Physics 100

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Newtons Universal Law of Gravitation

• Physics 100
• Chapt 10

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Very fast horizontal toss
t 0s
t 1s x 8km
t 2s x16km
t 3s x24km
V8km/s
5m
20m
45m
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Orbital motion is free fall
Circular Orbit!
Eliptical Orbit
V 4 km/s
V 6 km/s
V 8 km/s
V 10 km/s
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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 Earths center
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Artificial satellite
a
v
a v2/r g
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Moon-earth
v
av2/r
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Is the Moon in free-fall around the Earth?
v
a v2/r
r3.84x105km
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
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Moons 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 Earths center
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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
The moon is 60x further from the Earths center
than objects on (near) the Earths surface
r3.84x108m
60 x 6.4x106 m
60 x RE
1 60
1 3600
(
)2
RE 6.4x106m
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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 t1/3600 times weaker
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Gravity gets weaker as 1/dist2
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Universal law of gravity
M
m
r
F ? m
F ? M
Proportionality constant
1 r2
F ?
Newtons Constant
mM r2
mM r2
combine
F ?
F G
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Universal
applies to all objects!!!
Universal
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What is G?
mME RE2
W
W G
GME RE2
W m
W m g
GME RE2
g
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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!
Boys weight mg 80kg x 10m/s2 800 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
Half Moon
New Moon
Full Moon
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Measuring Weight
N
mg
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Weightlessness
N
0
N
mg
N
gtmg
N
ltmg
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Weightlessness means 0
N
compensating upward
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Weightlessness in action
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Floating is space isreally free-falling in
space
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What is g on the moon?
mMM RM2
W G
m
RM1.7 x 106m
GMM RM2
W
W m
W m gM
MM
GMM RM2
gM
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gM on the Moon
GMM RM2
g
6.7x10-11Nm2/kg2 x 7.4x1022Kg (1.7x106m)2

gM 1.7 m/s2
1/6 x gEarth
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summary
Obey the law!
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