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Your assignment is on the last slide

2. Newton’s Universal Law of Gravitation
Physics
Chapter 7

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

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. 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

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

7. Moon-earth v
a=v2/r

8. 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

9. 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

10. 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)

11. 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

12. 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

13. Gravity gets weaker as 1/dist2

14. 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

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

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

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. Moon’s gravity causes tides

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

21. Measuring Weight N mg

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

23. Weightlessness means =0
Normal

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

25. ‘zero-g’ the weightless experience
You can pay ~$5000 to experience ‘weightlessness’ aboard an airplane flying within earth’s gravity
Aboard our specially modified Boeing 727, G-FORCE ONE, weightlessness is achieved by doing aerobatic maneuvers known as parabolas. Specially trained pilots perform these aerobatic maneuvers which are not simulated in any way. ZERO-G’s passengers experience true weightlessness.
Before starting a parabola, G-FORCE ONE flies level to the horizon at an altitude of 24,000 feet. The pilots then begins to pull up, gradually increasing the angle of the aircraft to about 45° to the horizon reaching an altitude of 34,000 feet. During this pull-up, passengers will feel the pull of 1.8 Gs. Next the plane is “pushed over” to create the zero gravity segment of the parabola. For the next seconds everything in the plane is weightless. Next a gentle pull-out is started which allows the flyers to stabilize on the aircraft floor. This maneuver is repeated times, each taking about ten miles of airspace to perform.

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. HAND IN FOR CREDIT
On separate paper, Write a paragraph of 10 sentences summarizing this powerpoint. Also write the Law of Universal Gravitation and explain what each variable stands for And how to use it to calculate g (accel due to gravity.