerial telescope  He realized that the ‘tube’ isn’t necessary  The objective lens is at the top of the pole and the eyepiece is near the, ah, eye  The longer separation of the lenses provides for greater magnification

How it works  The magnification of a refractor comes from the ratio of f o to f e  That means a great f o gives greater magnification  But also f o + f e must be greater than the separation of the lenses

So bigger is better  The 150 ft aerial telescope of Johannes Hevelius (1611-1687)  In an age of no street lamps or headlights, aerial worked fine  Nowadays tubes are necessary to block ambient light

The King’s Astronomer  William Herschel (1738-1822)  Born in Hanover, Germany  Escaped the Seven Years War to England in 1757  A musician (organist) and music teacher  24 symphonies  7 violin concerti  2 organ concerti  1766: took a position as an organist in Bath

Astronomy becomes a passion  Herschel purchases an astronomy text and builds this in 1773  7 ft reflecting telescope  Reflectors have a magnifying mirror at one end  Like a shaving or make-up mirror  Cuts the length of the tube in half  Easier than a lens to make large  No chromatic distortion

“Sweeping the Heavens”  His sister *Caroline joins him and the two start a systematic search for two close stars  Mizar and Alcor in Ursa Major  Middle “star” in the Big Dipper’s handle  Albreo in Cygnus  Double stars were an exciting topic in 18 th C. astronomy  Herschel hoped to measure the parallax as the Earth orbited the Sun *rescued from family servitude

Going Pro “Seeing is in some respects an art that must be learnt. To make a person see with such a power is nearly the same as if I were asked to make him play one of Handel's fugues upon the organ. “Seeing is in some respects an art that must be learnt. To make a person see with such a power is nearly the same as if I were asked to make him play one of Handel's fugues upon the organ. “Many a night have I been practicing to see, and it would be strange if one did not acquire a certain dexterity by such constant practice. --William Herschel (1782)

The Discovery of Uranus  In March 1781 during a sweep he observed “a curious rather Nebulous star or perhaps a comet”  By checking the orbit Herschel determines that this object is a new planet  Had actually been recorded on star charts in 1690 “ Pollux is followed by 3 small stars at about 2’ and 3’ distance. Mars as usual. In the quartile near Zeta Tauri the lowest of two is a curious either nebulous star or perhaps a Comet. preceeding the star that preceeds ν Geminorium about 30” a small star follows the Comet at 2/3rds of the field’s distance”

Uranus from Voyager 2

Perturbations  Upon observation, Herschel saw that Uranus was moving more slowly than Saturn  More than that, Saturn apparently wasn’t moving exactly the way Kepler and Newton would have predicted  A change in a predicted path is called a perturbation  Saturn drags on Jupiter  Uranus drags on Saturn

England, 1782  Who was the king and what was he mostly concerned with?  Herschel wants to name the star Georges Sidderius  French observers prefer the name ‘Herschel”  German Astronomers decide on Uranus, god of mystery, in keeping with the Greco-Roman tradition  Still, King George is impressed and names Herschel ‘The King’s Astronomer”  Not the Astronomer Royal, Nevil Maskelyne  Herschel receives a royal pension

Meanwhile…  The Bode-Titius Law  A dip into numerology  Historically:  Kepler ~1600 was convinced that there was a mathematical series underlying the structure of the solar system  A series is a string of related numbers, like 0,1,1,2,3,5,8,13,21,33…  David Gregory ~1700 described the relative distances as 4, 7, 10, 15, 52, and 95  Johann Titius 1766 modified the series  4, 4+3=7, 4+6=10, 4+12=16, 4+48=52, 4+96=100  Something missing?  Johann Bode 1772 publishes the series in his popular Astronomy text n = 0, 1, 2…starting with Venus

Seems to work Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 5.2 Jupiter 109.6Saturn (X0.1) But only a curious footnote until…

Seems to work again Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 5.2 Jupiter 109.6Saturn 19.619.2Uranus (1781) (X0.1)

The Missing Piece (?)  So what about 4 + 24 = 28?  The search is on!  Sicilian astronomer, Giuseppe Piazzi (1746-1826), using new, more precise star charts, starts looking for the missing planet  January 1, 1801 he finds a faint object which, by the following night, had moved  First thought he had found a comet  But comets follow highly elliptical paths  The little guy’s orbit was nearly circular  AND its orbit was 2.7AU!  He named it Ceres  Roman goddess of agriculture and the patron saint of Sicily

Seems to really work! Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 Asteroids (1801) 5.2 Jupiter 109.6Saturn 19.619.2Uranus (1781) (X0.1)

A little too small  Further observation revealed that Ceres was too small to be a planet  Pluto—things never change!  March 1802, Heinrich *Olbers (1758- 1840), finds another planet in about the same orbit  Names it Pallas (god of wisdom)  But Pallas is even smaller than Ceres *Paradoxically, we’ll meet Olbers in a later presentation

A suggestion from the King’s Astronomer  Herschel thinks that these objects should be called asteroids to distinguish them from ‘real’ planets  1804: Karl Ludwig Harding (1765-1834) finds Juno  1804: Olbers finds Vesta  1845: Karl Ludwig Hencke (1793-1866) discovers Astraea  By 1900, 2000 asteroids had been found  Today, 30,000 named, 100,000 projected

Speaking of whom…  There are rewards for being the King’s Astronomer  George gives William and his sister a nice stipend so he can quit his job and pursue Astronomy  1788: Herschel builds this 20 ft reflector  Finds his new view reveals trouble

Star Gauging  In his sweeps Herschel and his sister had made some assumptions:  all fuzzy little objects are resolvable into clusters of stars  our sun is part of a similar cluster of stars  stars in our cluster are roughly the same brightness (variations in brightness are due to variations in distance)  stars in our cluster are distributed uniformly (thickness of the cluster in any given part of the sky can be deduced from the numbers of stars)  we can see to the edge of our cluster  But now with his new telescope he realized that earlier observations had not revealed the edge of our cluster after all

Charles Messier  A comet hunter  Annoyed when about 100 new ‘comets’ appeared not to move  Made a catalog of these nebulae (plural: means fuzzy thing) so he wouldn’t be fooled again  We still use his name in denoting many deep sky objects

M16, the Eagle nebula (partial)M31, The galaxy in Andromeda

Herschel eventually catalogs 2500 nebulae: “They now are seen to resemble a luxuriant garden, which contains the greatest variety of productions, in different flourishing beds; and one advantage we may at least reap from it is, that we can, as it were, extend the range of our experience to an immense duration.”

In 1811 he published the drawings in the Philosophical Transactions of the Royal Society to exhibit the rich variety of nebula types.

His astute (but incorrect) hypothesis:  “For, to continue the simile I have borrowed from the vegetable kingdom, is it not almost the same thing, whether we live successively to witness the germination, blooming, foliage, fecundity, fading, withering, and corruption of a plant, or whether a vast number of specimens, selected from every stage through which the plant passes in the course of its existence, be brought at once to our view?”

His Assumptions About nebulae:  stars and nebulae emit light (shining fluid)  light gathers together and forms nebulosity  nebulous matter is gravitationally attracted to star  some material falls into star; replenishes star  some material forms into comets  comets can form seeds of future planets  Mistakes a planetary nebula to be a forming system  a star is just a large planet with outer atmosphere of luminous clouds  our sun is inhabited; sunspots are holes in luminous clouds And the verdict…

 stars and nebulae emit light (shining fluid)  True, they emit light, but it’s not a fluid  light gathers together and forms nebulosity  False: matter gathers together and forms nebulosity  nebulous matter is gravitationally attracted to star  True, but also the reverse  some material falls into star; replenishes star  True, but not enough to ‘replenish’ it  some material forms into comets  True!  comets can form seeds of future planets  Absolutely not! They are leftovers from planetary formation  a star is just a large planet with outer atmosphere of luminous clouds  False: stars are nothing like planets  our sun is inhabited; sunspots are holes in luminous clouds  Hardly: the surface temperature is 5700K!

So Herschel wasn’t completely wrong  He did assume that all stars were the same (wrong), and that only distance differentiated them to our eyes  We’ll learn that stars can be vastly different from each other  He did get a feel for the distances he was seeing and the time lag  Fundamental: when you look at the sky you are seeing things as how they were, not as how they are  A major flaw in Astrology!  We can’t judge Herschel out of his time  He was working with the best data in a brand new field, a field not even named yet: Astrophysics

The Convoluted Discovery of Neptune  Out of Herschel’s (and others) work came new questions in the early 19 th century  What were these nebulae?  What was the shape of the Universe?  Why was Uranus also not following Newton’s path?  These questions concerned what they were seeing and how these objects were moving and evolving, not what they were made of.

Another planet?  1792: Jean-Baptiste Joseph Delambre (1749- 1822) creates new tables for planets Jupiter, Saturn, Uranus, and satellites of Jupiter  Uranus is observed to be moving faster in its orbit than expected Not observed (yet)

The Players: Images Copyright Sky and Telescope

Alexis Bouvard (director of Paris observatory; 1767-1843)  1808: Bouvard publishes revised, more accurate tables for the orbits of Jupiter and Saturn  1821: Bouvard corrects Delambres’ tables for Uranus  "...I leave it to the future the task of discovering whether the difficulty of reconciling [the data] is connected with the ancient observations, or whether it depends on some foreign and unperceived cause which may have been acting upon the planet."

George Biddell Airy (1801- 1892)  Astronomer Royal for 50 years  Ran a tight ship  “computers” calculated corrected tables  1832: describes the problem of Uranus's orbit as one of the chief problems of astronomy  Uranus’ orbital speed had decreased since 1792  Airy thinks that by looking at historical star charts this aberration can be better understood  Said Uranus had been recorded 17 time before Herschel (Galileo could have seen it, as well as Neptune)

John C. Adams (1819-1892)  Undergrad at Cambridge  Earnest, shy, lacking in social graces  Student of James Challis  Read Airy’s pamphlet on the Uranus problem  1841:"Formed a design in the beginning of this week, of investigating, as soon as possible after taking my degree, the irregularities of the motion of Uranus, which are yet unaccounted for; in order to find out whether they may be attributed to the action of an undiscovered planet beyond it; and if possible thence to determine the elements of its orbit, etc., approximately, which would probably lead to its discovery."

Competition  Urbain Jean Joseph Leverrier (1811-1877)  Well respected mathematical astronomer  June 1845: Tasked by Francois *Arago, starts work on the Uranus perturbation problem  Sept. 1845: Adams gets a better approximation based on Bode-Titius law  Takes his prediction to Airy at Greenwich  But Airy in France, so he leaves his paper  Tries again in Oct., but Airy’s having dinner  No appointment—won’t be interrupted! *Prime Minister of the French Republic (1848)

The Comedy of Errors continues  Airy reads the manuscript and unhurriedly replies, questioning the premises  Rem: Adams has no great reputation  Adams for whatever reason does not reply!  Nov. 1845: Leverrier publishes two papers on the proposed new planet  Summer 1846, Airy reads Leverrier’s paper, amazed at the similarity to Adam’s calculations  Both Adams and Leverrier predict a new planet to be located in the same part of the sky  However, the national observatory (Greenwich) is “not the proper place to do research”

 Airy tells James Challis (now director of Cambridge University Observatory) to look for the new planet  Challis looks in the specified location on the ecliptic, records an object but does not recognize Neptune  Summer in Greenwich very short, skies not very clear  Older, less complete charts  Methodical, unhurried  Didn’t see a disk, so dismissed observation

 Leverrier writes Johann Galle in Berlin, asks to look for new planet  Galle has superior star charts  Director Encke approves immediate search; Galle and assistant Heinrich d'Arrest find Neptune in 30 minutes (!) on Sept. 23 Meanwhile…

Franco-Prussian Cordiality*  Galle to Leverrier: "Monsieur, the planet of which you indicated the position really exists."  He replies: "I thank you for the alacrity with which you applied my instructions. We are thereby, thanks to you, definitely in possession of a new world." *25 years before the Franco-Prussian War

Neptune from Voyager 2

Sheepish John Bull  Challis (at Greenwich) finally learns of Leverrier's prediction that new planet should appear as a disk  Looks again and finds it on Sept. 29  Oct. 1: London Times: "Leverrier's Planet Discovered"

English scientific community gets shorts in a wad  Airy wasn’t congenial enough  Adams wasn’t forceful enough  Challis wasn’t observant enough  Herschel’s son John says Dec. 1846  "I do not call finding an individual object merely including it in a crowd of others (without knowing it is there...).... Until the planet was actually seen and shown to be a planet -- there is no discovery -- except in so far as a successful physical hypothesis is one...."  John is a successful astronomer in his own right, and is still the only observer to map the entire sky, northern and southern hemisphere  Despite national acrimony, Adams and Leverrier become life-long friends

And what of 4 + … ? Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 Asteroids (1801) 5.2 Jupiter 109.6Saturn 19.619.2Uranus (1781) 30.1Neptune (1846)

4 + 384 = 38.8: oops! Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 Asteroids (1801) 5.2 Jupiter 109.6Saturn 19.619.2Uranus (1781) 38.8 30.1Neptune (1846)

What the…? Bode-Titius series (1772)Planetary distances (AU)Planetary body 0.40.39Mercury 0.70.72Venus 11Earth 1.61.52Mars 2.8 Asteroids (1801) 5.2 Jupiter 109.6Saturn 19.619.2Uranus (1781) xxx 30.1Neptune (1846) 38.839.5Pluto (1930)

A note about curve-fitting  Excel has this feature  A series can be made to fit for a subset of the data, but it doesn’t describe a ‘law  Therefore, Bode- Titius is no law the way Newton’s Gravity is

Summary  Astrometry is all about measuring the stars  Nothing is said in the late 18 th, early 19 th century about what stars, nebulae are  Better instruments make for more questions  Not all science goes smoothly!