Cosmic Distances from antiquity to present day

1. Cosmic Distancesfrom antiquity to present day Manel Errando Trias IFAE Thursday Meeting - 13.01.2005

2. Outline • How to describe celestial motions • Ptolemy and the Greek astronomy • Copernican revolution • Tycho and Kepler • Venus transit of 1761 and the astronomical unit

3. The simplest example...

4. let’s make it a bit more complicated we require the radius from D to A to remain parallel to BC Not a perfect description... How would the inhabitants of planet B describe this universe? A and C can collide! • it allows AB to vary over the correct range • it keeps distances CB and CA fixed • it avoids collisions between C and A! this is what the Greeks called an Epicycle-Deferent system

5. what did the greeks know? • they knew the sun, the moon and the five classical planets: mercury, venus, mars, jupiter and saturn. • some planets present a bounded elongation respect to the sun. • planets exhibit retrograde motion at certain times. • they observed the phases of the moon, eclipses, conjunctions and oppositions, ... Mercury is allways found within 28º on either side of the sun and Venus within 46º and of course they had powerful mathematical tools to account for these phenomena...

6. Aristarchus of Samos • Aristarchus lived in the third century B.C. • He was the first to put forth the thesis that the earth rotates and also revolves around the sun, being it taken as the center of the cosmos. • His work On the Sizes and Distances of the Sun and Moon presents a method for determining the relative radii of the sun and the moon and also the relative distances of those objects from us.

7. Aristarchus of Samos The lunar dichotomy method • He estimated the ratio ES/EM to be between 18 and 20... The actual value is around 390. • The MES angle is not 87º but 89º50’. • This method depends strongly on a good determination of the moment when the moon is in half phase. • The results depend on an accuracy of measurement that was impossible to achieve.

8. Ptolemy • Claudius Ptolemy lived in the second century A.D. in Alexandria. • His treatise Almagest presents the “Ptolemaic Model”, that kept its validity over thirteen centuries. • His scheme of cosmic dimensions, derived from the mathematical models of the Almagest, are presented in his Planetary Hypotheses.

9. The Ptolemaic System • His model was based on the Epicycle-Deferent system, improved with the use of the eccentric circle and the equant • He had to account for retrograde motions • and bounded elongations

10. The Ptolemaic System

11. Nicholas Copernicus • Copernicus was born in 1473 and published De revolutionibus orbium coelestium in 1543, weeks before his death. • His work pointed out the need of changing from a geocentric and geostatic system to an heliocentric system. • His heliocentric theory was one of the most important breakthroughs on the history of science, transcending astronomy to philosophy and theology.

12. The Universe is spherical The Earth too is spherical The motion of the heavenly bodies is uniform, eternal, and circular or compounded of circular motions The Earth rotates and orbits around the Sun The heavens are immense compared to the size of the Earth The Sun is at rest in the middle of the universe The Copernican System Main Copernicus theses

13. The Copernican System • It accounts for the movement of the sun trough the ecliptic • It gives an explanation for the bounded elongation of mercury and venus • It also explains the retrograde motions of the outer planets

14. The Copernican System

15. Implications of the Heliocentric Theory • Copernicus showed that the annual orbit of the Earth around the Sun would explain the observed irregularities in the motions of planets. • His cosmological model was by far simpler and more elegant than the Ptolemaic and all its improvements made on the last thousand years. • Its philosophical implications transcended even its astronomical impact, moving away the earth, and humans, from their privileged position in the universe.

16. The absence of Parallax Effects of Earth’s motion Theological problems Implications of the Heliocentric Theory Book of Joshua 10:12 ...Joshua said to the LORD in the presence of Israel: O sun, stand still over Gibeon, O moon, over the Valley of Aijalon. 10:13 So the sun stood still, and the moon stopped… On equator, a person moves at about 1.500 km/h Due to translation, the Earth travels at 5.000 km/h

17. Tycho Brahe • Tycho was born in 1546 and was the finest pre-telescopic observer of all time. • He constructed the best astronomical observatory available at his time, where he attained unprecedented accuracy on measuring the position of an object in the heavens. • Tycho favored neither the Ptolemaic nor the Copernican system, but created his own one.

18. The Tychonic System • Brahe criticized the Ptolemaic system: • Use of the equant • Lack of elegance in accounting for retrogressions of the planets • and also the heliocentric view of Copernicus: • It violates physical principles • It necessitates a stellar parallax • It contradicts Holy Writ • All the planets orbit around the sun. • The sun revolves around the earth carrying the orbits of the planets with it. • The entire arrangement should rotate once a day to account for the daily motion of celestial bodies.

19. Johannes Kepler • Kepler was born in 1571 and published his Harmonices Mundi in 1619. • He worked with Tycho Brahe and was one of the first supporters of heliocentric theory. • He developed an heliocentric model compatible with the observations made by Tycho Brahe.

20. Kepler pondered three main questions: Why are there six planets? Why are their orbits positioned as they are? Why do planets farther from the sun move more slowly? 5 Perfect Solids The First Keplerian Model tetrahedron cube octahedron dodecahedron icosahedron

21. The First Keplerian Model

22. Kepler’s Synthesis • Perfect solids model had not enough predictive power, specially for Mars. After many attempts, Kepler proposed three conjectures that he could also extend to all the planets: • A planet orbits the sun in an ellipse, with the sun at one focus of the ellipse • A line connecting a planet with the sun sweeps out equal areas in equal times • The square of the orbital period divided by the cube of the orbital distance is a constant for any planet

23. Kepler’s Synthesis

24. Venus transit of 1761 • In 1716 Edmund Halley proposed a method to observe the parallax of Venus on the Sun during a Venus transit and infer the Sun-Earth distance from it. • With the instruments available, mainly telescopes, a very good accuracy could be achieved. • It was the first international scientific campaign, with almost 200 astronomers in more than 70 stations around the globe tried to observe the transit.

25. Earth Venus Sun a/2 = b V Observer 1 2r a 0.5 degrees S Observer 2 d a E d = r / tan(b) Venus transit of 1761

26. Up-to-date measurements • Bouncing a radar signal off another planet, the time it takes the radar signal to go to the planet and return divided by the speed of light gives twice the distance to the planet. • Nowadays the astronomical unit is calculated with great precision using the echo of radar signals sent to Venus and relating this distance to the earth’s orbital radius using Kepler’s the third law. • The actual value is 149.597.870 km and comes from the averaging of years of measurements.

27. Final conclusions • The first astronomers did not failed describing the universe, they just tried to be coherent with the observations they made. • These models could give estimations for the relative distances between heavenly bodies, but direct measurements of these distances needed instrumentation that was not available until the 17th century. • Maybe future scientists will think about some of the now accepted theories in the same way as we now see the first cosmological models.