Your assignment is on the last slide DO NOT KEEP THIS COPY Return at end of period for use by next class Your assignment is on the last slide

Newton’s Universal Law of Gravitation Physics Chapter 7

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

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

Centripetal acceleration a = v2/r for a circular orbit (v = 8km/s = 8x103m/s) (8 x103 m/s)2 6.4 x 106 m 64 x106 m2/s2 6.4 x 106 m a = = = g = 10 m/s2 Toward Earth’s center

Artificial satellite a v a = v2/r = g

Moon-earth v a=v2/r

Is the Moon in free-fall around the Earth? v a = v2/r r=3.84x105km what is v? 2pr 28d 2x3.14x 3.84x108 m 28dx(24h/d)x3.6x103s v = dist/time = = 24 x 108 m 2.4x106s = = 1.0 x 103 m/s

Moon’s centripetal acceleration amoon = v2/r; v = 1.0 x103 m/s) (1.0 x103 m/s)2 3.84 x 108 m 1.0x106 m2/s2 3.84 x 108 m amoon= =  g 1 3600 = 2.7 x 10-3 m/s2 Toward Earth’s center

Newton’s dreams Hmmmmm The Moon is in free-fall around the Earth It’s acceleration is only 1/3600 g (accel at the Earth’s surface)

Distances ( )2= The moon is 60x further from the Earth’s center than objects on (near) the Earth’s surface r=3.84x108m = 60 x 6.4x106 m = 60 x RE 1 60 1 3600 ( )2= RE = 6.4x106m

Newton’s big idea The force of gravity gets weaker as distance squared The moon is 60x further from the Earth’s center than objects on (near) the Earth’s surface The strength of Earth’s gravity near the Moon is (1/60)2 t=1/3600 times weaker

Gravity gets weaker as 1/dist2

Universal law of gravity M m r F  m F  M Proportionality constant: 1 r2 F  “Newton’s Constant” mM r2 mM r2 combine: F  F = G

Universal Universal: applies to all objects!!!

What is G? W mME RE2 W= G GME RE2 W= m W= m g GME RE2 g=

Force of gravity between “ordinary-sized” objects mM r2 F = G 80kg 60kg 1m 60 kg 80kg (1m)2 F = 6.7x10-11Nm2/kg2 F = 6.7x60x80x10-11N F = 32160.x10-11 N = 3.2x10-7 N  30x109 times bigger! Boy’s weight = mg = 80kg x 10m/s2 = 800 N

Measuring gravity force between “ordinary-sized” objects is very hard

Moon’s gravity causes tides

So does the Sun’s Half Moon New Moon Full Moon

Measuring Weight N mg

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

Weightlessness means =0 Normal

“Floating” is space is really free-falling in space

‘zero-g’ the weightless experience You can pay ~$5000 to experience ‘weightlessness’ aboard an airplane flying within earth’s gravity Aboard our specially modified Boeing 727, G-FORCE ONE, weightlessness is achieved by doing aerobatic maneuvers known as parabolas. Specially trained pilots perform these aerobatic maneuvers which are not simulated in any way. ZERO-G’s passengers experience true weightlessness. Before starting a parabola, G-FORCE ONE flies level to the horizon at an altitude of 24,000 feet. The pilots then begins to pull up, gradually increasing the angle of the aircraft to about 45° to the horizon reaching an altitude of 34,000 feet. During this pull-up, passengers will feel the pull of 1.8 Gs. Next the plane is “pushed over” to create the zero gravity segment of the parabola. For the next 20-30 seconds everything in the plane is weightless. Next a gentle pull-out is started which allows the flyers to stabilize on the aircraft floor. This maneuver is repeated 12-15 times, each taking about ten miles of airspace to perform. http://www.gozerog.com/index.cfm?fuseaction=Experience.How_it_Works

What is g on the moon? MM mMM RM2 m W= G GMM RM2 W W= m W= m gM GMM RM=1.7 x 106m GMM RM2 W W= m W= m gM MM GMM RM2 gM=

gM on the Moon gM = 1.7 m/s2 GMM RM2 g = 6.7x10-11Nm2/kg2 x 7.4x1022Kg (1.7x106m)2 = gM = 1.7 m/s2 1/6 x gEarth

HAND IN FOR CREDIT On separate paper, Write a paragraph of 10 sentences summarizing this powerpoint. Also write the Law of Universal Gravitation and explain what each variable stands for And how to use it to calculate g (accel due to gravity.