Download - Gravity Gravitation Gravitasi 1
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GRAVITATION
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FORCES IN THE UNIVERSE
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1. Gravity
2. Electromagnetism* magnetism* electrostatic forces
3. Weak Nuclear Force
4. Strong Nuclear Force
IncreasingStrength
Kinds of Forces
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+ 3810
Force nalGravitatio
Force neticElectromag ≅
proton
electron
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StrongForcebindstogetherprotons &neutronsinatomicnuclei
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n
Weak Force:
Decay of theNeutron
+
proton
electron
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GRAVITATION
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GRAVITY keeps the moon orbitingEarth . . . and Dactyl orbiting Ida . . .
It holds starstogether . . .
Prevents planets
from losing their
atmospheres . . .
And binds galaxies together for billions of years . . .
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FALLING BODIES
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Falling objects accelerate at a constant rate (Galileo):
Speed is gained at a constant rate:
9.8 m/sec/sec
“Acceleration due to gravity”
Ball
Earthp. 82
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Time (sec) Speed (m/sec)1 9.82 19.63 29.44 39.26 58.88 78.4
10 98
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Speed (m/sec)
Time (sec)
Acceleration is same for ALL OBJECTS, regardless of mass!
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• 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:
m F ∝
F
m
Ball
Earth
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F
• Newton’s 3rd law ⇒ ball pulls on Earth
Ball
FDoes Earth accelerate?
Earth
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UNIVERSAL GRAVITATION
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All bits of matter attract all other bits of matter . . .
M1 M2
d
F F
“Inverse square law”
d
1 F 2.
MM F 1.
2
21
∝
∝
p. 92
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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==
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Force Distance400 10178 15100 20
44.4 3025 4016 50
11.1 608.2 70
6.25 804 100
0
20
40
60
80
100
120
0 100 200 300 400 500
Distance
ForceForce never becomeszero.
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Putting the two parts of the force law together . . .
221
d
MGM F = (G = gravitational constant)
• Acts through empty space“action at a distance”
• Explains how gravity behaves – but not why
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WEIGHT
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p. 83
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Weight
• Measure of gravitational attraction of Earth (or any other planet) for you.
Earth
R
F
mM
Weight
2R
GMm F W ==
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Other planets: M and R change, so your weight must change
Mars: R = 0.53 x Earth’s radiusM = 0.11 x Earth’s mass
Earth MarsWeight 150 lbs 59 lbs
A real planet . . .
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“Weight” can bemade to apparentlyincrease . . .
p. 83
upward acceleration
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. . . or decrease!
downwardacceleration
“Weightlessness”
9.8 m/s/s
Free-fall
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EARTH’S MASS
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2R
GMm W =
your weight
your mass
Earth’s radius
Earth’s mass
M = 6 x 1024 kg
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HOW DO THE PLANETS GO?
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Planets appear‘star-like’
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Planets move, relative to the stars.
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Planets residenear Ecliptic.
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[SkyGlobe]
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Sun
Earth
Venus
Mars
Alien’s eye view . . .
Complicated!
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Yet, patterns may be discerned . . .
• Planets remain near ecliptic – within Zodiac.
• Brightness changes in a regular pattern.
• Mercury & Venus always appear near Sun in sky.
• Mars, Jupiter & Saturn may be near Sun, but needn’t be.
• Planets travel eastward relative to stars most of the time,but sometimes they reverse direction & go west!
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Jupiter & Venusare currently“in”Gemini.
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AncientGreek
geocentricsolar
system
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Motionless Earth* Earth too heavy to be moved* If Earth moved, wouldn’t we notice?
> Relative motion argument> Parallax argument
Earth at center of Universe* This is Earth’s ‘natural place’
> Heavy stuff sinks* This is the natural place of humankind
> We’re most important (?)
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Ptolemy(85 – 165 AD)
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Results: • Planet-Earth distance changes• Planet sometimes goes backward
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Nicolaus Copernicus (1473 – 1543)
• First modern heliocentric (sun-centered) model of solar system
• Founder of modern astronomy
• Not first astronomer!
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Copernicus’heliocentric
model, simplified
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Galileo Galilei1564 - 1642
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Galileo observes Jupiter’s
four largest moons
TelescopicView
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Jupiter’s moons in motion.
Allowedpossibilitythat thereare manycenters of motion –
not just Earth.
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Venus shows a full set of phases – like the moon’s
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Venus’ motion according to . . .
Ptolemy(new & crescent phases)
Copernicus(full set of phases)
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ORBITS
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• Any motion controlled only by gravity is an orbit
Without gravity
With gravity
NEWTON: Gravity explains how planets (andmoons & satellites & etc.) go.
Sun
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Several trajectories are possible. . .
Object is effectivelycontinuously fallingtoward the sun . . .. . . But never getsthere!
Circle
F
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Imagine launching aball sideways nearEarth . . .
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Possible trajectories:
• Circle• Ellipse• Parabola• Hyperbola v
Which one you get depends on speed (v)!
“Escape”
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Trajectories areconics
These are only possible orbits for inverse square law force.
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• Circles & Ellipses: “Bound” orbits• Parabolas & Hyperbolas: “Escape” orbits
vv ≅ 5 mi/sec
v > 5 mi/sec
Escape:v ≥ 7 mi/sec
Earth
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KEPLER’S LAWS
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Johannes Kepler (1571 – 1630)
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“By the study of the orbit of Mars, we must either arrive at the secrets of astronomy or forever remain
in ignorance of them.”- J. Kepler
Tycho Brahe
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1. Planets move in elliptical orbits with the sun at one focus
X
Sun (Focus)
Focus
Semi-major axis (a)
c
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PerihelionAphelion
Earth: a = 1.00 AU = 92, 980.000 mi aphelion = 1.0167 AU = 94,530,000 mi perihelion = 0.9833 AU = 91,420,000 mi
67,000 mi/hr
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Eccentricity (e): Measure of shape of ellipse
e = c/a a = semi-major axisc = dist center to focus
0 < e < 1
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a e Earth 1.0 AU 0.0167Mars 1.52 0.0934Pluto 39.5 0.250Halley’s Comet 17.8 0.967
A few objects orbiting the sun . . . . . .
Semi-major axis, or mean distance between planet & sun
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2. A line drawn from planet to sun sweeps out
equal areas in equal times
2nd Law Demo
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3. The cube of the mean planet-sun distance is
directly proportional to the square of the
planet’s orbit period
a3 = P2 a: AUP: years
Or,
a3/ P2 = 1 3rd LawDemo
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P a P2 a3 P2/a3
Mercury 0.241 0.387 0.058 0.058 1Venus 0.615 0.723 0.378 0.378 1Earth 1 1 1 1 1Mars 1.881 1.524 3.538 3.538 1Jupiter 11.86 5.203 140.7 140.8 0.999Saturn 29.46 9.539 867.8 867.9 1Uranus 84.01 19.19 7058 7068 0.998Neptune 164.8 30.06 27156 27165 1Pluto 248.5 39.53 61752 61768 1
0
10000
20000
30000
40000
50000
60000
70000
0 10000 20000 30000 40000 50000 60000 70000
Cube of semi-major axis
Sq
ua
re o
f p
eri
od
Solar System:
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Newton modified Kepler’s 3rd Law:
M
m
2
3
P
a 1 =
2
3
P
a m M =+
units of theSun’s mass
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SUN’S MASS
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32
2 a m) G(M
4 P
+
= π
Mass of the Sun
1 yr1 AU
Earth’s massSun’s Mass
M = 2 x 1030 kg ≅ 330,000 Earth masses (!)
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CENTER OF MASS ORBITS
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Finally (at last ) . . . the true story of orbits
We left something out . . .
SunPlanet
Sun pulls on planet . . . planet pulls on sun ⇒ Sun moves a little, too!
Yikes!
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Exaggerated view:
XS
P
X = center ofboth orbits
Circular orbits
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Consider Jupiter & the Sun . . .
X
5.2 AU0.0052 AU
⇒ Sun’s motion is small!
Center of Mass
GravitationalOrbits
Animation
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Earth & Moon:
X
2900 mi 235,500 mi
2900 mi < Earth’s radius!
GravitationalOrbits
Animation
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Discovery of Neptune
1846: Presence of Neptune predictedfrom irregularities in Uranus’ orbit.(J. C. Adams & U. J. J. Leverrier)
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Uranus
Neptune
Speeds up
Slows down