ASTR 101 Lecture 7 Outline of Last Lecture I. Gravity and ForceII. Newton’s Laws of MotionIII. Conservation Laws in AstronomyOutline of Current Lecture I. Gravitational Potential EnergyII. Mass and EnergyIII. Conservation of EnergyIV. Force of GravityA. Universal Law of GravitationB. Calculating Planetary OrbitsC. Changing orbitV. Tides and PhasesA. Tidal FrictionCurrent LectureGravitational Potential Energy- In space, an object or gas cloud has more gravitational energy when it is spread out thanwhen it contracts.- a contraction cloud converts to gravitational potential energy to thermal energyMASS-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 GravityWhat determines the strength of gravith?- The Universal Law of Gravitation:1. every mass attracts every other mass2. attraction is directly proportional to the product of their masses3. 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/r2Newton'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 massesHow 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 constantChanging an Orbit- So what can make an object gain or lose orbital energy?- Friction or atmospheric drag- a gravitational encounterEscape 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 EarthTides 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 tidesTidal 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
View Full Document
Unlocking...