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Unformatted text preview: January 8, 2009 celestial mechanics Celestial Mechanics • Lecture topics: planetary orbits, Kepler’s Laws, orbits – scale, gravity, energy… • Text readings: Chapter 3 – esp. pp. 4755 January 8, 2009 celestial mechanics The skinny triangle •We can relate an object’s physical size D , to its distance r and angular size θ : 360 2 θ π = r D At what distance would a loonie subtend an angle of 1”? Diameter=26.55 mm. D r this approximation valid for small angles only: i.e. if θ <<360º then arc “D” ~ chord “C” C January 8, 2009 celestial mechanics Size and Shape of Earth • Eratosthenes used the assumption of a spherical Earth and his observation of the difference of altitude of the Sun at Syene (directly overhead on a known date) and at Alexandria, 5000 stadia farther north. • Eratosthenes’ method gives a radius for Earth of ~6250km. This is very close to the modern value of 6378km. January 8, 2009 celestial mechanics Distance to the Moon Lunar eclipses can be used to determine distance to the Moon • Angular diameter of the Sun is 0.53 degrees • Knowing Earth’s diameter (13,000 km) you can find the extent of Earth’s shadow: 1.4 million km. • From observing the radius of curvature of the shadow we see the angular size of Earth’s shadow at the distance of the Moon is about 1.5 degrees. • Can use geometry to show distance to Moon is about 350,000 km January 8, 2009 celestial mechanics Distance to the Sun • Aristarchos observed the angle between the Moon and Sun at quarter phase; this told him the relative distances of Sun and Moon. ¾ Sun is about 400 times farther away than Moon ¾ Since Sun and Moon have the same apparent diameter when viewed from Earth, the Sun must also be 400 times larger than the Moon January 8, 2009 celestial mechanics Planetary motions • The planets move relative to the background stars. • Sometimes they show complex retrograde motions • a successful SS model needs to explain these motions January 8, 2009 celestial mechanics Saturn January 8, 2009 celestial mechanics Epicycles • Epicycles¡were¡introduced¡ to explain the nonuniform velocities of planets, in a geocentric, circularorbit theory January 8, 2009 celestial mechanics Retrograde motion • Retrograde motion is a natural outcome of the heliocentric model • Inner¡planets¡orbit¡more¡...
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This note was uploaded on 04/15/2009 for the course PHYS 275 taught by Professor Harris during the Winter '09 term at Waterloo.
 Winter '09
 HARRIS
 mechanics, Energy, Gravity, Orbits

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