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PHYS 155 – Introductory Astronomy - observing sessions: Sunday – Thursday, 9pm, weather permitting http://www.phys.uconn.edu/observatory - Exam - Tuesday March 20, - Review – Monday 6:30-9pm, PB 38 Marek Krasnansky Thursday 03/15/2007 • Models of the solar system – Geocentric – Heliocentric • Kepler's laws Models of the Solar System ● Successful model has to explain observations Experimental observations: motion of the Sun, Moon and planets movement on the ecliptic eclipses relative speed, how much they move with respect to each other retrograde motion Venus, Mercury – always close to the Sun phases of the planets stellar parallax Motion of the Sun, Moon, planets on the ecliptic everything orbits in one plane ● Venus, Mercury – always close to the Sun ● relative speed ● distances from the Earth – closer objects move faster ● Eclipses • the Moon orbits around the Earth Retrograde Motion Motion that is backward compared to the norm; we see a planet in apparent retrograde motion during the periods of time when it moves westward, rather than the more common eastward, relative to the stars. retrograde motion Phases of Venus • Venus: • Moon: • Crescent phase – Venus between the Sun and Earth – Galileo Galilei – the first to observe gibbous phase of Venus Stellar Parallax Parallax - the apparent motion of a relatively close object with respect to a more distant background as the location of the observer changes. Stellar Parallax - The apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in the Earth's orbit of the Sun each year. Geocentric Models - Ptolemy • the Earth (Geo, in Greek) – in the center, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn • the simplest model can't explain retrograde motion – Epicycle (Ptolemy) • Discrepancies between the predicted and true positions of the planets • artificial, the planets orbit around empty space Geocentric Models -Tycho Brahe - all planets (except the Earth) orbit around the Sun - the Sun and Moon orbit around the Earth - can not explain stellar parallax (not observed at that time) Heliocentric Models - the Sun (helios, in Greek) in the center - Aristarchus, Copernicus - planetary orbits – circles - naturally explains everything we need - not more accurate than Ptolemy's model Johannes Kepler • Believed Copernicus was correct. • Worked very hard to see if Tycho’s data matched with Copernicus’s theory. • Realized that the orbits cannot be perfect circles. The orbits were elliptical. • Discovered 3 mathematical laws of planetary motion. (1546 - 1601) Kepler's Laws of Planetary Motion Kepler's first law: The orbit of each planet is an ellipse with the Sun at one focus. Kepler's second law: As a planet moves around its orbit, it sweeps out equal areas in equal times. Kepler's third law: 2 P =a 3 P - is a planet's orbital period in years a – semimajor axis of a planet's orbit in AU. Astronomical Unit (AU) ● a unit of length defined by the distance from the Earth to the Sun 1 AU = 150 million kilometers = 93 million miles Kepler's Laws of Planetary Motion Ellipse • F1, F2 – foci (focus) • a – semimajor axis • b – semiminor axis • e - eccentricity c e= 0≤e1 a Ellipse Drawing an ellipse with a string of fixed length Eccentricity describes how much an ellipse deviates from a perfect circle ● ● Kepler's First Law The orbit of each planet is an ellipse with the Sun at one focus. animation Kepler's Second Law As a planet moves around its orbit, it sweeps out equal areas in equal times. animation Kepler's Laws - planets move faster near perihelion and slower near aphelion Kepler's Third Law Kepler's third law 2 P =a 3 Kepler's Third Law Generalizing Kepler's Laws - Kepler's laws - apply to the solar system, the Sun is in the focus - can be derived from Newton's law - more general result – applicable to any orbiting objects Generalizing Kepler's Laws Kepler's first law - the orbits are ellipses, the center of gravity is in the common focus - Orbits can also be unbound parabolas and hyperbolas Kepler's third law G – gravitational constant M1,M2- masses of the orbiting objects