1. Newton’s Universal Law of Gravitation

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

3. 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

4. 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

5. Artificial satellite a v
a = v2/r
= g

6. Moon-earth v
a=v2/r

7. 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

8. 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

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 ( )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

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

12. Gravity gets weaker as 1/dist2

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

14. Universal
Universal:
applies to all objects!!!

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

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

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

18. Moon’s gravity causes tides

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

20. Measuring Weight N mg

21. Weightlessness N =0 N
=mg N
>mg N
<mg

22. Weightlessness means =0
compensating upward

23. Weightlessness in action

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

25. 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=

26. 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

27. summary
Obey the law!