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epsc 200 ch 6 notes.docx

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McGill University
CHEM 222
Karine Auclair

6. Orbital Dynamics & Kepler’s Law - Planets and asteroids mostly follow elliptical orbits in the ecliptic plane (the plane of Earth’s orbit about the Sun) - Copernicus and Galileo promoted the heliocentric viewpoint - The Sun is so enormous compared to other masses that it is not affected by gravitational forces – it’s at a fixed point - Mercury orbits the Sun most quickly - Pluto (then Neptune) has the highest inclination angle 6.1 Kepler’s Laws - Kepler (student of Brahe) used Brahe’s observations to establish three laws: 1) The planets move about the Sun in ellipses 2) The orbits sweep out equal areas in equal amounts of time • The planet travels faster when closer to the Sun • Perihelion = closest • Aphelion = farthest • This variation in the speed of orbit has an effect on when the Sun appears to rise or set (In the Northern Hemisphere, winter solstice (shortest day, Dec. 21), and summer solstice) 3) The period (p) of the orbit is proportional to the semi-major axis (a) P  a 3 6.2 Newtonian Mechanics Allow Us to “Weigh” the Sun - Newton recognized that gravity was responsible for the ordered, Keplerian motion of the planets • The force of gravity contained planets into precisely Keplerian orbits 2 F = (Gmm)/(r ) Where G= Newtonian constant of universal gravitation - Centripetal Force – the force that opposes gravitational force F = (mv )/r2 - For planets to stay in orbit, gravitational force = centripetal force 6.2.1 Is there a Supermassive Black Hole at the Centre of our Milky Way? - Ghez – Observed the orbits and periods of stars in the direction of where the galactic centre is known to be - Ghez and her colleagues determined tha6 there is an invisible supermassive gravitational centre (mass = 3 x 10 solar masses) at the centre of our Milky Way • Stars orbit this supermassive black hole 6.2.2 The Orbit of Earth’s Moon: Weighing Earth Full Moon Phase - Hap
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