Download Measuring the Sky - Physics and Astronomy and more!

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 18th and 19th 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 million2 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 19th C,
instruments were precise
enough to measure tiny
parallax
 Parallax Second
 3.08568025 × 1016 meters
 3.26 LY
 Friedrich Bessel 1838
measured the distance
to 61 Cygni using a 14inch 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 19th C. it is all
about observing and
measuring
 Telescopy advanced greatly
in the 16th and 17th 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 fo to fe
 That means a great fo
gives greater
magnification
 But also fo + fe 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 18th 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.
“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)
(X0.1)
Planetary distances (AU)
Planetary body
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
5.2
5.2
Jupiter
10
9.6
Saturn
2.8
But only a curious footnote until…
Seems to work again
Bode-Titius series (1772)
(X0.1)
Planetary distances (AU)
Planetary body
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
5.2
5.2
Jupiter
10
9.6
Saturn
19.6
19.2
2.8
Uranus (1781)
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)
(X0.1)
Planetary distances (AU)
Planetary body
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
2.8
2.8
Asteroids (1801)
5.2
5.2
Jupiter
10
9.6
Saturn
19.6
19.2
Uranus (1781)
A little too small
 Further observation revealed that Ceres
was too small to be a planet
 Pluto—things never change!
 March 1802, Heinrich *Olbers (17581840), 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 19th 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?
Not observed (yet)
 1792: Jean-Baptiste
Joseph Delambre (17491822) creates new
tables for planets
Jupiter, Saturn, Uranus,
and satellites of Jupiter
 Uranus is observed to be
moving faster in its orbit
than expected
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 (18011892)




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
Meanwhile…

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
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
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
2.8
2.8
Asteroids (1801)
5.2
5.2
Jupiter
10
9.6
Saturn
19.6
19.2
Uranus (1781)
30.1
Neptune (1846)
4 + 384 = 38.8: oops!
Bode-Titius series (1772)
Planetary distances (AU)
Planetary body
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
2.8
2.8
Asteroids (1801)
5.2
5.2
Jupiter
10
9.6
Saturn
19.6
19.2
Uranus (1781)
38.8
30.1
Neptune (1846)
What the…?
Bode-Titius series (1772)
Planetary distances (AU)
Planetary body
0.4
0.39
Mercury
0.7
0.72
Venus
1
1
Earth
1.6
1.52
Mars
2.8
2.8
Asteroids (1801)
5.2
5.2
Jupiter
10
9.6
Saturn
19.6
19.2
Uranus (1781)
xxx
30.1
Neptune (1846)
38.8
39.5
Pluto (1930)
A note about curve-fitting
Temp vs Abs.Mag
40000
35000
30000
25000
Kelvin
 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, BodeTitius is no law the
way Newton’s
Gravity is
20000
15000
10000
5000
0
-6
-4
-2
0
Abs.Mag
2
4
6
Summary
 Astrometry is all about measuring the
stars
 Nothing is said in the late 18th, early 19th
century about what stars, nebulae are
 Better instruments make for more
questions
 Not all science goes smoothly!