L2GH09Celestial_Mechanics

L2GH09Celestial_Mechanics - Celestial Mechanics Lecture...

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January 8, 2009 celestial mechanics Celestial Mechanics Lecture topics: planetary orbits, Kepler’s Laws, orbits – scale, gravity, energy… Text readings: Chapter 3 – esp. pp. 47-55
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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
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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.
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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
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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
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