Astrophysics
• Théory: 12 chapters
• Exercises: ± 20 min talk on a chosen subject
• Exam: oral, 2 questions
• Final note: 2/3 exam + 1/3 talk
Structure of the course
1. The birth of astronomy
7. Stellar evolution
2. The solar system
8. Life in the Universe
3. Basic concepts in astrophysics
9. The Milky Way
4. Astronomical observations
10. Galaxies
5. Energy sources
11. The extragalactic Universe
6. Interstellar matter and stellar
birth
12. Cosmology
The birth of astronomy
• The Universe in prescientific civilisations
• Astronomy, daughter of astrology
• Astronomy in antique Greece
• The heliocentric world
The Universe in prescientific civilisations
Genesis 1.14 And God said, Let there be lights in the arch of heaven,
for a division between the day and the night, and let them be for signs,
and for marking the changes of the year, and for days and for years;
1.19 And there was evening and there was morning, the fourth day.
The biblical world :
(influenced by Babylon)
Flat earth, floating on waters
Firmament supported by pillars
(mountains)
The whole inside waters of heaven
The Universe in prescientific civilisations - 2
Creation of the world in babylonian mythology
The female monsterTiamat (primordial chaos) is killed by Marduk
(god of thunder)
Tiamat is cut in two pieces: one half forms earth and the other forms
heaven
The blood of Tiamat’s
partner gives birth to
men
Men’s mission : serve
the gods
The Universe in prescientific civilisations - 3
Creation of the world in egyptian mythology
(Heliopolis version )
Atum (primordial god) gives birth to Chu et Tefnu
Chu (god of air) and Tefnu (goddess of humidity) give birth to twins:
Geb and Nut
Chu (god of air) separates
Nut (goddess of heaven)
from Geb (god of earth),
→ birth of the world as we
know it
The Universe in prescientific civilisations - 4
Magical interpretation of events
Example: the daily cycle of the Sun corresponds to the trip of the god
Rê in the heaven, on his ‘million years boat’
During night, Rê enters the underworld where he has to fight against
the forces of darkness; victorious, he rises again
The unexplained phenomena
are interpreted as individual
actions of deities
No ‘natural laws’
Astronomy, daughter of astrology
Heaven/sky, domain of the gods
• gods live in heaven
• men’s life is subject to the whims of gods
→ watch the sky to find signs of men’s destiny
All celestial bodies keep the same relative
positions except:
– the sun
– the moon
– the 5 wandering stars (planets)
→ their positions are signs
Astronomy, daughter of astrology- 2
The zodiac
The ancients located positions in the sky with respect to arbitrary
stellar groupings that seem to draw easily recognizable pictures: the
constellations
The apparent motion of the Sun and
planets takes place in a zone of the
celestial vault named zodiac
That zone has been divided in 12
constellations (of slightly adapted
size) corresponding to the 12 months
in a year
(one month ~ one lunar cycle)
Astronomy, daughter of astrology- 3
Babylonian and greek astrologies
For the babylonians, the position of planets did influence the destiny
ok kings → it was important to predict the motion of sun, moon and
planets in order to:
– know their configuration at the
time of king’s birth
– predict their future positions
→ birth of astronomy
The greeks adopt the babylonian
ideas but generalize them to all
people
Astronomy, daughter of astrology- 4
Precession of the equinoxes
Planet earth is not perfectly spherical
Solar attraction on the equatorial bulge causes an
oscillation of Earth’s rotation axis with a period of
26000 years, around the perpendicular to the
orbital plane (ecliptic)
The equatorial plane also rotates
→ the intersection between the equatorial
plane and the orbital plane also rotates
→ the constellations of zodiac shift by one
astrological sign every 26000 / 12 = 2170
years, which is not taken into account by the
astrologers
Astronomy in ancient Greece
Thales of Miletus
The ‘first scientist’ born ca. 625 BC
Q : How is the world made?
A : The first and basic principle of all things
is water
(common element that can be found in the 3
phases: solid, liquid, gas)
Imagines the Earth as a disk floating on
waters
Astronomy in ancient Greece - 2
Anaximander
Student of Thales, born around 610 BC
Replaces the single element of Thales by the 4 elements:
– water
– earth
– air
– fire
+ Earth is not floating on waters but is
suspended in pace,
‘equally distant from all things’
Astronomy in ancient Greece - 3
Plato
Born around 430 BC
For him, true knowledge is acquired by reason (eye of the soul) and
not by observation (eye of the body)
Heavenly bodies must be perfect
→ they must move along perfect, immutable
orbits
The perfect geometric forms and the sphere
and the circle
The circular motion of heavenly bodies being
perfect, it can go on forever
Astronomy in ancient Greece - 4
Eudoxus
Student of Plato, born
around 410 BC
Imagines Universe as
concentric spheres
(Eudoxus spheres)
Earth at world’s center
Each sphere rotates with
its own speed
Only approximately
explains the planetary
motions
Astronomy in ancient Greece - 5
Eratosthenes
Alexandria, 3rd Century BC
Determines circumference of Earth
June 21st at noon, the Sun is straight above Syene
However, at Alexandria, its rays make a 7° angle with vertical
Distance between Alexandria and Syene : 5000 stadia
→ circumference of Earth:
5000 × 360 / 7 ≈ 257 000 stadia
Historians thinks that one stadium = 157.5 m
→ circumference = 40 500 km!
Astronomy in ancient Greece - 6
Did Eratosthenes prove that Earth is spherical?
Eratosthenes model: spherical Earth, Sun very far away
7°
Alexandria
d
7°
Syene
→
Astronomy in ancient Greece - 7
Alternative model: flat Earth, nearby Sun
d / D = tg 7° →
D = d / tg 7° ≈ 40 000 stadia ≈ 6400 km
7°
D
7°
d
Alexandria
Syene
Astronomy in ancient Greece - 8
Hipparcos (2nd Century BC)
Determines Earth-Moon distance
d
Max. duration of lunar eclipse: 2.5 h
Moon synodic period: 708 h
2πD/e = 708/2.5 → D/e = 45
2θ = 0.5° = 1/114 rad (ΦSun)
e + 2θD = d
(1/45 + 1/114) D = d
D
θ
θ
D = 32 d
Modern value: D = 30 d
e
Astronomy in ancient Greece - 9
Retrograde motion of planets
Just like the Sun and stars, planets rise East and set West
They seem to move slightly faster than the stars
→ their Eudoxus sphere rotates faster
However, one some occasions, a
planet seems to move more slowly
→ moves back with respect to
stars: retrograde motion
How can it be reconciled with
uniform circular motion?
Astronomy in ancient Greece - 10
Ptolemy
Born in Alexandria around 90 AD
Modifies the Eudoxus system to explain the retrograde motion
Each planet moves on a circle
called epicycle
The centre of the epicycle
moves an another circle called
deferent
epicycle
Earth is the center of deferent
→ reproduces the retrograde
motion, with one epicycle and
one deferent for each planet
deferent
Astronomy in ancient Greece - 11
Ptolemy (2nd act)
The original Ptolemy system does not reproduce accurately the
measurements of Hipparcos (variation of angular velocity)
→ Ptolemy complexifies it to
better match the observations:
– the deferent centre is shifted
with respect to Earth
– the circular motion is uniform
with respect to a point named
equant, symmetrical to Earth
with respect to the deferent
centre
epicycle
equant
deferent
Astronomy in ancient Greece - 12
Unexplained coincidences
• The centres of the Mercury and
Venus epicycles are on the EarthSun line
• For Mars, Jupiter and Saturn:
`radius’ of epicycle parallel to the
Earth-Sun line
→ tendancy of planets to position
with respect to the Sun
Astronomy in ancient Greece - 13
The legacy of the Greeks
+ recourse to reason and not to myths or revealed truths;
freedom of thought
– minor role of observation
+ they knex Earth is spherical (forgotten later)
+ might even have suggested Earth moved around the Sun
(Aristarchus of Samos, 3rd Century BC)
– the belief into `perfection’ of celestial phenomena
(→ circular motions) any progress of astronomy (and science in
general) for more than 1000 years
→ contrasted legacy
The heliocentric world
Nicolaus Copernicus (1473 – 1543)
Born in Torun in a wealthy family, studies 10 years in Italy
→ gets in contact with `new ideas’
Back in Pologne, canon in Frauenburg cathedral
Studies the texts of Ptolemy
Builds a small observatory in a tower
Uses the same measurements of planet
positions as Ptolemy
Shows that they can be interpreted in another
way
The heliocentric world - 2
Copernicus world
Central Sun
Earth and other celestial
bodies (Moon excepted)
revolve around the Sun
Circular orbits
Simply explains the
retrograde motion
Does not account
accurately for the
Hipparcos measurements
→ reintroduces epicycles
The heliocentric world - 3
How to choose between Ptolemy and Copernicus ?
In favour of Ptolemy:
In favour of Copernicus:
• tradition (mostly religion)
• simpler explanation of
retrograde motion
• common sense : if Earth moved,
we would feel it (but Nicolaus de
Cusa (1450) : passenger inside a ship)
• lack of stellar parallax
• decreasing amplitude of the
Mars – Jupiter – Saturn
retrogradations
Ex-aequo :
• similar complexity level
• similar accuracy ( ≈ 5°)
The heliocentric world - 4
Tycho Brahe (1546 – 1601)
Danish aristocrat, studies philosophy at university but is mostly
interested in mathematics
During an eclips, he is strongly impressed by the fact that such events
can be predicted → studies astronomy
1572 : a Nova is observed in the Cassiopeia constellation
Change in the heavens
→ contradiction with the ideas of the Greeks
→ attempt to measure its motion
(celestial or atmospheric phenomenon?)
Lack of accuracy → contradictory conclusions
The heliocentric world - 5
Tycho Brahe (2)
Builds a 5½ feet sextant → shows that the Nova does not move
→ established reputation; King Frederick II of Denmark grants him a
large sum of money + the Hven island where he builds an observatory
During 20 years, Tycho:
• holds court at the palace of Uranienborg
• carries out measurements with an accuarcy
never achieved before
After the death of Frederic II, Tycho’s
character causes troubles with the new king
→ exiles in Prague in 1597
The heliocentric world - 6
Johannes Kepler (1571 – 1630)
Exiled in Prague because of religions wars
Hired as assistant by Tycho Brahe, for
analyzing his planetary positions
measurements
Believed that there was some sort of
overall scheme in the Universe
Spent a large part of his life searching
for that scheme, which would reveal
the ultimate beauty of nature
The heliocentric world - 7
First model of Kepler
Based on the fact that 6 planets and 5 regular solids were known
Heliocentric
The 5 regular solids fit the space
in between the 6 planetary spheres
The heliocentric world - 8
Kepler’s laws (1)
Analysis of Tycho measurements > Kepler reject both geocentrism
and orbits based on circles et discovers 2 empirical laws (1609)
1st law:
2nd law:
Planets move on elliptical orbits
with one focus of the ellips at the
Sun
The line drawn from the Sun to
the planet sweeps equal areas in
equal times
f1
f2
The heliocentric world - 9
Kepler’s laws (2)
Ten years later, he publishes his 3rd law:
The square of the period T of a planet is proportional to the cube of the
semi major axis a of its orbit
3rd law:
T2 / a3 = Ct
b
Contrary to the models of
the Greeks, the Kepler laws
are based on a careful and
detailed analysis of
observations
a
The heliocentric world - 10
Galileo Galilei (1564 – 1642)
Born in an unwealthy family of italian minor nobility
Reads about the invention of the telescope, builds one for himself and
turns it toward the heavens
→ discovers:
• mountains on the Moon
• sunspots
• phases of Venus
• 4 satellites of Jupiter
→ challenges for the platonician /
geocentric system
The heliocentric world - 11
Galileo’s problems with catholic church
Becomes a strong advocate of the heliocentric system
Gifted writer, in italian → popularizes that world model
Dialog concerning the two world systems
• Salvatio (partisan of Copernicus)
(1630)
• Simplicio (partisan of the greek system)
• Sagredo (the one who seeks truth)
Puts into Simplicio’s mouth many arguments advanced by the pope
→ Trial: Galilée, old and sick, is force to recant the heretical doctrine
that the earth is moving
The heliocentric world - 12
Isaac Newton (1642 – 1727)
Born in a relatively wealthy english family
Studies natural philosophy at Cambridge university
1665 – 1666 : epidemy of pest
Newton isolates himself in Woolsthorpe
and invents or discovers:
• the differential and integral calculus
• the theory of colours
• the theory of universal gravitation
The heliocentric world - 13
Philosophiæ Naturalis Principia Mathematica (1687)
Newton shows that the whole mécanics can be deduced from a few
basic principles:
• the 3 laws of motion
including the fundamental law of mecanics :
F=ma
• the law of universal gravitation
m1 m2
F G 2
r
The birth of astronomy
• The Universe in prescientific civilisations
• Astronomy, daughter of astrology
• Astronomy in antique Greece
• The heliocentric world
End of chapter…