Gravity, Orbits & Tides How gravity controls most of the forces and motions in the solar system Johannes Kepler (1571 1630) (contemporary of Shakespeare) Kepler?s Three Laws Calculations on the orbit of Mars The Tuning of the World Robert Fludd (1617) Kepler?s Music of the Spheres nested Platonic solids one for each planet Kepler?s First Law Orbits are ellipses, with the Sun at one focus of the ellipse Kepler Astronomia Nova (1609)?Ridin? an ellipse!? Kepler?s Second Law ?Equal areas in equal times,? or ?Move faster when you?re closer? Kepler?s Third Law: P2 = a3 Newton?s Physics (60 years after Kepler) Isaac Newton (age 46) (1642 1727) Isaac Newton as seen by William Blake (1795) Nature and Nature?s laws lay hid in night; God said Let Newton be! and all was light. - Alexander Pope (1730) Isaac Newton?s Philosophiæ Naturalis Principia Mathematica (1687) Newton?s Three Laws of Motion F = ma or a = F/m * Orbits Newton?s ?Law? of Universal Gravitation The orbit is a constant ?tussle? between the Moon falling (accelerating) towards the Earth and the ?sideways? motion of the Moon now Kepler?s #2 makes sense EarthMoon system from Newton?s System of the World (1728) launching a satellite in the 18th century! Geosynchronous satellites central to today?s technology Kepler?s #3 implies that an orbit exists with exactly a 24hr period 10hr exposure shows star trails AND geosynchronous satellites In orbit?..?weightless? (concept of mass vs. weight) m F (and F = ma) F = ma F = GMm / r2 ma = GMm / r2 a = GM / r2 a does not depend on m ! a = ?the acceleration due to gravity? (acting on a given body); depends only on M and r of the ?other? body your ?weight? = F due to gravity that you feel = ma Newton?s 2nd Law Law of Gravitation ?The Hammer and the Feather? Dave Scott (Apollo 15) does the Galileo thing in 1971 (painting by Alan Bean, 1986) (on YouTube, search for ?feather & hammer drop?) ?The Hammer and the Feather? Dave Scott (Apollo 15) does the Galileo thing in 1971 (painting by Alan Bean, 1986) (on YouTube, search for ?feather & hammer drop?) Concept of center of mass Two objects mutually orbit about a common center of mass; The ?little guy? exerts a force on the big one, too! Tides & tidal forces Sullivan?s apple (in Cambridge, England) Tidal forces a consequence of objects having finite sizes A tide is a DIFFERENCE in two gravitational forces Spring and Neap Tides Earth rotates under the tidal bulge, slowing down its rotation (friction): length of the day is increasing 2 msec/century! But now consider conservation of angular momentum (spinning lecturer demo) If the Earth loses ang. mtm., then the Moon must pick it up Moon moves out today at ~2 cm per year; month is lengthening Eventually the Earth?s day and the month will be the same length What will be the consequence? Utah Limestone 900 Myr old Twicedaily tides, plus strata are thinner at neap and wider at spring tides Deduction: (Sidereal) Month was 23.5 days and the day was 18 hours And the proof is in the rocks Babylonian eclipse 136 BC Observed eclipse in Babylon Eclipse location if day has always been same length stromatolite strata showing 32 days in a lunar month 500 Myr ago Woody Sullivan PowerPoint Presentation
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