Gravity Gravitation Gravitasi 1

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 nalGravitatio

Force 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 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