Astronomy 2 Overview of the Universe Winter 2006 2. Lectures on Copernicus to Modern Times.

1. Astronomy 2Overview of the UniverseWinter 20062.Lectures onCopernicus to Modern Times. Joe Miller

2. Nicholas Copernicus (1473-1543) • Proposed heliocentric system. • Inferior planets, superior planets, planetary configurations. • Seasons. • Sidereal, synodic periods. • Distances of planets from the sun, assuming circular orbits. • Still had epicycles. • Parallax problem still there.

3. Siderial period: one revolution around the sun with respect to the stars.Synodic period: the time between two successive identical geometrical configurations. Geometrical configurations:Opposition: a planet is in opposition when it is opposite the sun in the sky.Conjunction: a planet is lined up with the sun.A superior planet has its orbit outside the earth’s orbit, an inferior planet’s orbit is inside.

4. Planetary Configurations

5. The time between two oppositions is one synodic period- easy to observe. But how do you determine the siderial period of another planet? We know what the earth’s is- one siderial year.Inferior planet case:Let S = synodic period, E =period of the earth,and P = siderial period of planet.In one day earth goes 360o/E degrees around the sun.In one day planet goes 360o/P degrees around the sun.In one synodic period, earth goes S(360o/E), and planet goes S(360o/P) . But an inferior planet makesone extra trip around the sun (it “laps” the earth), so it goes an extra 360o. ThereforeS(360o/P) - 360o = S(360o/E),or dividing through by S and 360o, we have1/P - 1/S = 1/E. Since E = 1 year, we can write 1/P = 1 + 1/S Inferior planets.In like manner, for superior planets it is the earth that travels the extra 360o, so 360o has to be subtracted from the distance the earth travels and we get 1/P = 1 - 1/S. Superior planets.

6. The general formula: 1/S = 1/P(faster) - 1/P(slower)The earth is the faster for superior planets, while it is the slower for exterior planets.

8. Copernicus determined the relative distances of the planets from the sun. He made direct use of the heliocentric system, the known sidereal and synodic periods of the planets, and observations of the times of specific planetary configurations: greatest elongation for inferior planets, and quadrature and opposition for superior planets.He made two basic assumptions:1) Orbits of planets are perfect circles.2) All planets travel at constant speed in their orbits.He defined the distance of the earth to the sun to be 1.0, so that all other distance would be in terms of the earth-sun distance.

9. Inferior planets (Mercury and Venus)

10. Superior planets (Mars, Jupiter, and Saturn)

11. Results

12. The seasons: primarily the result of the tilt of the earth’s axis.

13. Tycho Brahe (1546-1601) • A Danish nobleman a disagreeable snob. • A clever instrument builder and excellent observer. • Supernova of 1572 was beyond the moon’s orbit. • Comet of 1577 was at least three times the distance to the moon- no detectable parallax- and probably in orbit around the sun. • 30 years of very accurate data on planetary positions. • Hired Johannes Kepler. • Invented the “Tychonic System.”

17. The “Tychonic” System

18. Johannes Kepler (1571-1630)

19. Kepler was a staunch believer in the Copernican System • His assignment by Tycho was to go over the observations of Mars’ positions. He spent 25 years doing this. • He was driven to find order and harmony in the heavens. His reasoning could flip rapidly between the mystical and the rigorously scientific. • He fit the five regular solids of Euclid between the orbits of the planets, which he thought was demonstration of the harmony of the universe.

21. Kepler first investigated the shape of Mars’ orbit. The approach was to use pairs of observations of Mars separated by one sidereal period of Mars. These pair would be made when Mars was in the same position in its orbit, but the earth was at a different position in its orbit.

22. By this approach Kepler finally worked out that the orbit of Mars was not a circle, as had been believed for nearly 20 centuries, but a mathematical curve called an ellipse. The ellipse is a conic section:

23. Another view of conic sections:

24. C a

27. Kepler’s First Law:A planet travels around the sun in an orbit of elliptical shape with the sun at one focus.

28. Kepler’s Second Law:The line from a planet to the sun sweeps over equal areas in equal times.In modern terminology, this is a result of the conservation of angular momentum.

32. P. 70

33. Galileo Galilei (1564-1642) • Contemporary of Kepler • Modern scientist- rejected Aristotelian approach. • Excellent observer and experimenter. • Explained earthshine. • Discovered the law of the pendulum • Noticed speed of hailstones. • Founded the science of mechanics. • Heard about a telescope and immediately built one. His observations of the sky profoundly confronted modern beliefs.

35. Galileo founded modern mechanics: the study of the motions of objects. • The Law of Falling Bodies: • In a vacuum, all bodies fall with the same uniform acceleration, regardless of their size or mass. • Acceleration is the rate of change of velocity. It has funny-looking units: km/sec/sec or ft/sec/sec, etc. • This contrary to Aristotle, who held that the heavier a body was, the faster it would fall compared to a lighter body.

36. Uniformly accelerated motionVelocity changes the same amount over each identical period of time. Consider dropping an object:Acceleration of gravity is 9.8m/sec/sec=32 ft/sec/secAfter 1 sec falling 9.8 m/sec 2 sec 19.6 m/sec 3 sec 29.4 m/sec

37. Distance fallen:

38. Galileo’s Law of InertiaA body set into uniform motion will remain in uniform motion until interfered with.By “uniform motion” we “mean moving with a constant speed in a straight line.” So the object neither changes speed nor direction.This also means that an object at rest will remain at rest until it is interfered with. This idea is fundamental to our understanding of physics. Why did it take us 2000 years to get to this? Aristotle taught it is “natural” for all objects to remain at rest. Motion is unnatural and would be resisted.

39. Some examples:1. A weight dropped from the mast of a ship.2. Playing catch in an airplane.3. A billiard ball.

41. Galileo’s discoveries with a telescope • Craters and mountains on the moons- a tremendous challenge to prevailing.thinking. • Sunspots. • The Milky Way consists of many unresolved stars. • Saturn was not always round, but sometimes had two blobs near it. • Venus went through phases: a real challenge to Aristotelian views. • Discovered four moons of Jupiter! Caused tremendous excitement.