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Universal Gravitation Formulas F G = Gmm / d 2 G = 6.67 x 10 -11 (“sto” this!) Go over last night’s HW... Biggest = Jupiter (MASSIVE!) at 4.17 x 10 23 N Smallest = Neptune ( f a r a w a y !) at 6.75 x 10 20 N Note – units of mass & distance MUST be in kg and meters! Start one from HW ditto #6-15; #13...

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Part 2 - Universal Gravitation F G = G mm / d 2 and: F g = mg So set them equal: g = Gm / d 2 (mass of object cancels, mass of planet left over!) Note – units of mass & distance MUST be in kg and meters! Using p.173, find g of the “dwarf planet” Pluto: HW = after doing question 20 on the ditto, then do #72 a on page 192

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T = 2 sqrrt (r 3 /GM central mass ) or, T = Called “Newton’s version of Kepler’s 3 rd Law” (This one you do NOT have to memorize!) UNITS must be seconds, kg, and meters!! Start one from HW ditto #17-20; #17...Use the Earth’s data to calculate the mass of the sun.... Part 3 - Universal Gravitation

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Universal Gravitation Part 4a T = 2 sqrrt (r 3 / GM central mass ); square both sides... T 2 = 4 2 r 3 / GM; move r 3 to other side... T 2 / r 3 = 4 2 / GM central mass For 2 objects going the SAME “central mass” {4 2 / GM central mass } is a CONSTANT, so you can do: T 2 / r 3 = T 2 / r 3 HW: planets all = 3 x 10 -34 if used book distances, or 3 x 10 -7 if used handout distances Could you compare the moon & Mars? Could you compare an asteroid and the earth? Could you compare a ATT communications satellite & the moon? Could you compare a moon of Jupiter’s with Jupiter?

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Universal Gravitation Part 4b T 2 / r 3 = T 2 / r 3 Because its a ratio, this is the ONLY one of the 4 formulas where UNITS don’t matter... The units must “match”, like in the gas laws! Some units we use: 1 AU = 1 lunar month = Start one from HW ditto #1-5; #3

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Newton’s Universal Law of Gravitation

Newton’s Universal Law of Gravitation

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