Exam 2 Outline

# The many body problem star clusters galaxy clusters

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The many-body problem Star clusters, galaxy, clusters of galaxies o Conservation of angular momentum o Tides (by Sun and Moon) [Fig. 4.23; Fig. 4.25] Newton Explained Kepler’s Discovery o The physics behind Kepler’s discovery (3 rd Law) Kepler found that p 2 =constant x a 3 for planetary orbits o Newton found for actual units Masses in gm or kg Distances in cm or meters Period in seconds o Legacy Physics of everyday life Determinism Fig 19.1; Fig 19.2 Lecture 14 Gravity: A New Description Albert Einstein o “The eternal mystery of the world is its comprehensibility. the fact that it is comprehensible is a miracle.” o Two revolutions Special Relativity (effects with v=constant) General Relativity (acceleration effects) o “curved paths of motion” caused by gravity (action at a distance) vs. “space itself is curved by mass” the distortion accounts for the observed change from straight line motion to curved motion. [fig s3.2] o New Terminology 4 dimensional spacetime

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equivalence of effects of gravity and acceleration [fig s3.4] Demo: BU Elevator Experiment! Visualizing Spacetime o We “accept” 2 dimensional analogies because we have the third dimension available to demonstrate them (in space) + time, ex: balloon expansion o The four dimensions are x, y, z, t [fig s3.8] The presence of mass changes the spacial curvature around it. Special relativity occurs at a constant speed. General relativity occurs at an accelerated speed. the sun curves spacetime like how a heavyweight curves a rubber sheet. o Fig s3.13 Rubber Sheet Analogies o For solar system, a family of bowl-shaped distortions for sun, planets, moons, asteroids, etc. o The size (“domain”) of each bowl depends on object’s mass formerly its gravitational field’s “sphere of influence” o “picture” of simple orbital motion in spacetime (fig s3.14) o effects of density: if same mass is squeezed into a smaller volume (i.e. higher density), the influence upon distant spacetime is not changed, but Local Effect dramatic Black Holes! No light comes from a black hole so you don’t know where it is. Concepts from Einstein o Gravity affects light Example: Sun, Black Holes o Gravity (acceleration) affects time Clocks run slowly near massive objects [fig s3.16] If the sun became compressed, spacetime would become more curved near its surface (but unchanged farther away) If compression continued, the curvature would create a black hole. Gravitational lensing (focusing) Lecture 15 Light Tells Us Things Light tells us things o Uses of light Positions of things (“Old Astronomy”) Tool to investigate the physical/chemical nature of those things (Modern Astrophysics) o Interaction of light and matter o Light and matter interact via Emission, Absorption, Transmission, Reflection, Scattering [fig 5.3, 10.9] Remote Sensing o Use light coming from an object to study it.
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