théory: 12 chapters exercises: ± 20 min talk on a chosen subject exam: oral, 2 questions final...
TRANSCRIPT
• Théory: 12 chapters
• Exercises: ± 20 min talk on a chosen subject
• Exam: oral, 2 questions
• Final note: 2/3 exam + 1/3 talk
Astrophysics
1. The birth of astronomy
2. The solar system
3. Basic concepts in astrophysics
4. Astronomical observations
5. Energy sources
6. Interstellar matter and stellar birth
Structure of the course
7. Stellar evolution
8. Life in the Universe
9. The Milky Way
10. Galaxies
11. The extragalactic Universe
12. Cosmology
• The Universe in prescientific civilisations
• Astronomy, daughter of astrology
• Astronomy in antique Greece
• The heliocentric world
The birth of astronomy
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
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 - 2
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 - 3
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’
The Universe in prescientific civilisations - 4
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
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
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- 2
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- 3
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, daughter of astrology- 4
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
Thales of Miletus
The ‘first scientist’ born ca. 625 BC
Q : How is the world made?
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 - 2
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 - 3
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 - 4
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 - 5
Did Eratosthenes prove that Earth is spherical?
Eratosthenes model: spherical Earth, Sun very far away
Alexandria
Syene
→ 7°
7°
d
Astronomy in ancient Greece - 6
Alternative model: flat Earth, nearby Sun
d / D = tg 7° → D = d / tg 7° ≈ 40 000 stadia ≈ 6400 km
Alexandria Syene
7°
d
7°D
Astronomy in ancient Greece - 7
Hipparcos (2nd Century BC)
Determines Earth-Moon distance
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 = 32 d
Modern value: D = 30 d
θ θ
d
D
e
Astronomy in ancient Greece - 8
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 - 9
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
Earth is the center of deferent
→ reproduces the retrograde motion, with one epicycle and one deferent for each planet
deferent
epicycle
Astronomy in ancient Greece - 10
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
deferent
epicycle
equant
Astronomy in ancient Greece - 11
Unexplained coincidences
• The centres of the Mercury and Venus epicycles are on the Earth-Sun 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 - 12
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
Astronomy in ancient Greece - 13
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
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
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 - 2
How to choose between Ptolemy and Copernicus ?
In favour of Ptolemy:
• tradition (mostly religion)
• common sense : if Earth moved, we would feel it (but Nicolaus de Cusa (1450) : passenger inside a ship)
• lack of stellar parallax
In favour of Copernicus:
• simpler explanation of retrograde motion
• decreasing amplitude of the Mars – Jupiter – Saturn retrogradations
Ex-aequo :
• similar complexity level
• similar accuracy ( ≈ 5°)
The heliocentric world - 3
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
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
The heliocentric world - 4
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
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
The heliocentric world - 5
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
Johannes Kepler (1571 – 1630)
Exiled in Prague because of religions wars
The heliocentric world - 6
Heliocentric
The 5 regular solids fit the space in between the 6 planetary spheres
First model of Kepler
Based on the fact that 6 planets and 5 regular solids were known
The heliocentric world - 7
1st law:
Planets move on elliptical orbits with one focus of the ellips at the Sun
Kepler’s laws (1)
Analysis of Tycho measurements > Kepler reject both geocentrism and orbits based on circles et discovers 2 empirical laws (1609)
2nd law:
The line drawn from the Sun to the planet sweeps equal areas in equal times
f1 f2
The heliocentric world - 8
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
b
a
3rd law:
T2 / a3 = Ct
Contrary to the models of the Greeks, the Kepler laws are based on a careful and detailed analysis of observations
The heliocentric world - 9
→ discovers:
• mountains on the Moon
• sunspots
• phases of Venus
• 4 satellites of Jupiter
→ challenges for the platonician / geocentric system
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
The heliocentric world - 10
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 - 11
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
Isaac Newton (1642 – 1727)
Born in a relatively wealthy english family
Studies natural philosophy at Cambridge university
The heliocentric world - 12
• the 3 laws of motion including the fundamental law of mecanics :
F = m a
• the law of universal gravitation
Philosophiæ Naturalis Principia Mathematica (1687)
Newton shows that the whole mécanics can be deduced from a few basic principles:
221
rmm
GF
The heliocentric world - 13