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Michael RosaSpace Telescope European Coordinating Facility

European Space Agency & European Southern Observatory

ESA ESO

Tycho Brahe and the Foundations of

Observational Astronomy

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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 Tycho Brahe (accurate observations)

(2) why is it as it is Kepler, Galileo, Newton (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 AstronomyFounded 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 such small difference of 8 minutes of arc 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 .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 Theorythat 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 alonethese 8 minutes alone will lead us along a path

to the reform of the whole of Astronomyreform of the whole of Astronomy,, and they are the matter for a great part of this workthey 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 Instead secretly studies Astronomy (Dedication)o everything measured on sky differs from “text books”

• Builds larger, better instruments (Augsburg 5m) o Nov 1572 a SN appears in Cassiopeia (Fortune)o Controls distances to many stars – realizes the variable star

must be in “fixed star sphere” – no parallax, no p.m. o Variability in Eights Sphere, no crystal spheres, universe is

“earthly”

• 1574 called back to Denmark for a state career tracko Marries non-noble woman o Refuses post as Governor on fiefdom (Decisiveness)o 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 - Overhaul of Astronomy • Canonical Tasks in order = entirety of Astronomy textbook prior to Astrophysics 1 - establish latitude of Uraniborg (without fundamental star cat) -- brilliantly achieved 2 - accurate solar orbit -- 1582/83, publ 1602 - tainted by wrong Parallax 3 - construct system of fundamental stars (without good clock) -- very good new value for Precession

4 - establish catalogue of 777 / 1014stars -- published 1602 -- high precision / accuracy 5 - orbits of all planets -- 1582 – 1601 the math was Kepler’s agreed upon job 6 - parallaxes, orbits of comets -- quite a number (~11) break the Crystal Spheres 7 - lunar theory (difficult) -- finds inequalities #3 & #4 -- ventilates “Longitude-Problem” 8 - solar/lunar eclipses -- very good account of many establish zero-points FK 9 - variable stars -- SN 1572, o Ceti (Mira)

• Appealing Stuff Tests to decide between Ptolemaean vs Copernican vs Tychonian

Martian Parallax -- may be the Achilles heel Parallax for Venus -- several trials 0 result

Distances / Sizes of stars -- wrong interpretation of “data”, nothing known about diffraction

• Instrumentation / Calibration / Refraction and other annoyances -- a lot of effort into that / big firsts • Non-Astronomy Astrology -- (not really liked but some neat extra income) Alchemy -- the fashion of the time, everyone had to have a lab Weather -- rich daily weather record for 20 years Poetry -- the signature of “gentlemen” in Renaissance days

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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 ) 55° 54′ 30″

Today’s best value 55° 54′ 28”.7

Tycho is off by only 1”.3

At Uraniborg 1” corresponds to 31 m

Scale of Uraniborg gardens 100 m

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UMi - Polaris – Distance to PoleEpochEpoch LocationLocation 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 alonethese 8 minutes alone will lead us along a path to the reform of the whole of Astronomyreform 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

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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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Sca

le o

f pro

blem

at

Per

ihel

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Ellipse and Circle at Aphel

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How to test Keplerian Theoryin 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

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Refraction

• Tycho first to systematically study refraction

• Adopts 3 tablesSun , Moon (almost =) 0 – 45 AltStellar (=modern) 0 – 20 AltSolar table = Stellar + 4.5’

• Consequences:Obliquity of Ecliptic 2’ wrong“Erroneous” Solar parallax 3’ built inMars to show a spurious parallax

• Why ????Such a diligent and excellent observerSo 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’ accuracyGood 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 and almost equal quantities, plan for comparable refraction)

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~ 300 000 Spherical Triangles to solve