Transcript
GravityXII IPA 6
Group 2
• Fita Aliftariasa (08)• Kartikya Ishlah Utami (10)• Rifda Latifa (16)• Shinta Sigit Agustina (19)• Muhammad Fauzi Dharmawan (23)• Muhammad Ramadhani S. (25)
FORCES IN THE UNIVERSE
1. Gravity
2. Electromagnetism* magnetism* electrostatic forces
3. Weak Nuclear Force
4. Strong Nuclear Force
IncreasingStrength
Kinds of Forces
Do you know what is Gravity?
• Gravitation, or gravity, is a natural phenomenon which all physical bodies attract each other.
• It is most commonly experienced as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped.
GRAVITY keeps the moon orbitingEarth
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 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==
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
d
MGM 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
2R
GMm 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
2R
GMm 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
vv ≅ 5 mi/sec
v > 5 mi/sec
Escape: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)
Focus
Semi-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 70000
Cube of semi-major axis
Sq
ua
re o
f p
eri
od
Solar System:
Newton modified Kepler’s 3rd Law:
M
m
2
3
P
a 1 =
2
3
P
a m M =+
units of theSun’s mass
SUN’S MASS
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 (!)
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:
XS
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
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