Philae Lander Found!Course AnnouncementsAssignmentsNewtonian GravityNewtonian GravityExample Gravity QuestionExample Gravity QuestionExample Gravity QuestionExample Gravity QuestionHard Gravity QuestionHard Gravity QuestionNewtonian GravityPutting something in orbitRocket Science – Leaving the EarthUsing Newtonian Gravity to Weigh ThingsWhat makes planets orbit?Newton’s Modifications to Kepler’s LawsModified Kepler’s LawsModified Kepler’s LawsModified Kepler’s LawsModified Kepler’s LawsModified Kepler’s LawsUniv. of Colorado’s Online Orbit SimulatorChapter 3Light: Our source of informationLight and RadiationThe Nature of Light“Invisible” LightLight – It’s a wave (and particle)Anatomy of WavesAnatomy of a WaveAnatomy of a WavePhilae Lander Found!Credit: ESA/Rosetta/MPSImage taken by the Rosetta spacecraft from a distance of 2.7 km. The image scale is about 5cm/pixel.Course Announcements•OSIRIS-REx successfully launched!•Please get 3 x 5 Notecards for upcoming Notecard Q’sAssignmentsReading Assignments•Chapter 3. Sections 3.1 – 3.3[Read for Monday, 12 Sept.]Parallel Lectures•CC Astronomy – Episode 24: Light[Watch for Monday, 12 Sept.]Mastering Astronomy•Chapter 2 Homework[Due Tuesday, 13 Sept. at 11:59 PM EDT]Newtonian Gravity•How strong the gravitational force is depends only on TWO components: The masses involved, and the distance between them•The force of gravity is proportional to the product of the masses (m1 and m2) divided by (inversely proportional) the square of the distance between them, usually labeled as r or R•The Inverse-Square Law–Know what an inverse-square law isAn inexorable attractionDouble the distance;Reduce gravity by a factor of 22 = 4Five times the distance; Reduce gravitational force by a factor of 52 = 25Newtonian GravityAn inexorable attraction•Gravity only operates in ONE direction. IT IS ALWAYS ATTRACTIVE, AND NEVER REPULSIVE•G, sometimes called “Big G” is the Gravitational Constant measured experimentally to beG = 6.67 x 10-11 N m2/kg2–You don’t have to know this numberDouble the distance;Reduce gravity by a factor of 22 = 4Five times the distance; Reduce gravitational force by a factor of 52 = 25Example Gravity QuestionExact Form(You don’t need to know the exact form)You do need to know the proportionalities (i.e., dependency on masses and distances involved)How much (stronger or weaker?) does the force of gravity become when we triple the distance between two masses, M and m?M m3xDistanceM = mTriple the DistanceM1xDistancemExample Gravity QuestionExact Form(You don’t need to know the exact form)You do need to know the proportionalities (i.e., dependency on masses and distances involved)Answer: The force of gravity is inversely proportional to the square of the distance. So, if I double the distance (farther away), the inverse proportionality tells me that gravity will be weaker with the larger distance, and it will be so by a factor (that means number) of the distance squared. 3x more distance => 32 = 9 x weaker (or 1/9th as strong)MmM m1xDistance3xDistanceM = mTriple the DistanceExample Gravity QuestionExact Form(You don’t need to know the exact form)You do need to know the proportionalities (i.e., dependency on masses and distances involved)How much (stronger or weaker?) does the force of gravity become when we double (2x) one of the mass, M, and quadruple (4x) the other mass, m?Mm1xDistanceSame DistanceDouble One of the masses; 4x the otherM -> 2MM -> 4m4m1xDistance2MExample Gravity QuestionExact Form(You don’t need to know the exact form)You do need to know the proportionalities (i.e., dependency on masses and distances involved)Answer: The force of gravity is directly proportional to the product of the masses. With one of the masses doubled (M -> 2M) and the other quadrupled (m -> 4m), we have (4m x 2M = 8mM) and therefore the force of gravity is 8 times stronger. So, the force of gravity is stronger by a factor of 8.Mm1xDistanceSame DistanceDouble One of the masses; 4x the otherM -> 2MM -> 4m4m1xDistance2MHard Gravity QuestionHow much (stronger or weaker?) does the force of gravity become in when we change the masses to be 2x and 3x more massive, respectively, AND triple the distance between them?m1m2Change masses (2x and 3x)Triple Distance3m12m23xDistance1xDistanceHard Gravity QuestionSolution Method: Take it one step at a time.Step 1: The Mass Dependence: Change in the product of the masses: m1 x m2 3m1 x 2m2 = (3x2)(m1 x m2) = 6m1m2. So, due to the masses, gravity has increased by a factor of 6Step 2: The Distance-squared Dependence: Change in distance is 3 times farther away. 32 = 9, so due to the distance change, gravity has decreased by a factor of 9.Step 3: Compare: Increase by factor of 6, decrease by factor of 9. Looking at the gravity equation, we see the change in gravity is by a factor of 6/9 = 2/3. So, overall, the force of gravity has decreased (weaker) by a factor of two-thirds.m1m21xDistanceChange masses (2x and 3x)Triple Distance3m12m23xDistanceNewtonian Gravity•The Earth has mass… a lot of it at 5.87 x 1024 kg (A trillion trillion kilograms! 1 kg = 2.2 pounds… on Earth)–We live in the gravitational field the causes. It is always acting on us.•On Earth, the acceleration due to Earth’s gravity (often written as g) is approximately constant and directed toward the center of Earth–Earth gravitational acceleration, g = 9.8 m/s2 (So-called, 1 g [gee])–It never stops and is always applying a force to everything... In the Universe!Gravity on EarthUnder gravity, objects fall back to Earth with an every increasing velocity (they are accelerating), which makes them move in parabolic pathsAlways pulling at a constant force ofF = mg [mass x 9.8 m/s2]Putting something in orbit•The speed at which the Force of Gravity balances out Centripetal Force (Circular Motion force) is orbital speed–Set both forces equal to each other [in balance]GmMR2=mv2RImagine firing a cannon with progressively more and more forceForce of GravityCentripetal ForceFg == FcVorb gives you the velocity an object will orbit a object with mass, M, at a distance R away from it.I’m falling, but constantly missing!Rocket Science – Leaving the Earth•If we fire the cannon ball with even more force, then we can break orbit and go out into interplanetary space!•The speed to escape entirely, escape speed, is the square root of 2 (1.414 times) greater than
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