1. Newton’s Universal Law of Gravitation
Physics 100
Chapt 10

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. 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

4. 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

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

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

16. Determine G from g, RE & ME
10m/s2x(6.4x106m)2
6x1024kg
G =
10m/s2x 41x1012m2
6x1024kg
G =
410x1012m3/s2
6x1024kg
G =
G = 6.7.x10-11 m3/kg s2
G = 6.7x10-11 Nm2/kg2
A very small number

17. 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

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

19. I weighed the Earth Cavendish’s measured the gravitational
Force between known masses & from
this deduced the value of Newton’s
Constant G. From this and the
relation for g he deduced ME, the mass
of the Earth, which turned out to be
about twice the value people had
guessed it to be at that time.
I weighed the Earth

20. Moon’s gravity causes tides

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

22. Measuring Weight N mg

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

24. Weightlessness means =0
compensating upward

25. Weightlessness in action

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

27. 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=

28. 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

29. Does Minertial = Mgravitational ?
Eotvos experiment .. .. .. ..
Lorand Eotvos
Devised a sensitive test of the equality between inertial & gravitational mass

30. q
Miv2/r Mi MG
MGg q
If Mi = MG,
q is the same
for every object

31. twist different amounts
If Mi = MG,
different materials
twist different amounts
inertia
same masses
different materials

32. Minertial = Mgravitational.. ..
Eotvos saw no effect, all materials
felt the same twist to 1 part in 109
Minertial = Mgravitational
to very high precision

33. summary
Obey the law!