AST 115 1nd Edition Lecture 8 Outline of Last Lecture I. Arguments against astrologyII. Heliocentric Theorya. Nicholas CopernicusIII. Tycho Brahea. Johannes KeplerOutline of Current LectureI. Johannes Keplera. Properties of an ellipseb. Laws of Planetary MotionII. Galileoa. Telescopic observations and their implicationsIII. Sir Isaac Newtona. Laws of MotionCurrent Lecture Johannes Keplero Kepler only had small amounts of Tychos planetary data.o He could not make any process until receiving it all, after Tychos death.o He spent the next 25 years in search for the true motions of the planets.o In 1609, Kepler published “The New Astronomy”, in which he revealed that the orbit of Mars was an ellipse.o Properties of an ellipse:Semi major axis: cut Major axis in halfThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. + ------ + -----+ = Focus(Plural = foci) Aphelion: point in orbit of a planet, asteroid, or comet at which it is furthest from the Sun.Perihelion: point in the orbit of a planet, asteroid, or comet at which it is nearest to the Sun.- Eccentricity = Distance between fociLength of major axis Example: 40 centimeters = 0.66 centimeters 60 centimeters Curve Eccentricity, ɛ Circle 0 Ellipse 0 ˂ ɛ ˂ 1Parabola ɛ = 1Hyperbole ɛ > 1o Kepler’s three Laws of Planetary Motion:- 1) Each planet moves in an orbit that is an ellipse with the Sun at one focus.- 2) A planet moves faster when close to the Sun and vice versa.- 3) The square of the period of a planet [is equal to] the cube of the semi-major axis of its orbit.P^2 = a^3[“P” must be in years and “a” must be in A.U. to be an equation] Example: a = 5.2 A.U.P^2 = (5.2)^3P^2 = 140.6P = √140.6~ 11.9 years Galileo (1564 – 1642) Italyo Famous for his telescopic observations (about 1609)- Observations: Venus goes through phases The Moon has mountains; the Sun has spots Jupiter has 4 moons There are stars that are too faint for eye to see- Implications of these observations: Venus must orbit the Sun Heavenly bodies are imperfect If the 4 moons can keep up with Jupiter, why can’t the Moon keep up with Earth? The Greeks didn’t know it allo He was convinced that the Copernican theory was correct.o He was brought before public Inquisition; forced to recant- Galileo spent the remainder of life under house arrest. He used this time to study “mechanics”. Tower of Pisa experiment:“The acceleration due to gravity is independent of an object’s mass (if air resistance is negative).”*If you drop one heavier object and one lighter object at the exactsame moment, they will hit the ground at the same time. Sir Isaac Newton (1643 – 1727) Englando Newton contributed new ideas to many fields:- Optics- Heat- Mechanics- Astronomyo He was the co-inventor of Calculus.o He published important results in his book “The Principia” including his:- 3 Laws of Motion 1) An object remains at rest or moves in a straight line at a constant speed, unless acted on by a force. 2) The acceleration of an object is proportional to the force acting on it and in the same direction. 3) For every action (force) there is an equal and opposite reaction
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