KANT and HERSCHEL
- the interaction of theory and
observation ?
Michael Rowan-Robinson
Imperial College
May 20th 2011
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Kant’s cosmogony
Universal Natural History and Theory of the Heavens (1755)
Kant notes that Thomas Wright (1750) explains
Milky Way as due to a planar distribution of
stars confined between two planes.
He asks why stars are distributed relative to a
fixed plane. Argues that it is the effect of gravitational attraction between
the stars, since the force of gravity extends to infinity.
‘Thus all the systems of the universe are found so constituted by their
mutual approach, which is incessant, and is hindered by nothing, that
they will fall together sooner or later into one mass, unless this ruin is
prevented by the action of centrifugal forces, as in the globes of our
planetary
system.’
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Thomas Wright’s explanation of Milky Way
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Kant’s cosmogony (2)
Suggests by analogy with the solar system that the orbits of the stars are
confined to a plane. The Milky Way is like a vast solar system, in
circular motion.
‘The breadth of this luminous zone, which represents a sort of zodiac,
will be determined by the different degrees of deviation of the said
wandering stars from the plane of their relation, and by the inclination of
their orbits to this plane.’ [actually they weave in and out of the plane]
Since he is arguing that all the stars are in motion, he estimates what the
orbital period of the nearest star about the sun would be. Uses Huygens
(1698) estimate of distance of Sirius as 21000 AU, and Kepler’s law, to
estimate that it would take 1.5 million years to orbit the Sun. So proper
motions of nearest stars would be small. Kant believes observers should
try to
detect these motions.
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Kant’s cosmogony (3)
‘I now come to that part of my theory which gives it its greatest
charm, by the sublime idea which it presents of the plan of creation.’
Kant asks what a system like our Milky Way would look like from a
great distance and concludes that it
‘will appear under a small angle as a patch of space whose figure will
be circular if its plane is presented directly to the eye, and elliptical if it
is seen from the side or obliquely. The feebleness of its light, its
figure, and the apparent size of its diameter will clearly distinguish
such a phenomenon when it is presented, from all the stars that are seen
single.’
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Kant’s cosmogony (4)
‘ We do not need to look long for this phenomenon among the observations of the
astronomers. It has been distinctly perceived by different observers. … It is the
‘nebulous’ stars which we refer to, or rather a species of them, which M. de
Maupertuis thus describes: ‘They are’, he says, ‘small luminous patches, only a little
more brilliant than the dark background of the heavens; they are presented in all
quarters; they present the figures of ellipses more or less open; and their light is much
feebler than that of any other object we can perceive in the heavens.’
[de Maupertuis, 1742, Discours sur la Figure des Astres]
Christopher Wren had also speculated along these lines:
future astronomers might find ‘the Galaxy to be myriads of stars; and every nebulous
star appearing as if it were the firmament of some other world, at an
incomprehensible distance, buried in the vast abyss of intermundious vacuum’
[Inaugural address as 9th professor of astronomy at Gresham College, London, 1657]
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Kant’s cosmogony (5)
Kant also speculates on how such systems might have formed and comes up with the
idea that if a region of the universe has a slightly higher density that average then
nearby matter would tend to fall towards this region. His picture is that the galaxies
represent regions were development of order has proceeded strongly, whereas outside
there is still primordial chaos. [a very modern picture]
Kant’s idea of a rotating Milky Way system was not demonstrated conclusively until
radio astronomers’ maps in the 1950s and 1960s. The slower fall of the rotation
speed with distance than Kepler’s law would predict demonstrated in the 1980s that
there must by a dark matter halo around the Milky Way.
Kant’s idea of growth of structure from density perturbations became firmly
established through computer simulations, matched to large-scale galaxy surveys, in
the 1980s and 90s.
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Evidence for Dark Matter
The speed at which stars
orbit round a galaxy points
to the existence of a halo
of dark matter.
Sensitive surveys show
that this can not be due to
stars, or gas.
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Kant’s cosmogony (6)
In Part 2 of Universal Natural History Kant goes on to discuss origin of solar system
from a diffuse cloud of gas, contracting under the influence of gravity. A central
condensation develops, with centrifugal force determining the orbits of material
further out.
‘This body at the middle point of the force of attraction, which, on account of of the
large amount of its assembled material, has accordingly become the main piece of the
planetary structure, is the sun, although at this time it does not yet immediately have
that flaming glow, which breaks out on its surface when its development is fully
complete.’
‘The planets are developed out of particles, which, at the heights where they are
suspended, have precise movements in circular orbits. Thus, the masses formed by
their combination will continue exactly the same movements at precisely the same
level and in exactly the same direction. This is sufficient to understand why the
movement of the planets is approximately circular and why their orbits are on a single
plane.’
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This picture is known as the Kant-Laplace nebular hypothesis.
comments on Kant’s contribution
Kant’s treatise is hard to read, because like medieval theologians and modern
creationists he is far too interested in deducing the attributes of God from the universe
or vice versa. But it does read like the work of a professional: he has read the
literature and cites it effectively. This is not just armchair speculation. However
there is no mathematical detail at all and so Kant’s musings are but a prelude to the
work of the great Laplace (1749-1827), ‘the French Newton’, who laid the
foundations of gravitational astrophysics.
Kant is aware of the observations of his time. He speculates, he makes suggestions
about future observations, eg proper motion. But we can’t really call him a
theoretician, compared with Euler, Lagrange, Laplace. He deserves about as much
credit for his speculations about the origin of structure as Goethe does for the theory
of evolution [and Darwin does cite Goethe in Origin of Species].
His work does not seem to have been noticed by Herschel or Laplace, and it was not
till the 1840s that Arago and von Humboldt drew attention to Kant’s astronomical
speculations. [Note: the lives of Kant, Herschel and Laplace overlapped for 55 years.]
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comments on Kant’s contribution (2)
The only philosopher after Kant to make a significant contribution to astronomy and
cosmology was Ernst Mach (1838-1916), who influenced Einstein, although Mach’s
Principle has dropped out of fashion today.
Edgar Allan Poe’s Eureka (1848), written in a similar discursive style to Kant’s
treatise, contains an insightful discussion of why the sky is dark at night and has hints
of big bang cosmology, and of the concept of a cosmological horizon.
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Laplace’s nebular hypothesis
Laplace’s theory appears as Note VII at the very end of his Exposition
du Systeme du Monde (1824).
‘On a, par le chapitre precedent, pour remonter a la cause des
movemens primitifs du systeme planetaire, les cinq phonomenes suivans:
Les movements des planetes dans le meme sens, et a peu pres dans un
meme plan; les movemens des satellites dans le meme sens que ceux des planetes; les
mouvements de rotation de ces differens corps et du soleil, dans le meme sens que
leur mouvemens de projection et dans des plans peu differens; le peu d’excentricite
des orbes des orbes de planetes et des satellites; enfin, la grande d’excentricite des
orbes de cometes, quique leurs inclinasions aient ete abandonnees au hasard.’
[refers to Buffon, Mitchell, Mayer, Olbers,Bouvard, Nicollet, Dalembre, but not
Kant]
Other achievements: Laplace equation, Laplace transform, stability of solar system,
conservation of eccentricity and inclination, spherical harmonics, potential theory,
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proofMayof20th
method
of least squares, probability
theory, speed of sound.
William Herschel’s impact
• Discovery of Uranus 1781
• Construction of giant telescopes
• Surveys for nebulae 1783-1817 [stimulated by Messier’s 1783 list]
• Solar motion
• Star counts to map structure of Milky Way 1784,1785
[One problem is the distances of the stars. Even if all stars had same luminosity, the
conversion from magnitude to apparent flux was not known. Herschel tended to
assume that stars of magnitude
1
2
3
4
5
6
7
8
9
10
were at relative distance
1
2
3
4
5
6
7
8
9
10
whereas the correct value (for a star of fixed luminosity) is
1
1.6
2.5
4.0
6.3
10
16
25
40
63
ie not too bad an assumption for magnitudes 2-5, but gets exponentially worse.
Second problem: dust plays major role in determining star-density in different
directions. So Herschel could not in fact determine structure of our Galaxy from starMay 20th 2011
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counts.]
William Herschel’s impact (2)
The problem of distances in the Milky Way not solved till 1920s, using Cepheid
variable stars. Hubble’s application to other galaxies was off by a factor 8. Resolved
by Allan Sandage in 1958, to accuracy 20%. Accuracy of 2% in scale of universe
(Hubble constant) reached in 2006 (WMAP satellite).
Role of dust in determining appearance of Milky Way not appreciated until
Trumpler (1936).
Star counts have in fact been used to determine structure of our Galaxy in modern
times, especially at infrared wavelengths (eg Bahcall 1986, Rowan-Robinson and
Chester, 1987). Advantage of infrared wavelengths is greatly reduced effect of dust.
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The key modern distance indicator –
Cepheid variable stars
Delta Cephei is the prototype of the
Cepheid variable stars, massive stars
which pulsate and vary their light output
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Henrietta Leavitt’s breakthrough
In 1912, Henrietta Leavitt, working
at the Harvard Observatory, discovered
from her studies of Cepheids in the
Small Magellanic Cloud that the period
of Cepheid variability was related to
luminosity
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The distances of the
galaxies
In 1924 Edwin Hubble used
Leavitt’s discovery to estimate
the distance of the Andromeda
Nebula. It clearly lay far
outside the Milky Way
System.
System
This opened up the idea of a
universe of galaxies.
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Bahcall 1986: star counts and galactic
structure
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William Herschel’s impact (3)
* Concept of evolution of nebulae and star clusters 1789
[ but it needed infrared and submillimetre astronomy of 1970s and 80s to understand
star formation in molecular gas clouds]
* Formation of structure (star clusters) through gravity 1785
[but no mathematical detail, so no real advance on Kant]
* Infrared radiation 1800
[for me, Herschel’s most significant discovery, opening the way to the astronomy of
the whole electromagnetic spectrum]
In his discussion of nebulae and the Milky Way and its structure, Herschel seems to
be unaware of, and certainly makes no reference to, Wright and Kant. However to be
fair, Laplace does not refer to Kant either in his discussion of the nebular hypothesis
for the origin of the solar system (he refers to Herschel at least twice in Systeme du
Monde). Herschel actually refers very rarely to other scientists in his papers, perhaps
a relic of his amateur beginnings.
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the meeting of Herschel and Laplace
In 1802 Herschel travelled to Paris and had several meetings with Laplace.
He had an audience with Napoleon, at which Laplace was present.
Herschel gave an outline of his findings on the structure of the heavens.
Napoleon then invited Laplace to explain how this might come about.
An interaction of sorts between observation and theory ?
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Modern galaxy surveys
• the survey of nebulae by William, Caroline and John Herschel (1864,
5000 objects) was updated by J.L.E.Dreyer in 1880 in the
New General Catalogue of Nebulae and Clusters of Stars(7840 objects)
• de Vaucouleurs 1976: 2nd Reference Catalogue of Bright Galaxies
(4364 galaxies)
• the IRAS (Infrared Astronomical Satellite) all-sky galaxy survey
- Rowan-Robinson et al 1991 (17664 galaxies)
- used to map 3-D galaxy distribution (redshift gives distance)
- demonstrated origin of our Galaxy’s motion through the
cosmic frame (cf Herschel’s estimate of Solar motion)
- estimate of density of universe in form of dark matter
• today: surveys planned from ground (eg LSST) and space (eg EUCLID)
to study details of ‘dark energy’
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Mapping the Universe
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Large scale structure
The 3-dimensional
distribution of
galaxies shows
structure on
different scales.
This can be used
to estimate the
average density
of the universe
  ~ 0.27
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IRAS PSCz survey galaxy density 3-D map
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Modern ideas on formation of stars and
galaxies
• Jeans 1902: condition for collapse of a gas cloud
• Hoyle 1953: on the fragmentation of gas clouds into stars and galaxies
• Mestel 1963: on the galactic law of rotation
• Lin and Shu 1964: on the spiral structure of disk galaxies
• Toomre 1964: on the gravitational stability of a disk of stars
- spiral structure due to an instability, a wave that rotates through
the disk of gas causing star formation, triggered by interaction with a
companion galaxy
• White and Rees 1978: core condensation in heavy halos
- dark matter aggregates into halos, then gas condenses in the
gravitational potential well of these halos and forms a disk of stars
- this picture confirmed by n-body simulations
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Lin and Shu 1964: on the spiral structure
of disk galaxies
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final thoughts
astronomy advances through interaction of theory and observation
- it’s certainly how we do things today
does the case of Kant-Herschel-Laplace bear this out ?
Kant’s speculations were prescient, but they do not seem to have
influenced Herschel (or Laplace)
Herschel and Laplace met, but was it a meeting of minds ?
What does modern astronomy owe to these three great contemporaries?
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