2. Very fast horizontal toss
t = 0s
t = 1s
x= 8km
5m
t = 2s
x=16km
t = 3s
x=24km
20m 45m
V=8km/s
3. Orbital motion is free fall
VV == 46 km/s V = 8km/10km/km/s
CEilirpctuilcaarl OOrrbbiitt!
4. 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
7. Is the Moon in free-fall around the
Earth?
r=3.84x105km
v
a = v2/r
what is v?
v = dist/time = 2pr
28d =
2x3.14x 3.84x108 m
28dx(24h/d)x3.6x103s
= 24 x 108 m
2.4x106s = 1.0 x 103 m/s
8. Moon’s centripetal acceleration
amoon = v2/r; v = 1.0 x103 m/s)
amoon= (1.0 x103 m/s)2
1.0x106 m2/s2
3.84 108 m = x 3.84 x 108 m
= 2.7 x 10-3 m/s2
» 1 3600
g
Toward Earth’s center
9. 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)
10. Distances
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
11. 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
15. What is G?
W= G
mME
R2
E
W
W= m
GME
R2
E
W= m g
g=
GME
R2
E
16. Force of gravity between
“ordinary-sized” objects
80kg
60kg
1m
F = G
mM
r2
F = 6.7x10-11Nm2/kg2 60 kg 80kg
(1m)2
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
