Lecture #5: Plan. The Beginnings of Modern Astronomy Kepler s Laws Galileo

Transcription

1 Lecture #5: Plan The Beginnings of Modern Astronomy Kepler s Laws Galileo

2 Geocentric ( Ptolemaic ) Model Retrograde Motion: Apparent backward (= East-to-West) motion of a planet with respect to stars Ptolemy (~150 A.D.): explained it with epicycles = small spheres attached to larger ones

3 Heliocentric Universe Nicolas Copernicus (Poland, ) Revived Sun-centered model of the Heavens (On the Revolutions of Celestial Orbs) Explained retrograde motion (circular orbits)

4 Copernicus and Planetary Distances He was able to calculate a planet s distance from the Sun by noting the planet s position at various times Opposition: When the Earth lies directly between the Sun and the planet Conjunction: When the planet lies directly on the Earth-Sun line Inferior conjunction: Planet is between the Earth and the Sun Superior conjunction: When the Sun lies directly between the Earth and the planet Quadrature: When the planet s position makes a right angle with the Earth-Sun line

5 Mercury and Venus Mercury and Venus are closer to the Sun than the Earth, since they are never found very far from the Sun in the sky Mercury s greatest elongation, or angular separation from the Sun, is never more than 28 o Venus s greatest elongation is never more than 47 o Mercury is therefore closer to the Sun than Venus

6 Distances to the Other Planets Copernicus measured the time it took a planet to move from opposition to quadrature, and calculated the planet s relative distance from the Sun Remarkably accurate! Planet Copernicus s Calculation (AU) Actual Distance (AU) Mercury Venus Earth Mars Jupiter Saturn

7 Heliocentric Universe (Copernicus version) Assumption: heavenly motion must occur in perfect circles Problem: the predicted planet positions were off! His Solution: added complexities to his model including circles on circles much like the epicycles of Ptolemy!

8 Heliocentric Universe (Copernicus version)

9 Heliocentric Universe (Copernicus version) Assumption: heavenly motion must occur in perfect circles Problem: the predicted planet positions were off! His Solution: added complexities to his model including circles on circles much like the epicycles of Ptolemy! his model gained relatively few converts over the next 50 years

10 The Beginnings of Modern Astronomy Tycho Brahe (Denmark, ) Made detailed observations of planetary positions (to within ~1/60 th degree = 1 arc min) Found that comets moved outside of the Earth s atmosphere In 1572, he witnessed a supernova & concluded that it was much farther away than any celestial sphere Did not detect parallax! seemingly measurable size of stars implied gigantic objects >> Sun!! planets go around the Sun, but Sun orbits around the Earth

11 The Beginnings of Modern Astronomy Tycho Brahe (Denmark, )

12 Tycho Brahe ( C.E.) Built instruments to measure the positions of planets very accurately (~1 arc minute) Found that comets moved outside of the Earth s atmosphere Witnessed a supernova and concluded that it was much farther away than any celestial sphere As he could detect no parallax motion in the stars, he held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth

13 The Beginnings of Modern Astronomy Johannes Kepler (Denmark, ) Used data of Tycho (his mentor) to derive the laws of planetary motion Kepler s Laws

14 Johannes Kepler ( Using Tycho Brahe s data, discovered that planets do not move in circles around the Sun, rather, they follow ellipses with the Sun located at one of the two foci!

15 Kepler s First Law (1609) 1. Planets move in elliptical orbits with the Sun at one focus of the ellipse a

16 Kepler s First Law (1609) 1. Planets move in elliptical orbits with the Sun at one focus of the ellipse eccentricity = 0 for a circle

17 Kepler s Second Law (1609) 2. Planets sweeps out equal areas in equal times = Equal Area Law

18 Kepler s Third Law (1619) 3. Orbital period is related to orbital size: P 2 = a 3 P is the period (in years) a is the semi-major axis (in A.U.)

19 Kepler s Third Law (1619) Example: Jupiter is 5.2 A.U. from the Sun. What is its Period? P 2 = a 3 P 2 = (5.2) 3 = 5.2 x 5.2 x 5.2 = P = sqrt(140.6) ~ sqrt(12 x 12) ~ 12 years (11.9 years)

20 Galileo Galilei (Italy, ) Applied telescope to study the Heavens Discovered moons (satellites) orbiting Jupiter Earth is not at the center of all motions Discovered phases of Venus Venus orbits Sun, not the Earth Observed craters on the Moon and sunspots on the Sun Moon & Sun are imperfect like Earth Roman Inquisition found him vehemently suspect of heresy! Forced to recant + house arrest rest of his life One of the principal founders of the experimental method for studying scientific problems.

21 Galileo Galilei (Italy, ) Inertia: Tendency of an object at rest to remain at rest & an object in motion to keep moving mass = measure of an object s inertia

22 Question #3 Describe in one sentence one of Kepler s three laws