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Celestial Sphere • Constellations are patterns of stars on the sky: these are are not actually close to each other • Celestial Sphere: a large imaginary sphere centered on the Earth • Celestial poles: points directly above the earth’s poles • Celestial equator: great circle directly above the earth’s equator • The angle between the horizon and the NCP is the same as your latitude • What part of the celestial sphere you can see depends upon you latitude (from the NCP you can only see half the sky) • Celestial Sphere appears to rotate around the celestial poles (1 day cycle) • This is because of Earth’s rotation • Sun’s path on the Celestial Sphere: Ecliptic • The Sun’s position relative to the stars appears to change (1 yr. cycle) • Reason: Earth’s revolution around the Sun • The Moon’s position relative to stars also appears to change (1 month cycle: sidereal month: 27.3 days) • Reason: Moon’s revolution around the Earth Seasons and Calenders • The cause of seasons: NOT the varying earth–Sun distance • It’s the tilt of the Earth’s axis relative to the orbit around the Sun • Therefore the ecliptic is tilted relative to the celestial equator • Equinoxes: the Sun crosses the celestial equator • Solstices: the Sun furthest away from the celestial equator • 1 Year: time between one Vernal equinox to the next • 1 synodic month: from new moon to new moon: 29.5 days Aristotle, Ptolemy & Copernicus • Aristotle showed that the earth is spherical • Earth’s circumference was measured by noting different positions of the Sun at noon at two different places • Problem with the Geocentric view of the Universe: retrograde motions of planets • Ptolemy’s explanation: epicycles • Copernicus : Heliocentric model — can naturally explain retrograde motions if outer planets are slower Kepler & Galileo • Kepler: laws of planetary motions – 1: orbits of planets are ellipses with the Sun at one focus – 2: A line from a planet to the Sun sweeps equal areas in equal times – 3. The square of the orbital period is equal to the cube of the semi-major axis • Galileo observed with a telescope: found rotating Sunspots, mountains on the moon, discovered Jupiter’s moons and phases of Venus • Strongly supported heliocentric model Newton’s Laws • 1. An object remains at rest, or moves in a straight line at constant speed unless acted upon by an outside force • An object moving in a circle is being accelerated • 2. Acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass • 3. For every action, there is equal and opposite reaction • Gravity is an attractive force between two masses • Gravitational force varies directly with mass and as inverse square of the distance Application of Newton’s laws • Orbits of any pair of objects are conic sections with the center of mass at one focus • Elliptical orbits possible if orbital speed is smaller than the circular velocity or larger than the circular velocity but smaller than the escape velocity • Angular momentum is conserved • Kepler’s third law also comes naturally from laws of gravity