# Physics 100 Chapt 10 Newtons Universal Law of Gravitation.

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Physics 100 Chapt 10 Newtons Universal Law of Gravitation

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

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

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

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

Moon-earth v a=v 2 /r

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

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

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

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

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

Gravity gets weaker as 1/dist 2

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

Universal Universal: applies to all objects!!!

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

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

Measuring gravity force between ordinary-sized objects is very hard

Moons gravity causes tides

So does the Suns Full Moon New Moon Half Moon

Measuring Weight mg N

Weightlessness N=mg N>mgN<mg N=0

Weightlessness means =0 N compensating upward

Weightlessness in action

Floating is space is really free-falling in space

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

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

summary Obey the law!