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The “Geocentric Model” Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. Aristotle vs. Aristarchus (3rd century B.C.): Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth. Aristarchus: Used geometry of eclipses to show Sun bigger than Earth (and Moon smaller), so guessed Earth orbits Sun. Also guessed Earth spins on axis once a day => apparent motion of stars. Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the planets". However, Ptolemy (c. A.D. 140) invented a model where planets circle in “epicycles” that orbit the Earth. This helped to explain retrograde motion for a long time, until astronomical observations became more precise. The Ptolemaic Model. "Heliocentric" Model ● Rediscovered by Copernicus in 16th century. ● Put Sun at the center of everything. Much simpler. Almost got rid of retrograde motion. ● But orbits circular in his model. In reality, they’re elliptical, so it didn’t fit the data well. ● ● Not generally accepted then. Copernicus 1473-1543 Galileo (1564-1642) Built his own telescope in 1609. 400 years ago. Discovered four moons orbiting Jupiter => Earth is not center of all things! Co-discovered sunspots. Deduced Sun rotated on its axis. Discovered phases of Venus, inconsistent with geocentric model. Johannes Kepler • (1571 - 1630) • Born near Stuttgart • Studied philosophy and theology at Tubingen • Developed love for astronomy as a child • Showed high level of mathematical skill • Had a reputation as a skilled astrologer • Wanted to be a minister; became instead a teacher of astronomy and math in Graz, Austria • Became assistant to Tycho Brahe in 1601 • Developed Laws of Planetary Motion Kepler's First Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse. eccentricity = e = CIRCLE e=0 distance between foci major axis length ELLIPSE moderately so ELLIPSE highly elliptical Kepler's Second Law A line connecting the Sun and a planet sweeps out equal areas in equal times. Translation: planets move faster when closer to the Sun. slower faster Kepler's Third Law The square of a planet's orbital period, P, is proportional to the cube of its semi-major axis, a. P2 α a3 (for circular orbits, a=radius). Translation: the larger a planet's orbit, the longer the period. With the scale of the Solar System determined, can rewrite Kepler’s Third Law as: P 2 = a3 So compare Earth and Pluto: Object a (AU) Earth Pluto 1.0 39.53 as long as P is in years and a in AU. P (Earth years) 1.0 248.6 Newton (1642-1727) Kepler was playing with mathematical shapes and equations and seeing what worked. Newton's work based on experiments of how objects interact. His three laws of motion and law of gravity described how all objects interact with each other. Newton's Correction to Kepler's First Law The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus. x Star center of mass planet Center of mass is not at the geometric center of the star, but because stars are so much more massive than it’s usually beneath the surface of the star. Timelines of the Big Names Galileo Copernicus 1473-1543 1564-1642 Brahe 1546-1601 Kepler 1571-1630 Newton 1642-1727 The Celestial Sphere An ancient concept, as if all objects at same distance. North Celestial pole But to find things on sky, don't need to know their distance, so still useful today. Features: - Does not rotate with Earth - Poles, Equator: Celestial Equator Projections of Earth’s Pole’s and Equator out onto the sky South Celestial pole The Year Earth’s rotation axis is inclined (tilted) 23 1/2 degrees to the plane of its orbit. Spring Sun Winter Summer N. Hemisphere tilted towards the sun Fall Direction of Earth’s motion in orbit N. Hemisphere tilted away from the Sun Inclined view of the Earth’s orbit The Earth revolves around the Sun in 365.256 days (“sidereal year”). Note: the projection of Earth’s orbital plane onto the sky (the Celestial sphere) is called the Ecliptic The "Solar Day" and the "Sidereal Day" Solar Day How long it takes for the Sun to return to the same position in the sky (24 hours). Sidereal Day How long it takes for the Earth to rotate 360o on its axis. These are not the same! The Motion of the Moon The Moon has a cycle of "phases", which lasts about 29 days. Half of the Moon's surface is lit by the Sun. During this cycle, we see different fractions of the sunlit side. Which way is the Sun in each case? Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth. Cycle of phases or "synodic month" 29.5 days Orbit time or "sidereal month" 27.3 days Eclipses Lunar Eclipse When the Earth passes directly between the Sun and the Moon. Sun Earth Moon Solar Eclipse When the Moon passes directly between the Sun and the Earth. Sun Moon Earth Solar Eclipses Diamond ring effect - just before or after total Total Partial Annular - why do these occur? Lunar Eclipse Q: Why don't we get eclipses every month? Q: How can there be both total and annular eclipses? A: Look at Moon's orbit tilted compared to Earth-Sun orbital plane: Sun Moon Earth 5.2o Side view Also, moon's orbit slightly elliptical: Moon Distance varies by ~12% Earth Top view, exaggerated ellipse Types of Solar Eclipses Explained Sun Moon Earth Total Annular Partial Certain seasons are favorable for eclipses. Solar “eclipse season” lasts about 38 days. Likely to get at least a partial eclipse somewhere. It's worse than this! The plane of the Moon's orbit precesses, so that the eclipse season occurs about 20 days earlier each year.