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UA PTYS 206 - Orbits and Gravity

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PYTS/ASTR 206 – Orbits and Gravity1z Announcements D2L site up Homework 1 posted after class on website http://www.lpl.arizona.edu/~shane/PTYS 206pp_ Look at the homework early! You have a week to finish – not a week to start!Due in class next ThursdayDue in class next ThursdayTA i l K i J fTA is only Kevin Jones for now Priyanka will join us in ~3 weeks – please don’t visit her until then. Office hours: Kevin – Tuesday 2-4pm, Gould-Simpson 511Myself – Tue./Thur. 1.45-4pm, Kuiper 524PYTS/ASTR 206 – Orbits and Gravity2z Observations Craters, Trenches, Bright/white surface Higher ground on the right, more craters on the leftOrbits and GravityPTYS/ASTR 206 – The Golden Age of Planetary ExplorationShane Byrne – [email protected]/ASTR 206 – Orbits and Gravity4In this lecture…In this lecture…z Gravity Newton and GalileoPl t ShzPlanetary Shape Flattening The Geoidz Tides Fate of the MoonzOrbits of planetary objectszOrbits of planetary objects Kepler’s lawsPYTS/ASTR 206 – Orbits and Gravity5Where does gravity operate?Where does gravity operate?z Gravity is one of 4 physical forces in nature Relatively unimportant on small scales  …but it dominates the universe at large scalesHolds planetsHolds planets togetherHolds galaxies togetherProvides pressure for fusion reactions in starsHolds planets in their orbitsPYTS/ASTR 206 – Orbits and Gravity6O()What’s gravity?What’s gravity?zObjects that contain matter (they have mass) attract each other This attractive force is called gravity, e.g. Your body and the EarthThe Moon and the EarthThe Moon and the Earth The Earth and the Sun Your body with a comet billions of km away The force of this attraction depends on three things Mass of the first object Mass of the second object How far apart the objects are – e.g. distance between center of planet and objects on the surface On Earth this force is the weight of the first objectPYTS/ASTR 206 – Orbits and Gravity7z Galileo was first to systematically investigate gravity Objects accelerate as they fall i.e. the longer the drop the faster they hit the groundAll bj t l t t th tAll objects accelerate at the same rate The famous leaning tower of Pisa experiment Some doubt about whether this actually happenedThis acceleration is 9 8 m/s2zThis acceleration is 9.8 m/s2 0 m/s when you let it go 9.8 m/s after 1 seconds2*9 8 / ft 2 d t2*9.8 m/s after 2 seconds etc… This acceleration is not the same on other planetssame on other planets e.g. it’s 3.7 m/s2on MarsPYTS/ASTR 206 – Orbits and Gravity8z What gives?Is gravity a force or an acceleration?Is gravity a force or an acceleration? It’s a force that produces an accelerationz Isaac Newton developed modern mechanics ith bil–using three basic laws With no forces operating an object doesn’t change its momentum (m1* v1)A force (F) causes a change in momentumA force (F) causes a change in momentum F = M1* v1–M1* v2= M1* (v1–v2) = M1* a1 When one body exerts a force on another then there is an equal an opposite reactionF=M1*a1qppF M1 a1Fgravity= M1* agravityMF80 k * 9 8 /2My Fgravity= 80 kg * 9.8m/s2784 Newtons (or ~175 lbs)PYTS/ASTR 206 – Orbits and Gravity9z Newton also figured out how to calculate the ggravitational force between objects. Mass of object 1 (M1) Mass of object 2 (M2)j(2) Distance between them (R)z Objects behave like points at their centers of gravitygravityM1M2RF=G*M*MWhat’s my Fgravitywith Earth?Fgravity= G M1 M2R2M1= Me… 80 kgM2= Earth… 5.97 * 1024kgR = Radius of Earth… 6371 kmR = Radius ofEarth… 6.371*106m‘G’ is a constant number 6.67 * 10-11m3kg-1s-3The universal gravitational constant.…plug in the numbers…784 NewtonsPYTS/ASTR 206 – Orbits and Gravity10z Reality checkWhich is greater the attraction between you and the Earth or you and theWhich is greater, the attraction between you and the Earth or you and the Sun?PYTS/ASTR 206 – Orbits and Gravity11z Reality checkWhich is greater the attraction between you and the Earth or you and theWhich is greater, the attraction between you and the Earth or you and the Sun? The Earth – much closer…PYTS/ASTR 206 – Orbits and Gravity12z Reality checkWhich is greater the force on you from the Earth or force on the Earth fromWhich is greater, the force on you from the Earth or force on the Earth from you?PYTS/ASTR 206 – Orbits and Gravity13z Reality checkWhich is greater the force on you from the Earth or force on the Earth fromWhich is greater, the force on you from the Earth or force on the Earth from you? They’re the same – equal and opposite.PYTS/ASTR 206 – Orbits and Gravity14z It turns out that gravitational acceleration doesn’t depend on how big your mass isdoesn’t depend on how big your mass is More mass makes it harder to accelerate…but…ltittil more mass also means a greater gravitational attractionz Just like Galileo’s falling object experimentFgravity= G * M1* MEARTHFgravity=M1*agravitygravity1EARTHR2M1* agravity = G * M1* MEARTHR2Fgravity M1 agravityagravity= G * MEARTH= 9.8 m/s2z You can do this for any ltgravity EARTHR2planetPYTS/ASTR 206 – Orbits and Gravity15zGravity has a strong influence on big bodiesThe shape of planetsThe shape of planetszGravity has a strong influence on big bodies Planets are round  Particles that formed them we’re reorganized into a spherical shapeand a eak infl ence on the small onesz …and a weak influence on the small ones. Asteroids tend to be irregular  Particles that formed them remain stuck together in haphazard shapePYTS/ASTR 206 – Orbits and Gravity16z So gravity makes planets round…That’s not the end of the storyThat s not the end of the story Planets are also spinning – creates a centrifugal force All planets bulge at the equatorThe faster the spin the bigger the bulgeThe faster the spin the bigger the bulgePolar areaSpinsSlowEquatorEquatorSpinsFastWhat Jupiter would look like ifWe make it spin fasterWhat Jupiter currently looks likePYTS/ASTR 206 – Orbits and Gravity17z We can figure out the expected shape by iflidltPlanetEquatorialPolarassuming a fluid planetz The ‘Hydrostatic approximation’z Combination of gravity and PlanetEquatorial RadiusPolarRadiusEarth 6378 km 6357 kmM3396 k3376 kgycentrifugal forces


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UA PTYS 206 - Orbits and Gravity

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