Physics 100
Chapt 10
Newton’s Universal Law of Gravitation
Very fast horizontal toss
t = 0s
t = 1sx= 8km
5m
t = 2sx=16km
t = 3sx=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 = v2/r for a circular orbit (v = 8km/s = 8x103m/s)
a =(8 x103 m/s)2
6.4 x 106 m=
64 x106 m2/s2
6.4 x 106 m
= 10 m/s2
Toward Earth’s center = g
Artificial satellite
av
a = v2/r = g
Moon-earthv
a=v2/r
Is the Moon in free-fall around the Earth?
r=3.8
4x105 km
v
a = v2/r
what is v?
v = dist/time = 2r28d =
2x3.14x 3.84x108 m28dx(24h/d)x3.6x103s
= 24 x 108 m2.4x106s = 1.0 x 103 m/s
Moon’s centripetal acceleration
amoon = v2/r; v = 1.0 x103 m/s)
amoon=(1.0 x103 m/s)2
3.84 x 108 m=
1.0x106 m2/s2
3.84 x 108 m
= 2.7 x 10-3 m/s2
Toward Earth’s center
g13600
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
r=3.84x108m = 60 x 6.4x106 m
The moon is 60x further fromthe Earth’s center than objectson (near) the Earth’s surface
= 60 x RE
160
13600( )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 Mr
F m
F M
F 1r2
combine: F mMr2 F = G
mMr2
Proportionality constant:
“Newton’s Constant”
Universal
Universal:applies to all objects!!!
What is G?
W= GmME
RE2
W
W= mGME
RE2
W= m g
g=
GME
RE2
Force of gravity between “ordinary-sized” objects
80kg60kg
1mF = G
mMr2
F = 6.7x10-11Nm2/kg260 kg 80kg(1m)2
F = 6.7x60x80x10-11N
Boy’s weight = mg = 80kg x 10m/s2 = 800 N
30x109 times bigger!
F = 32160.x10-11 N = 3.2x10-7
N
Measuring gravity force between “ordinary-sized” objects is very hard
Moon’s gravity causes tides
So does the Sun’s
Full Moon
New Moon
Half Moon
Measuring Weight
mg
N
Weightlessness
N =mg
N >mg N <mg
N =0
Weightlessness means =0N
compensating upward
Weightlessness in action
“Floating” is space isreally free-falling in space
What is g on the moon?
W= GmMM
RM2
W= mGMM
RM2
W= m gM
gM
=
GMM
RM2
WRM=1.7 x 106m
mMM
gM on the Moon
g =
GMM
RM2
6.7x10-11Nm2/kg2 x 7.4x1022Kg(1.7x106m)2
=
gM = 1.7 m/s2
1/6 x gEarth
summary
Obey the law!