Simple Harmonic Oscillator Trust me. It’s simple. Simple Harmonic Oscillator: Start with a spring resting on a horizontal, frictionless (for now) surface. Fix one end to an unmovable object and the other to a movable object. Start the system off in an equilibrium state — nothing moving and the spring at its relaxed length. Simple Harmonic Oscillator: Now, disturb the ...

Read More »## Springs

discussion summary practice problems Summary bullet

Read More »## Elasticity

discussion summary practice problems introduction Elasticity is the property of materials to return to their original size and shape after being deformed (that is, after the deforming force has been released). Since it is really a property of materials, a more complete discussion will have to wait until later. For now we’ll stick to a very simple elastic system (the coil spring) ...

Read More »## 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. ...

Read More »## 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

Read More »## 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 ...

Read More »## 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 ...

Read More »## 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 ...

Read More »## 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 ...

Read More »## 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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