"LIFE IS ALL ABOUT NEXT STEP"

1. GRAVITATION

2. Kinds of Forces

3. IsaacNewton, (1642-1727)

4. + 38
10
ForcenalGravitatio
ForceneticElectromag

proton
electron
rˆ
r
mm
GF 2
21


r
MmG
)r(Ug 
1.Newton’s Law of Universal Gravitation
2.Gravitational Potential Energy (long-range form)

5. r
MmG
rd
r
MmG
rdFrU
rr
g 



 2
)(
)(


6. Old: )yy(gm)y(U 0g 
New:
r
MmG
)r(Ug 
How could these be the same?
Consider a location near the surface of the earth, y0
= R, y = R+h.
The only thing that matters is U, not U itself.
Old: hgm)RhR(gmUg +
New: 





+







+

hR
1
R
1
MmG
R
MmG
hR
MmG
Ug






+






+

hRR
h
MGm
hR
1
R
1
MGm 2
(h << R)
hgmh
R
MG
m
R
h
MGm 22


7. “Acceleration due to gravity”
Ball
Earth

8.  Newton’s 2nd law  force (F) is acting on
falling ball (mass = m)
 All masses have same acceleration
. . . so more mass means more force
needed:
mF 
F
m
Ball
Earth

9. F
 Newton’s 3rd law  ball pulls on Earth
Ball
F
Does Earth accelerate?
Earth

10. All bits of matter attract all other bits of matter . . .
M1 M2
d
F F
“Inverse square law”
d
1
F2.
MMF1.
2
21



11. 1.  Increase one or both masses, and force increases.
2.  Force decreases as distance increases.
Force Distance
400 N 10 m
100 N 20 m
25 N 40 m
16 N 50 m
4 N 100 m
d
M1 M2F F
4
400
2
400
100 2


12. Force Distance
400 10
178 15
100 20
44.4 30
25 40
16 50
11.1 60
8.2 70
6.25 80
4 100
0
20
40
60
80
100
120
0 100 200 300 400 500
Distance
Force
Force never becomes
zero.

13. Putting the two parts of the force law together . . .
2
21
d
MGM
F  (G = gravitational constant)
 Acts through empty space
“action at a distance”
 Explains how gravity behaves – but not why

14. p. 83

15. Weight
 Measure of gravitational attraction of Earth
(or any other planet) for you.
Earth
R
F
m
M
Weight
2
R
GMm
FW 

16. Other planets: M and R change, so your
weight must change
Mars: R = 0.53 x Earth’s radius
M = 0.11 x Earth’s mass
Earth Mars
Weight 150 lbs 59 lbs
A real planet . . .

17. “Weight” can be
made to apparently
increase . . .
upward acceleration

18. . . . or decrease!
downward
acceleration
“Weightlessness”
9.8 m/s/s
Free-fall

19. 2
R
GMm
W 
your weight
your mass
Earth’s radius
Earth’s
mass
M = 6 x 1024 kg

20. By 1915, Einstein had worked through all the math (with some help)
to show that his postulates led to a new theory of gravity based on
the effect of mass and energy to curve the structure of space and
time. His theory has some startling implications, one being the
existence of “black holes” – regions of space where the gravity field
is so high that even light cannot escape. The predictions of General
Relativity, including the existence of black holes, have been
confirmed by all experiments to date.

21.  Any motion controlled only by gravity is an orbit
Without gravity
With gravity
NEWTON: Gravity explains how planets (and
moons & satellites & etc.) go.
Sun

22. .
Object is effectively
continuously falling
toward the sun . . .
. . . But never gets
there!
Circle
F

23. Imagine launching a
ball sideways near
Earth . . .

24. Johannes
Kepler
(1571 – 1630)
1. Planets move in elliptical orbits with the
sun at one focus
X
Sun (Focus)
Focus
Semi-major axis (a)
c

26. M
m
2
3
P
a
1 
2
3
P
a
mM +
units of the
Sun’s mass

27. 3
2
2
a
m)G(M
4
P 





+


1 yr
1 AU
Earth’s massSun’s Mass

28. CENTER OF MASS ORBITS
We left something out . . .
Sun
Planet
Sun pulls on planet . . . planet pulls on sun
 Sun moves a little, too!

29. Exaggerated view:
X
S
P
X = center of
both orbits
Circular orbits

30. Consider Jupiter & the Sun . . .
X
5.2 AU0.0052 AU
 Sun’s motion is small!
Center of Mass
Gravitational
Orbits
Animation

31. Earth & Moon:
X
2900 mi 235,500 mi
2900 mi < Earth’s radius!
Gravitational
Orbits
Animation