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Physics 100 Chapt 10 Newtons Universal Law of Gravitation

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Very fast horizontal toss t = 0s t = 1s x= 8km 5m t = 2s x=16km t = 3s x=24km 20m 45m V=8km/s

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Orbital motion is free fall V = 4 km/sV = 6 km/sV = 8 km/sV = 10 km/s Circular Orbit!Eliptical Orbit

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Centripetal acceleration a = v 2 /r for a circular orbit (v = 8km/s = 8x10 3 m/s) a = (8 x10 3 m/s) 2 6.4 x 10 6 m = 64 x10 6 m 2 /s 2 6.4 x 10 6 m = 10 m/s 2 Toward Earths center = g

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Artificial satellite a v a = v 2 /r = g

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Moon-earth v a=v 2 /r

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Is the Moon in free-fall around the Earth? r=3.84x10 5 km v a = v 2 /r what is v? v = dist/time = 2 r 28d = 2 x 3.14 x 3.84 x 10 8 m 28d x (24h/d) x 3.6 x 10 3 s = 24 x 10 8 m 2.4 x 10 6 s = 1.0 x 10 3 m/s

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Moons centripetal acceleration a moon = v 2 /r; v = 1.0 x10 3 m/s) a moon = (1.0 x 10 3 m/s) 2 3.84 x 10 8 m = 1.0 x 10 6 m 2 /s 2 3.84 x 10 8 m = 2.7 x 10 -3 m/s 2 Toward Earths center g 1 3600

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Newtons dreams Hmmmmm The Moon is in free-fall around the Earth Its acceleration is only 1/3600 g (accel at the Earths surface)

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Distances r=3.84x10 8 m = 60 x 6.4x10 6 m The moon is 60x further from the Earths center than objects on (near) the Earths surface = 60 x R E 1 60 1 3600 ()2=)2= R E = 6.4x10 6 m

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Newtons big idea The force of gravity gets weaker as distance squared The moon is 60x further from the Earths center than objects on (near) the Earths surface The strength of Earths gravity near the Moon is (1/60) 2 t=1/3600 times weaker

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Gravity gets weaker as 1/dist 2

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Universal law of gravity m M r F m F M F 1r21r2 combine:F mM r 2 F = G mM r 2 Proportionality constant: Newtons Constant

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Universal Universal: applies to all objects!!!

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What is G? W= G mM E R E 2 W W= m GM E R E 2 W= m g g=g= GM E R E 2

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Force of gravity between ordinary-sized objects 80kg 60kg 1m F = G mM r 2 F = 6.7x10 -11 Nm 2 /kg 2 60 kg 80kg (1m) 2 F = 6.7 x 60 x 80 x 10 -11 N Boys weight = mg = 80kg x 10m/s 2 = 800 N 30x10 9 times bigger! F = 32160. x 10 -11 N = 3.2x10 -7 N

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Measuring gravity force between ordinary-sized objects is very hard

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Moons gravity causes tides

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So does the Suns Full Moon New Moon Half Moon

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Measuring Weight mg N

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Weightlessness N=mg N>mgN

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Weightlessness means =0 N compensating upward

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Weightlessness in action

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Floating is space is really free-falling in space

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What is g on the moon? W= G mM M R M 2 W= m GM M R M 2 W= m g M gM=gM= GM M R M 2 W R M =1.7 x 10 6 m m M

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g M on the Moon g = GM M R M 2 6.7x10 -11 N m 2 /kg 2 x 7.4x10 22 Kg (1.7 x 10 6 m) 2 = g M = 1.7 m/s 2 1/6 x g Earth

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summary Obey the law!

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Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation

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