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GRAVITATION. FORCES IN THE UNIVERSE. Increasing Strength. Kinds of Forces. Gravity Electromagnetism * magnetism * electrostatic forces 3. Weak Nuclear Force 4. Strong Nuclear Force. + . proton. electron. Strong Force binds together protons & neutrons in atomic nuclei. - PowerPoint PPT Presentation
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GRAVITATION
FORCES IN THE UNIVERSE
1. Gravity
2. Electromagnetism* magnetism* electrostatic forces
3. Weak Nuclear Force
4. Strong Nuclear Force
IncreasingStrength
Kinds of Forces
+ 3810
Force nalGravitatioForce neticElectromag
proton
electron
StrongForcebindstogetherprotons &neutronsinatomicnuclei
n
Weak Force:
Decay of theNeutron
+
proton
electron
GRAVITATION
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 . . .
FALLING BODIES
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
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!
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
F
Newton’s 3rd law ball pulls on Earth
Ball
FDoes Earth accelerate?
Earth
UNIVERSAL GRAVITATION
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
1. Increase one or both masses, and force increases.
2. Force decreases as distance increases.
Force Distance400 N 10 m100 N 20 m25 N 40 m16 N 50 m4 N 100 m
d
M1 M2F F 4
400 2
400 100 2
4400
2400 100 2
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.
Putting the two parts of the force law together . . .
221
dMGM F (G = gravitational constant)
Acts through empty space“action at a distance”
Explains how gravity behaves – but not why
WEIGHT
p. 83
Weight
Measure of gravitational attraction of Earth (or any other planet) for you.
Earth
R
F
mM
Weight
2RGMm F W
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 . . .
“Weight” can bemade to apparentlyincrease . . .
p. 83
upward acceleration
. . . or decrease!
downwardacceleration “Weightlessness”
9.8 m/s/s
Free-fall
EARTH’S MASS
2RGMm W
your weight
your mass
Earth’s radius
Earth’s mass
M = 6 x 1024 kg
HOW DO THE PLANETS GO?
Planets appear‘star-like’
Planets move, relative to the stars.
Planets residenear Ecliptic.
[SkyGlobe]
Sun
Earth
Venus
Mars
Alien’s eye view . . .
Complicated!
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!
Jupiter & Venusare currently“in”Gemini.
AncientGreek
geocentricsolar
system
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 (?)
Ptolemy(85 – 165 AD)
Results: Planet-Earth distance changes Planet sometimes goes backward
Nicolaus Copernicus (1473 – 1543)
• First modern heliocentric (sun-centered) model of solar system
• Founder of modern astronomy
• Not first astronomer!
Copernicus’heliocentric
model, simplified
Galileo Galilei1564 - 1642
Galileo observes Jupiter’s
four largest moons
TelescopicView
Jupiter’s moons in motion.
Allowedpossibilitythat thereare manycenters of motion –
not just Earth.
Venus shows a full set of phases – like the moon’s
Venus’ motion according to . . .
Ptolemy(new & crescent phases)
Copernicus(full set of phases)
ORBITS
Any motion controlled only by gravity is an orbit
Without gravity
With gravity
NEWTON: Gravity explains how planets (andmoons & satellites & etc.) go.
Sun
Several trajectories are possible. . .
Object is effectivelycontinuously fallingtoward the sun . . .. . . But never getsthere!
Circle
F
Imagine launching aball sideways nearEarth . . .
Possible trajectories:
Circle Ellipse Parabola Hyperbola v
Which one you get depends on speed (v)!
“Escape”
Trajectories areconics
These are only possible orbits for inverse square law force.
Circles & Ellipses: “Bound” orbits Parabolas & Hyperbolas: “Escape” orbits
v v 5 mi/sec
v > 5 mi/secEscape:v 7 mi/sec
Earth
KEPLER’S LAWS
Johannes Kepler (1571 – 1630)
“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
1. Planets move in elliptical orbits with the sun at one focus
X
Sun (Focus)
FocusSemi-major axis (a)
c
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
Eccentricity (e): Measure of shape of ellipse
e = c/a a = semi-major axisc = dist center to focus
0 < e < 1
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
2. A line drawn from planet to sun sweeps out equal areas in equal times
2nd Law Demo
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
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 70000Cube of semi-major axis
Squa
re o
f per
iod
Solar System:
Newton modified Kepler’s 3rd Law:
M
m
2
3
Pa 1
2
3
Pa m M +
units of theSun’s mass
SUN’S MASS
32
2 a m) G(M
4 P
+
Mass of the Sun
1 yr1 AU
Earth’s massSun’s Mass
M = 2 x 1030 kg 330,000 Earth masses (!)
CENTER OF MASS ORBITS
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!
Exaggerated view:
X S
P
X = center ofboth orbits
Circular orbits
Consider Jupiter & the Sun . . .
X
5.2 AU0.0052 AU
Sun’s motion is small!
Center of Mass
GravitationalOrbits
Animation
Earth & Moon:
X
2900 mi 235,500 mi
2900 mi < Earth’s radius!
GravitationalOrbits
Animation
Discovery of Neptune
1846: Presence of Neptune predictedfrom irregularities in Uranus’ orbit.(J. C. Adams & U. J. J. Leverrier)
Uranus
Neptune
Speeds up
Slows down