This document discusses key topics in gravitation and cosmology, including: 1) Kepler's laws of planetary motion and Newton's theory of universal gravitation. 2) Stellar evolution from gas nebulae to red giants and supernovae. 3) Evidence for the Big Bang theory, such as redshift of starlight and cosmic microwave background radiation. 4) Dark matter and dark energy, which are required to explain the acceleration of the universe's expansion.

1. 2. Gravitation & Cosmology
1. Introduction
2. Geocentric model & Copernicus
3. Kepler´s laws
4. Newton & Gravitation theory
5. Solar system
6. Life of stars
7. Black holes
8. Big bang
9. Space research

2. 1. Introduction
o Motion of stars
o Motion of planets: retrogradation

3. 1. Greek Astronomy
Eudoxus of Cnidus
( IV BC)
o Spheres
o Central position of Earth

4. 1. Greek Astronomy
Ptolemy (II AC)
o Almagest
o Retrogradation
o Epicycles & deferents

5. 1. Greek Astronomy

6. 2. Heliocentric model
Copernicus (1473-1543)
o 1514: “Comentariolus”
heliocentruc
o 1543: “De revolutionibus
orbis coelestium”

7. 2. Heliocentric model
Galileo (1564-1642)
o 1609: Telescope
o 1610: “Sidereus nuncius”
o 1616: Banned by Inquisition
o 1632: “Diálogos sobre los dos
sistemas”
o 1633: Emprisoned

8. 3. Kepler´s laws
32
.rkT =
Johannes Kepler
(1571-1630)
o T. Brahe assistant
o First Law: orbits law
o Second Law: areal velocity
o Third Law:

9. 4. Gravitation theory
Isaac Newton (1643-1733)
“Two bodies are attracted by a
force proportional to their masses
and inversely proportional to the
squared distance between them”
2
.
.
M m
F G
r
=

10. 4. Gravitation consequences
o Gravity force
o Planets motions (Kepler´s laws)
o First Unification of Physics
o Tides prediction
o New planets prediction

11. 5. Solar system
o Sun
o 8 planets & 172 bodies
o Ecliptic
o Orbits

12. 5. Inner planets

13. 5. Outer planets

14. 5. Other bodies
o Dwarf planets: Ceres,
Pluto & Charon, Eris,
Makemake, Haumea
o Comets
o Asteroids, asteroid belt,
Kuiper belt

15. 6. Stellar evolution
o Nebula: gas cloud (mainly
hydrogen)
o Gravitational contraction.
o Protostar. Fusion reaction

16. 6. Stellar evolution
o Red giant , white dwarf
o Red supergiant,
supernova, black holes

17. 7. Black holes
o Body with such a gravitational attraction, that light
cannot be spread
o Huge mass and small size

18. 8. Cosmology
Science which studies
formation, evolution and
state of the universe

19. 8. Edwin Hubble (1889-1953)
o Redshift of star spectra
o Hubble´s law (1929)
V = Ho. d
o Expansion of the
universe

20. 8. Big bang
o Primeval atom hypothesis
(G. LeMaitre, 1927)
o Radiation stage: photons,
quarks, leptons
o Inflation: fast expansion
o Hadrons formation
o Nucleosinthesis
o Stars & galaxies formation

21. 8. Experimental evidence
o Redshift. Edwin Hubble (1924)
o Microwave background radiation
A. Penzias, R. Wilson (1964).
Nobel prize 1978
o Helium and hydrogen composition

22. 8. Dark matter
o No visible matter, identified
by gravitational measurements
© http://www-sk.icrr.u-tokyo.ac.jp

23. 8. Dark energy
o Type of energy , opposite to
gravitational attraction,
required to explain the
accelerated expansion of the
universe

24. 9. Space research
o 1957: First satellite: Sputnik
o 1961: Firs astronaut: Yuri
Gagarin
o 1965: Mariner programme
to Venus
o 1969: Apolo XI on the
Moon
o 1976: Vicking I & II to
Mars
o 1980: Voyager I & II Solar
system

25. 9. Satellites
o Geostationary, polar...
o Communications,
metheorological
o Geolocation: GPS, Galileo
o Research: COBE, Soho,
Hubble