Gravity Of Extended Bodies

discussion summary practice problems Gravity Of Extended Bodies Discussion tidal forces The tides, tidal forces, prolate spheroid, Roche limit Let… r = separation between planet and moon a, b = radius of planet and moon, respectively ma, mb = mass of planet and moon, respectively Derive the tidal force formula. gtidal =  gfront  −  gback     gtidal =  Gmb  −  Gmb   (r − a)2 (r + a)2 Work that algebra. ...

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Orbital Mechanics II

discussion summary practice problems Orbital Mechanics II Discussion closed orbits circular orbits, virial theorem, energy elliptical orbits, apogee-perigee, aphelion-perihelion, energy and angular momentum open orbits parabolic-hyperbolic orbits, energy unusual orbits slingshot effect, translunar insertion, co-orbital moons

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gravitational potential energy

discussion summary practice problems Gravitational Potential Energy Discussion introduction Short bit of calculus. Ug = −  ⌠ ⌡ F · ds   r       Ug = −  ⌠ ⌡  −  Gm1m2  dr r2   ∞       Ug = −  Gm1m2  ⎛ ⎝ 1  −  1 ⎞ ⎠ r ∞ and here it is… Ug = −  Gm1m2 r where… Ug =  gravitational potential energy m1m2 =  masses of ...

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orbital mechanics i

discussion summary practice problems orbital mechanics 1 Discussion circular orbits Newton’s laws only. Nothing about energy or momentum. Centripetal force and gravitational force.       Fc  =  Fg       mv2  =  GMm rp rp2 v = √ Gm r Kepler’s third law. Derive Kepler’s third law of planetary motion (the harmonic law) from first principles. v = √ Gm  =  2πr ...

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universal gravitation

discussion summary practice problems universal gravitation Discussion the comet Isaac Newton was born on Christmas Day, 1642 in the village of Woolsthorpe (near Grantham), Lincolnshire, England. In 1661 he enrolled in Trinity College, Cambridge University (about midway between Woolsthorpe and London) where he studied mathematics. In 1665 the Black Plague made it’s way to England forcing the closure of Trinity and sending ...

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Heliocentrism

discussion summary practice problems Heliocentrism Discussion early Aristarchus of Samos (310–230 BCE) Greece the earth is bigger than the moon (~3 times larger – 8:3 to be more exact) can be seen from the shadow of the Earth on the moon during a lunar eclipse the sun is very much farther away than the moon, as can be seen by the fact the ...

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Geocentrism

discussion summary practice problems Geocentrism Discussion astronomy Think of your life now and think of how it used to be ten years ago. What did you do that was different? How was the world different? The Internet? What’s that? Why would I ever want a computer in my home? Go back even further and imagine yourself living one hundred years ...

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Coriolis Force

discussion summary practice problems Coriolis Force Discussion Talk, Talk, Talk Gustave Coriolis (1792–1843) France Mémoire sur les équations du mouvement relatif des systèmes de corps. Gaspard-Gustave Coriolis. Journal de l’École polytechnique. Vol. 15 No. 24 (1835) 142–154. Should this be changed to a discussion of radial vs. tangential acceleration? Forces in a rotating coordinate system direction real fictitious radial  ar =  radial ⎛ ⎝ d2r ⎞ ...

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Rolling

discussion summary practice problems Rolling Discussion Rolling without slipping is a combination of translation and rotation where the point of contact is instantaneously at rest. When an object experiences pure translational motion, all of its points move with the same velocity as the center of mass; that is in the same direction and with the same speed v(r) =  vcenter of mass ...

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