2. VII
Cosmic

3. The infinite (apeiron) is inexhaustible
The infinite (apeiron) is inexhaustible. Wherever the warrior stands he can stretch out his spear.
Anaximander of Miletus ( ) pupil of Thales

4. Anaxagoras ( )
To every great there exists a greater.
Empedocles ( )
The universe is three times as large as the system earth moon.
Democritus ( )
Milky way consists of many stars.
The universe has no center.
Aristotle ( )
The earth is tiny compared to the universe.
The earth is in the center of the universe.
When sailing to south always new stars appear:
The earth is a sphere.

5. Aristarchus of Samos (310-230)
First proponent of the heliocentric system
His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface. (reported by Archimedes)

6. Aristarchus of Samos (310-230)
First proponent of the heliocentric system
Ratio of distances to moon and sun
Angle measured: 87°  cos 87° = 1 : 19
Improved by Kepler: 89°51'  1 : 380

7. Eratosthenes ( )
Born in Cyrene
(today Schahhat, Libya)
240: third chairman of the Museion
Educator of the crown prince
Very universal scholar
Invented the leap day.
Produced the first astronomical map with over 600 stars.
Mesolabium, doubling the cube
Commited suicide when gone blind.
Sieve of Eratosthenes

8. Determined the circumference of the earth.
Alexandria (31°)
Well diggers in Syene (= Assuan, 24°)
Result: km
improved in 1670: km
correct: km (measured over the poles)

9. Titus Lucretuius Carus (95-55)
The universe is not bounded in any direction. Otherwise there had to exist a border. But then something had to exist at the other side.
Claudius Ptolemaios (85-165)
Worked in Alexandria
Fair skin, small feet, red birthmark at his chin, black beard ???
Geocentric system
Deferent
Epicycle

10. Nicolaus Copernikus
( )
1510: Foundations of his heliocentric system.
1543: De revolutionibus orbium coelestium

11. Nicole d‘Oresme ( )
Heliocentric system. The revolution of earth explains the movement of the stars.
Jean Buridan ( )
Prof. at Univ. Paris
Concept of impetus (inertia)
Thought like Oresme.
Buridan's donkey
Nikolaus Cusanus ( )
Cardinal
The universe is endless.
It has no centre and looks the same from every position.

12. William Gilbert ( )
Physicist and physician
Invented the word electricity
1651: De mundo nostro sublunari
The Gilbert-epoch is a paleomagnetic epoch million years ago with reversed direction of the terrestrial magnetic field.

13. Thomas Digges ( )
Dark sky paradox
1576: Infinite World
"But there can be no movement of infinity and of an infinite body, and therefore no diurnal revolution of that vastest Primum mobile."

14. Tycho Brahe ( )
1599 imperial mathematician and astronomer in Prague
Refused Copernican circles and epicycles because of his better data.
All planets revolve around the sun, but the sun revolves around the earth. Declined to accept crystal spheres.
1600 employed Kepler as his assistant.
Johannes Kepler ( )
Accepted the Copernican system.
Found the laws of planetary motion, based on Brahe's precise measurements.
"The universe is unmeasurably great."

15. Giordano Bruno ( )
Dominican, accused of heresy. Escaped to Germay, France, England and taught there. Was promised to remain untouched and returned in The inquisition nevertheless caught and imprisoned and charged him of heresy and burnt him in Rome at the stake.
Most important natural philosopher of the renaissance.
There are infinitely many inhabited worlds.
The universe has no border, it cannot grow nor shrink nor move.
It has not been created and cannot cease.

16. Edmond Halley ( )
1720 second Astronomer Royal and director of the Greenwich-observatory.
Formula for barometric detemination of altitude.
Calculated the trajectories of 24 comets, tree of them 1531, 1607, and 1682, were so similar that he recognized them as only one comet: Today called comet Halley with a period of 76 years. Halley pedicted its return for 1759 but did not live to see it.
"I have heard urged that if the number of Fixt Stars were more than finite, the whole superficies of their apparent Sphere would be luminous ..."

17. Thomas Wright ( )
1750 first explanation of milky way.
Nebulae are distant galaxies.
Immanuel Kant ( )
1770: Professor of logic und metaphysics
: Rector of Königsberg university
One of the greatest German philosophers
founded by his three critiques a new epoch of philosophy.
1754: Tides caused by the moon. Responsible for its bounded rotation.
1755: There are many Welteninseln.
Kant's elaboration of the nebular hypothesis founded the scientific cosmogeny.

18. Astronomer and physician at Bremen
Heinrich Olbers ( )
Astronomer and physician at Bremen
Olbers' paradox: Why is the sky dark at night?
Solid angle covered by a star ~ A/r2
Number of stars in a spherical shell ~ r2Dr
Solid angle covered by stars of a shell ~ ADr
Stars of infinitely many shells cover the whole sphere. r

19. Friedrich Wilhelm Bessel (1784-1846)
First merchant, then professor of astronomy and director of the observatory at Königsberg, supported by Olbers.
1838 first measuremet of the distance of a fixed star: Angular difference in summer and winter: Parallax 0,5'' = 1/3600 angular diameter of the moon.  11 light years distance.
From the ondulatory motion of Sirius he concluded the existence of an unseen companion.

20. Vesto Slipher ( )
1912 measured redshift of galaxies.
36 of 41 galaxies move off of us.
Edwin Hubble ( ) found, using the 254-cm-reflector on Mount Wilson, Andromeda nebula consists of stars, among them variables with known absolute brightness.  2 mio light years distance.
1929: Expansion of the universe.
Hubble-constant: v = Hr.
Finite universe with Doppler-redshift
Expansion of the universe started 13.7109 years ago.
age = 4.31017 s
radius: 46.5109 light years

21. George Gamow ( )
1949: predicted cosmic background radiation
remaining from the big bang.
Arno Penzias (*1933) Robert Woodrow Wilson (*1936)
1965: Discovery of cosmic background radiation

22. 2,7 K
Maximum at l = 1,1 mm
375 photons / cm3

23. 3 March 1972: Start of Pioneer 10
Directions of 14 pulsars including present frequencies.
Binary numbers in units of the length and frequency of the hydrogen molecule.
Pioneer 10 left the solar system at 12 June 1983.
Last signal received at 22 Jan 2003 from 11 light hours distance.
After 2 mio years it will meet Aldebaran (67 light years away).
The closest man has ever come to infinity.

24. Voyager I took this picture 18 September 1977 from 11 million km away.
The spacecrafts will probably survive mankind and earth.

25. The earth at a distance of 6 billion km (Voyager I)

30. Two things are infinite:
The universe
and
human stupidity.
With the universe I am not totally sure.

31. Radius of the universe = 46.5109 lightyears
Volume of the universe = 1080 m3
1080 atoms
1088 photons
1080 m3 / (10-95 m)3
 less than elementary cells

33. Appendix

34. n-dimensional Cube Diagonal an Circumference 4a
the zero-dimensional interval is the point
the one-dimensional interval is the set {x  0  x  a}
the two-dimensional interval {(x1, x2)  0  x1  a, 0  x2  a}
the three-dimensional interval {(x1, x2, x3)  0  xn  a}
the four-dimensional interval {(x1, x2, x3, x4)  0  xn  a}
...
Diagonal an
Circumference 4a
an n V/a
One-dimensional (linear) beings populating the surface (edges) of a square have to go 4a for a full circumnavigation of their world.
Two-dimensional (areal) beings populating the surface of a three-dimensional square (cube) have to go 4a for a full circumnavigation of their world.
Three-dimensional (spatial) beings populating the surface of a four-dimensional cube have to go 4a for a full circumnavigation of their world.
A 4d cube can be imagined as a 3d cube moving or growing or shrinking on the time axis. Each of its six areas gives a cube, just like initial and final state.

35. n-dimensional Sphere: {(x1,x2,x3,...,xn)  0 Sxn2 r2 } Volume:
(n-1)-dimensional Surface: {(x1,x2,x3,...,xn)  Sxn2 = r2 }
Area: An = Vn/r
Diameter 2r
Circumference 2pr
One-dimensional (linear) beings populating the surface (periphery) of a circle have to go 2pr for a full circumnavigation of their world.
Two-dimensional (areal) beings populating the surface of a three-dimensional circle (sphere) have to go 2pr for a full circumnavigation of their world.
Three-dimensional (spatial) beings populating the surface of a four-dimensional sphere have to go 2pr for a full circumnavigation of their world.
Universe: r = 46.5 billion light years, so we have to travel c. 300 billion light years.