Lesson 2 - Kepler, Newton, Gravity
Lesson 2 - Kepler, Newton, Gravity ASTR 101
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This 5 page Class Notes was uploaded by Mariac77 on Tuesday October 13, 2015. The Class Notes belongs to ASTR 101 at University of Washington taught by Dr. Oliver Fraser in Summer 2015. Since its upload, it has received 36 views. For similar materials see ASTRONOMY (NW,QSR) in Environmental Science at University of Washington.
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Date Created: 10/13/15
1 Use Kepler39s Laws to relate orbital speeds periods and distances Learning goals 2 Quantitatively compare the strength of gravitational forces between different pairs of objects CHAPTER 3 Laws of Motion pg 4671 31 Studies of Planetary motions by LG 1 Describe planetary orbits and explain how astronomers found out that Astronomers in the these orbits are elliptical around the sun Ancient Times GEOcentric Model where Earth is the center of the Solar System HELIOcentric Model where Sun is the center of the Solar System System used to measuredescribe positions amp motions Frame of reference using coordinates ex distance and time latitude and Vocabulary longtitude Using prior data to make predictions about future behavior but doesn t explain the reason behind the behavior 0 Ex Kepler s Laws are empirical Empirical Ellipse A specific kind of oval shape where it s only symmetric H93 fr top to bottom and tr left to right The size oi an elll is i i t 0 Half of the on axis ma39or axis of an Elli se specified by its semimajor Semlmajor axsA L x x axis A Semim im axis gt 0 Determined by distance btwn foci plural of focus 2 special points along the maior axis inside ellipsel c l EccentHC39ty Measures how elongated an ellipse is e The greater the distance btwn foci the more The shape of an ellipse is elongated ell39pse 393 speci ed by its eccentnc y e eccentricity of circle O bc there is 0 distance btwn a circle s foci Apparent retrograde motion 0 How ancient people used to thinkthe planets move in the sky in 7 E ic cle quot 206 geocentric system j o Planets appear to travel in their regular eastward direction but sometimes M I turn around to move westward for a while before going back to normal W E eastward travel It s really just an illusion o In reality it occurs when Earth passes the planets during its orbit so it only seem like planets are moving backwards but truth is both Earth and neighboring planets are still going in same direction z S quotK Planets visible to the naked eye seen fr Earth Mercury Venus Mars Jup39ters Saturn 0 First to develop mathematical model to prove heliocentric theory but Nicholas Co ernicus p claimed planets in that system travel in Circular orbits around sun Why Heliocentric o Heliocentric explains why planets are the only ones that appear to have make more sense than retrograde motion but not the sun Geocentric More evidence found by Kepler Galileo and Newton Kepler s 15 Law 0 Shape of a planet s orbit is an ellipse w the Sun located at one of its Law of Ellipses focus 0 Area 39 l h m n matterwhere the lanet is Keplers 2nd Law IS awayst esa e o p Law of Equal Areas m 39t3 Orb39t 0 Shows that planets moves faster when closer to sun moves slower when farther fr Sun 1 1 Planet on elrptical orbit 1 Visual of L l I These three areas A B and C will be equal n Kepler s 2nol Law Figure 35 Pg51 mil these time Intervals are equal o P Period in years time it takes for object to complete one 2 39 ll orbit xAAl o A Semimajor axis in astronomical unit useful for measuring size of orbits Kepler s 3 Law P Law of Harmonies u an rs 33 Newton s Laws Govern Motion LG 2 List the physical laws that govern the motion of all obiects Vocabulary Force a push or a ull Acceleration 0 Net force When a pair of forces are not equal in strength andor direction object moves according to the greater force Galileo Galileo 0 First to use a telescope and 1St modern scientist bc unlike prior hiloso hers he conducted ex eriments to understand the universe Some of Galileo s Theories of Motion 2 Free Fall any object regardless of mass and w the absence of air resistance will fall at the sameland on earth at the same time these are later elaborated by Newton Newton s 13 Law 0 Describes inertia 1 at rest 2 moving in constantuniform velocity in a strai ht line Newton s 2 Law Acceleration m Magnitude of acceleration FCHCG I I l depends on strength of net Mass m 39 force and mass of object Mass and Inertia are interchangeable Greater mass greater inertia less likely to acceleraterespond to net force Newton s 3 d Law 0 All forces comes in pairs that cancels each other out o The pair always have equal strength and goes in opposite directions How can a nonmoving object exert a force on another object 0 Ex situation When riding a skateboard one foot pushes against the ground so you can move forward You would not have accelerated forward it a force had not acted on you But you did accelerate so the force must have come from the ground when you pushed against it The ground is a nonmoving object that exerted a force on you 34 Gravity is a Force Between Two Massive Objects LG 3 Combine motion and gravitation to explain planetary orbits The mutual attractive force acting along a straight line between 2 objects with mass Gravitational force Vocabulary Wei ht Name of the gravntatlonal force a PLANET exerts on an object Weight Equation o F Gravitational Force of weight in Newton Same as Imp m L o m mass in kilogram Newton s 2nOI Law g gravitational acceleration in ms2 or msz Newton s Universal Law for Gravitation m1m2 A Gravitational force between 2 objects is proportional to the product of the mass of each object Gravitational Force F a M assl m1 x M assz m2 B Gravitational force between 2 objects is inversely proportional to the square of the distance between the 2 objects 1 distance btwn objectsr2 C The Something is a constant of proportionality called Universal Gravitational Constant G ia strenith of iraviti that all objects w mass have in common about D Together Gravitational Force F a Massl x Massz Gravitational Force Universal Gravitational Constant x 2 distance btwn objects A Explanation Newton s 2nOI Law strength of force depends on mass of object Gravity is just a type of force that involves massive objects Newton s 3rOI Law for every force there is an equal and opposite force Ex if Earth exerts a force of 196N on a 2kg ob39ect the object must also exert a similar degree of force 196N on Earth so between them Ex1 if you double the mass m of one of the object Gravitational force F also doubles 2mobject1 X 1mobject2 239 Ex2 If you double m of both objects F doubles 2 times 2x24 2mobject1 X 2mobject2 439 Note we are not talking about gravitational acceleration but gravitational force B Explanation Planetstaretc are in the shape of a sphere so the area its gravitational force influences must be spread out in all direction in a spherical shape 0 Surface area equation for a sphere is A 4m2 In this case r by itself is just a distance that applies to any objects even if it s not spherical But rx I or 12 together finds the area similar to length x width area Why area because gravitational force has influence over areas of space not in 1 dimension The farther away an object is from planetssunetc the weaker their gravitational force is to each other 1 Mathematically represented as F r Z aka the inverse square lawquot 34 Orbits are simply one body falling around another LG 3 Combine motion and gravitation to explain planetary orbits Vocabulary Concept that any object regardless of mass and in the absence of air resistance will have the same Free Fa constantuniform gravitational acceleration towards center of earth Satellite Title referred to any less massnve object orbiting around a more massive object Escape velocity Lowest speed limit that allows object to escape a gravitational force field Uniform Circular Motion Circular path an object moves at constant speed Centripetal Force Force towards the center of a circle Why do planetsstarsetc ORBIT Orbit happens when 2 things happen at the same time 1 Circular Velocity satellite moving in the horizontal direction at just the right velocity not too fast not too slow 2 Centripetal Force satellite falling freely wo air resistance down in the vertical direction due to the pull of gravity Together Centripetal Force changes direction of Velocity constantly making it travel in a circular path causing satellite to fall along the exact Visual of force and motion acting during orbit curve of the more massive object Velocity X I Velocity 39etal How come orbital paths are shaped in ELIPSE When satellite gains speed in its orbit gravity won t bend motion of satellite sharply enough to keep it moving in a circular path Satellite will climb above normal circular path and gainincrease distance away fr more massive object Kepler s 2nOI LawNewton s Gravitational Law as distance INCREASE btwn satellite and more massive ob39iect satellite slows down Satellite reaches max height then begins falling back towards more massive object Kepler s 2nOI LawNewton s Gravitational Law as distance DECREASE btwn satellite and more massive object satellite speeds up Cycle repeats Greater speed of satellite pulls away more greater eccentricity longer ellipse Bound orbit Satellite Is bound to gravntatlonal force of more massive object Remains In orbit regardless off eccentncnty Unbound orbit Satellite not bound to any gravntatlonal force never returns Reaches speed Escape Velocity
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