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 ThursdayDue in class next ThursdayTA i l K i J fTA 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 EarthThe Moon and the EarthThe 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 tAll 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 t2*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 momentumA 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 checkWhich is greater the attraction between you and the Earth or you and theWhich is greater, the attraction between you and the Earth or you and the Sun?PYTS/ASTR 206 – Orbits and Gravity11z Reality checkWhich is greater the attraction between you and the Earth or you and theWhich 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 checkWhich is greater the force on you from the Earth or force on the Earth fromWhich is greater, the force on you from the Earth or force on the Earth from you?PYTS/ASTR 206 – Orbits and Gravity13z Reality checkWhich is greater the force on you from the Earth or force on the Earth fromWhich 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 storyThat s not the end of the story Planets are also spinning – creates a centrifugal force All planets bulge at the equatorThe 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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