universal_gravitation - Uniform Circular Motion-planetary...

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Newton’s 2 nd Law Uniform Circular Motion -planetary motion due to gravity requires understanding of circular motion (though most orbits are elliptical) r A B v1 v2 Figure 1 Figure 2 -figure 1 shows the circular motion of an object with radius and speed constant -velocity is perpendicular to radius ( tangential ) -v 1 and v 2 are instantaneous velocities at A and B, respectively -figure 2 shows Δ v = v 2 – v 1 -if A and B are very close together, then arc AB chord AB -thus, because of similar triangles in figures 1 & 2… r v t v a t v v v AB chord v v 2 r r = = -this describes centripetal (or “center-seeking”) acceleration (a c ) r v a c 2 = -since T r v p 2 = in a circle (where T is the period of revolution), substituting… 2 2 4 T r a c p = -force that causes circular motion is called centripetal force (F c ) 2 2 4 2 T r m r mv ma F F c net p = = = = V1 V2 Δ V PDF created with pdfFactory Pro trial version www.pdffactory.com
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Kepler’s Laws of Planetary Motion -Tycho Brahe (1546-1601) carefully recorded, tracked & predicted movements of planets and comets -he believed Earth as center of planetary orbits -his student, Johannes Kepler (1571-1630), believed Sun as center -also believed planetary motion could be studied using geometry & math Tycho Brahe Johannes Kepler Kepler’s 1 st Law of Planetary Motion The paths of the planets are ellipses with the centre of the Sun at one focus. Kepler’s 2 nd Law of Planetary Motion An imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals. Thus planets move fastest when closest to the Sun, slowest when farthest away. Kepler’s 3 rd Law of Planetary Motion The ratio of the squares of the periods of any two planets revolving around the Sun is equal to the ratio of the cubes of their average distances from the Sun. Thus if Ta and Tb are their periods and ra and rb are their average distances, then: 3 2 = b
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universal_gravitation - Uniform Circular Motion-planetary...

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