ASTR 101 Lecture 7 Outline of Last Lecture I Gravity and Force II Newton s Laws of Motion III Conservation Laws in Astronomy Outline of Current Lecture I Gravitational Potential Energy II Mass and Energy III Conservation of Energy IV Force of Gravity A Universal Law of Gravitation B Calculating Planetary Orbits C Changing orbit V Tides and Phases A Tidal Friction Current Lecture Gravitational Potential Energy In space an object or gas cloud has more gravitational energy when it is spread out than when it contracts a contraction cloud converts to gravitational potential energy to thermal energy MASS ENERGY Mass itself is a form of potential energy E mc2 A small amount of mass can release a great deal of energy concentrated energy can spontaneously turn into particles for example particle accelerators Conservation of Energy energy can be neither created nor destroyed it can change form or be exchanged between objects the total energy content of the universe was determined in the Big ang and remains the same today 4 4 The Force of Gravity What determines the strength of gravith The Universal Law of Gravitation 1 every mass attracts every other mass 2 attraction is directly proportional to the product of their masses 3 attraction is inversely proportional to the square of the distance between their centers Fg G M1M2 d2 How does Newton s law of gravity extent Kepler s laws Kepler s first two laws apply to all orbiting objects not just planets Ellipses are not the only orbital paths orbits can be bound ellipses unbound parabola hyperbola Calculating Planetary Orbits F ma GMm r2 mv2 r v 2 pi r P GM 4 pi 2r3 P2 P2 4 pi 2r3 GM Fgravity GMm r2 Newton s version of Kepler s third law p2 4 pi 2 G M1 M2 a3 p orbital period a average orbital distance between centers M1 M2 sum of object masses How do gravity and energy together allow us to understand orbits Total orbital energy gravitational kinetic stays constant if there is no external force orbits cannot change spontaneously further from the sun More gravitational energy less kinetic energy closer to the sun Less gravitational energy more kinetic energy total orbital energy stays constant Changing an Orbit So what can make an object gain or lose orbital energy Friction or atmospheric drag a gravitational encounter Escape Velocity If an object gains enough orbital energy it may escape change from a bound to an unbound orbit Escape velocity from earth about 11km s from sea level about 40 000 km hr How does gravity cause tides The Moon s gravity pulls harder on near side of Earth than on far side the difference in the Moon s gravitational pull stretches Earth Tides and Phases spring tides occur at new moon and full moon neap tides occur at the first and third quarter moons size of tides depends on the phase of the moon tidal forces from the sun and moon work together leading to enhanced spring tides tidal forces from the sun and moon work against each other leading to a smaller neap tides Tidal friction Tidal friction gradually slows Earth s rotation and makes the moon get farther from earth moon once orbited faster or slower tidal friction caused it to lock in synchronous rotation
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