L4GH09_Light_and_Matter

L4GH09_Light_and_Matter - Radiation, matter and atomic...

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January 15, 2009 Matter, spectra… Radiation, matter and atomic structure • Lecture topics: blackbody radiation, spectral lines, states of matter • Text readings: Chapter 3 – p 51; Chapter 4…; main resource = this lecture
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January 15, 2009 Matter, spectra… Tidal Forces From Newton’s law of Gravitation, for two masses M 1 (call it M Earth ) and M 2 (M Moon ), separated by distance r: The differential force on mass 1 (Earth) by mass 2 (Moon) is therefore: This differential force raises a tidal bulge of mass m T . This mass must be proportional to the force, so: Now, the net force on mass 2 (Moon), due to this tidal bulge , is also a differential force: So, for example, the tidal force on the Moon due to the bulging oceans is proportional to 1/r 12 6 . 12 2 2 1 r M GM F = 12 3 r dr dF Earth dr r dF m Earth T 12 3 1 12 6 12 3 1 r dr r m dF Moon
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January 15, 2009 Matter, spectra… • Tides result in a net force which slows Earth’s rotation and speeds the Moon’s orbital velocity. Tidal Friction • As a result the day is getting longer by ~1 second/century and the distance between the Earth and Moon is increasing. There is evidence for this in the fossil record on Earth
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January 15, 2009 Matter, spectra… Synchronous Rotation • How does tidal drag explain the fact that the Moon always shows the same face to Earth? ¾ This effect causes Pluto and Charon to always show the same face to one another ¾ Similarly, Mercury rotates exactly 3 times for every two orbits of the Sun .
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January 15, 2009 Matter, spectra… Tidal heating • A tidal bulge is raised on Io, due to Jupiter. ¾ Other large moons perturb Io’s orbit, which cause it to vary its distance to Jupiter • This causes the tidal bulge to rise and fall, generating internal heat
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January 15, 2009 Matter, spectra… Roche limit •The tidal force gets very large as the distance between objects decreases. •At a critical distance, the tidal forces will exceed the gravitational force holding the satellite together, and it will be torn apart. For two touching bodies, the force to separate is •More generally we can write: where α ranges from ~1.19 – 2.44 d = R 2 ρ M m 1/3 3 / 1 = m M R d α for instance, α =2.5 for two touching particles, 1.38 for an icy body, and 1.19 for two bodies about to collide; 1.26 for two touching bodies
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January 15, 2009 Matter, spectra… Rings • Ring features (gaps, edges) due primarily to resonant perturbations • In densest regions, ring particles collide with one another every few hours. • Extend out to Roche
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L4GH09_Light_and_Matter - Radiation, matter and atomic...

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