Download Polaris – Distance to Pole

Tycho Brahe
and the Foundations of
Observational Astronomy
Michael Rosa
Space Telescope European Coordinating Facility
European Space Agency & European Southern Observatory
ESA
ESO
1
A New Place to Teach the Science of the Universe
• Science builds on the understanding of those who came before
– sometimes adding new understanding,
– sometimes modifying,
– and sometimes replacing.
• Without first understanding the best previous facts, ideas, vocabulary
and skills, a better understanding cannot be built.
• It is not sufficient to just have better tools available. Dedication in
both, observation and analysis, is required.
• Two step process
(1) how is it
(2) why is it as it is
Tycho Brahe
Kepler, Galileo, Newton
(accurate observations)
(Physics)
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Already Known to the Ancients
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Using this Knowledge in Imperial Style …
Rome – Horologium Augusti
Britain – Stonehenge
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… or for mundane tasks – time at night
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… learning that the Earth is a globe …
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… finally search for an
underlying “Mechanism”
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Mars
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New Astronomy
Founded upon Causes,
or Celestial Physics,
Handed over as Commentaries
on the Motions of the Planet Mars,
according to the Observations
of the splendid master Tycho Brahe
By order and at the cost of
Rudolph II. , Roman Emperor etc.
Elaborated during many years of
pertinacious study at Prague
By His Cesarean Majesties Imperial
Mathematician
Johannes Kepler
Anno 1609
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Kepler relies on Tycho’s data quality …
And from this such small difference of 8 minutes of arc it is clear why
Ptolemy , … accepted a fixed Equant point. ... For Ptolemy set out that he
actually did not get below 10 minutes of arc … in making observations.
To us, on whom Divine benevolence has bestowed the most diligent of
observers, Tycho Brahe, from whose observations this 8-minute error of
Ptolemy's in regard to Mars is deduced, it is fitting that we accept with grateful
minds this gift from God, and both acknowledge and build upon it.
So let us work upon it so as to at last track down the real form of celestial
motions .
For if I thought the 8 minutes in longitude were unimportant, I could make a
sufficient correction to the hypothesis found in Chapter 16.
(…that is the Vicarious Theory)
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Kepler’s assessment of Tycho’s data quality 2
• Now, because they could not be disregarded,
these 8 minutes alone will lead us along a path
to the reform of the whole of Astronomy,
and they are the matter for a great part of this work.
(that will be the elliptic orbits and non-uniform speed … )
Astronomia Nova (Heidelberg, 1609) Chapter 19, p 113-114
• Why was Kepler so sure that Tycho Brahe’s data are accurate
to better than a few arcminutes ?
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Tycho’s Starting Point
I have studied all available charts of the
planets and stars,
and none of them match the others.
There are just as many measurements and methods
as there are astronomers, and all of them disagree.
What is needed is a long term project with the aim of
mapping the heavens conducted from a single
location over a period of several years.
1563 - age 17
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Tycho principles
Tycho very early on realized , that progress in astronomy
could be achieved
• not by occasional haphazard observations,
(No pains - no gains -------- or "Garbage in, Garbage out“)
•
•
•
•
but only by systematic and rigorous observation programs,
(clear) night after night, for 20 years
by building instruments of the highest accuracy obtainable
by continuous refinement of observational techniques
• For that he secured funding, and he gave up the born-into personal
security of his social rank (royal court nobility)
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Tycho Brahe – Early Years
•
* 14-12-1546 into Danish Upper Nobility
•
At age 17 sent to Germany to study Law
(political career)
o
o
•
Builds larger, better instruments (Augsburg 5m)
o
o
o
•
Instead secretly studies Astronomy
(Dedication)
everything measured on sky differs from “text books”
Nov 1572 a SN appears in Cassiopeia
(Fortune)
Controls distances to many stars – realizes the variable star
must be in “fixed star sphere” – no parallax, no p.m.
Variability in Eights Sphere, no crystal spheres, universe is
“earthly”
1574 called back to Denmark for a state career track
o
o
o
Marries non-noble woman
Refuses post as Governor on fiefdom
(Decisiveness)
Persuades King to give him the means to build worlds most
modern super-observatory
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Tycho’s European Observatory
• Total amount spent: ~ 1 ton of gold = 5 * 109 EUR (= ESO-VLT, HST)
• Starting 1576 it became a top scientific place in Europe
• In total 100 “fellows”, typically 15-20 at a time
• These later became the stock of European scientists
• Very large library – books “Ex Libri T B” go for astronomical amounts
• Lost funding in May1597 - Uraniborg/Hven abandoned after 20 years
• Tycho moves to Rostock, Hamburg, Wittenberg, finally Prague
• Died in October 1601 age 54
• Last words:
Ne frustra vixisse videar
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Kepler on Tycho’s data quality
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Kepler on Tycho’s data quality
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Uraniborg
on Hven
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Stjerneborg
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Kepler on Tycho’s data quality
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Key Instruments
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Tycho’s Astro Program (dies age 54 !)
•
Astronomia Instaurata
•
Canonical Tasks in order
123456789-
•
- Overhaul of Astronomy
= entirety of Astronomy textbook prior to Astrophysics
establish latitude of Uraniborg
(without fundamental star cat)
-- brilliantly achieved
accurate solar orbit
-- 1582/83, publ 1602
- tainted by wrong Parallax
construct system of fundamental stars (without good clock)
-- very good new value for Precession
establish catalogue of 777 / 1014stars
-- published 1602
-- high precision / accuracy
orbits of all planets
-- 1582 – 1601
the math was Kepler’s agreed upon job
parallaxes, orbits of comets
-- quite a number (~11)
break the Crystal Spheres
lunar theory (difficult)
-- finds inequalities #3 & #4
-- ventilates “Longitude-Problem”
solar/lunar eclipses
-- very good account of many
establish zero-points FK
variable stars
-- SN 1572, o Ceti (Mira)
Appealing Stuff
Tests to decide between Ptolemaean vs Copernican vs Tychonian
Martian Parallax
Parallax for Venus
Distances / Sizes of stars
-- may be the Achilles heel
-- several trials 0 result
-- wrong interpretation of “data”, nothing known about diffraction
•
Instrumentation / Calibration / Refraction and other annoyances
•
Non-Astronomy
Astrology
Alchemy
Weather
Poetry
-- (not really liked but some neat extra income)
-- the fashion of the time, everyone had to have a lab
-- rich daily weather record for 20 years
-- the signature of “gentlemen” in Renaissance days
-- a lot of effort into that / big firsts
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Accuracy
&
Precision
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Altitude of Pole from ~1500 Observations
• “Latitude” of Uraniborg
Tycho ‘s value (A.I.M. 29 )
Today’s best value
Tycho is off by only
At Uraniborg
Scale of Uraniborg gardens
55° 54′ 30″
55° 54′ 28”.7
1”.3
1”
corresponds to
31 m
100 m
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 UMi - Polaris – Distance to Pole
Epoch
Location
Tycho
FK5
T-FK5
“
1573
Augsburg
3 0 15
3 0 10.2
4.8
1577
Uraniborg
2 58 50
2 58 50.4
-0 . 4
1581
Uraniborg
2 57 30
2 57 30.5
-0 . 5
1585
Uraniborg
2 56 10
2 56 10.7
-0 . 7
1589
Uraniborg
2 54 50
2 54 50.9
-0 . 9
2000
0 44 9.2
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Tycho’s Catalogue vs the Almaghest
Almaghest (Ptolemy)
spread of +/- 30’ about the positions that
“should have been” observed
Tycho‘s Catalogue
spread of +/-3’ about 0
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Tycho Star Cat - Accuracy
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Kepler’s Assessment correct
“ Now, because they could not be disregarded, these 8 minutes alone will
lead us along a path to the reform of the whole of Astronomy, “
since 8’ are  5 * σ [1’.5] and more than 4 * Δx0 [1’.8],
as follows from scrutiny of the TB Catalogue
Residuals in Ecliptic Longitude (Tycho-FK5)
100
%
σ
x0
============
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1.5
0.2
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7.5
2.0
2
flat
90
80
Occurances
70
60
50
40
30
20
10
0
-15
-10
-5
0
arcmin
5
10
15
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Inner Solar System to scale
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http://www.pafko.com/tycho/index.html
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A very obnoxious handicap – Refraction
• Tycho spent a large effort on understanding empirically
atmospheric refraction
– basically comparing where stars and Sun seem to be and ought to be
– without exactly knowing where they ought to be …
• Unbeknownst to him …. Nicolaus Oresme in 1356 wrote booklet
– Utrum stelle videantur ubi sint
“Are the stars really where they seem to be?”
– Developed correct model of atmospheric refraction, using infinitesimals
…. All of that had to be re-invented again 200-300 years later
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Kepler on Tycho’s data quality
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Kepler on Tycho’s data quality
In Tycho’s own words
And hence also it happens that the Sun daily appears to rise more quickly, and to sink more
slowly, then its real ascent or descent requires, and this with an enough perceptible difference
that it takes 4 or 5 minutes.
Progymnasmata Ch. 1, p. 12
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``Is the Sun really where it seems to be?”
By the way, it only was in that
direction (refracted or not) 8
minutes and 20 seconds ago
… but that is yet another story,
waiting for Ole Roemer to
answer
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Apparent Positions of Mars
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Some of the last Hven observations
on Mars
1595 Oct 25-27
•
One of the best
oppositions
•
Yet - only one useful
set
•
Tycho not present.
•
Longomontanus not
present
•
Clearly enthusiasm
for Mars campaign
had waned
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0.0075
-- - Kepler ellipse,
Sun in near focus
0.006
0.0045
0.003
Diameter
of Sun
Scale of problem
at Perihel
0.0015
0
0.988
0.99
0.992
0.994
0.996
0.998
1
-0.0015
-0.003
Moon's
orbit
-0.0045
-0.006
- - - "Vicarious" best
fitting excentric circle
Centered
circle 1 AU
-0.0075
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Ellipse and Circle at Aphel
0.1
0.08
0.06
- - - “Vicarious”
best fitting
excentric circle
Centered
circle1 AU
0.04
0.02
0
-1.009
-1.007
-1.005
-1.003
-1.001
-0.999
-0.02
-0.04
-0.06
- - - Kepler
ellipse, Sun
in far focus
-0.08
-0.1
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How to test Keplerian Theory
in mid 17th century
• No other data nearly as good available
– for another 2 centuries no other classical observational data available,
simultaneously as homogenous, accurate and precise as T Brahe’s.
– testing “Kepler-from-TB” against “TB” is not decisive
• So what to do ?
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How to test Keplerian Theory 2
• Church / Jesuits come to help
– using the Meridiana in Bologna (Basilica of San Petronio)
– 4500 observations for solar timings, diameters
-- compiled in Manfredi’s (1735) register
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How to test Keplerian Theory 3
Solar image either 3.4% or only
1.7% larger/smaller in the
two apsides depending on
model (Ptolemy/Kepler)
Cassini (1695) concludes from these
data that Kepler’s theory of planetary
motion “most likely to be correct”
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The End (1598 – 1601)
•
Imperial Astronomer of Emperor Rudolf II (Prague)
•
Few observations, “finalize” the WORKS
– Hire good, young people (Kepler and others) to
compute Planetary Ephemeris from obs. data
•
Sept 1601 meets Emperor
– to have Kepler designated as successor for Imperial
Mathematician
•
On 24 Oct 1601 dies (urological congestion)
•
1990 - analysis of beard hair finds enormously
large Mercury dose (factor 1000 above normal)
Myths:
•
– Drank to much and did not leave table
– Poisoned (to get onto his data, for private reasons, for
stately reasons)
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Ellipse and Circle at Aphel
0.1
0.08
0.06
- - - “Vicarious”
best fitting
excentric circle
Centered
circle1 AU
0.04
0.02
0
-1.009
-1.007
-1.005
-1.003
-1.001
-0.999
-0.02
-0.04
-0.06
- - - Kepler
ellipse, Sun
in far focus
-0.08
-0.1
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Refraction
•
•
Tycho first to systematically study
refraction
Adopts 3 tables
Sun , Moon (almost =) 0 – 45 Alt
Stellar (=modern)
0 – 20 Alt
Solar table = Stellar + 4.5’
•
Consequences:
Obliquity of Ecliptic 2’ wrong
“Erroneous” Solar parallax 3’ built in
Mars to show a spurious parallax
•
Why ????
Such a diligent and excellent observer
So marvelous data
•
•
Myth: He did not know better and was
fooled, so his entire legacy was
corrupted
My proposition: He did it to hide the big
thing being stolen before a complete
theory was published
– the “universe” is 32 times larger
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How to secure sub 1’ accuracy
Good is good, but better carries it
Better is the enemy of good
• Instrument design
– 1’ = 1 mm at 3 m distance
 large unwieldy instruments
 prone to bending, wind shaking, temperature effects
– 1’ limit of resolution for perfect acuity (but pupil wide open at night)
 contrast is a problem (light spot against dark background)
 specially designed diopters TB
• Observing Program & Data Analysis
– Accept new Instruments only after scrutinizing tests (repeatability)
– Accept observations only if == from several diff. instruments
– Plan observations to minimize evil effects (avoid subtraction of large
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and almost equal quantities, plan for comparable refraction)
~ 300 000 Spherical
Triangles to solve
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