Transcript Galileo, Newton, and Einstein

Pick
rd
3
hour stuff!
 It
will first appear in the center of the room
before lecture.
 It will then be moved to the box labeled
“3100” outside the planetarium
• All 3rd hours will collect there until the end of the
semester
 Scores
posted just outside the planetarium
(listed by 4-digit ID number)
 Homework now due at 11:59pm Friday!
 Extra Credit: see page 41 (25 pts max, 10 must be
done before midterm)
© Sierra College Astronomy Department
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Lecture 2: An Earth-Centered Universe
Review of Terms
Earth
in CS
 Observer
coordinates: altitude,
azimuth, zenith, horizon, meridian
 Earth coordinates: latitude, longitude,
north pole, equator
 Celestial coordinates: declination,
right ascension, north celestial pole,
celestial equator
 Angles: degree, minute of arc,
second of arc, angular separation
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Observation: The Planets
 Five
planets are visible to the naked eye:
Mercury, Venus, Mars, Jupiter, Saturn.
 Planets lack the simple, uniform motion of
the Sun and Moon.
 These planets always stay near the ecliptic.
 Mercury and Venus never appear very far
from the position of the Sun in the sky.
Thus their elongation is small.
© Sierra College Astronomy Department
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Lecture 3a: An Earth-Centered Universe
Observation: The Planets
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 Planets
sometimes stop their eastward
motion and move westward against the
background of stars. This is called
retrograde motion.
Ptolemaic
Model
Model: Epicycles
 Epicycle is the circular orbit of a planet in
the Ptolemaic model (A.D. 150), the center
of which revolves around the Earth in
another circle (called the deferent).
01-20C
Retrograde
01-22
Ptolemy, Mars
© Sierra College Astronomy Department
01-23C
Ptolemy,
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Mercury and
Venus
Lecture 3a: A Sun-Centered System
Nicolaus Copernicus (1473 – 1543)
 Copernicus,
a contemporary of
Columbus, worked 40 years on a
heliocentric (sun-centered) model
for two reasons:
 Ptolemy’s predicted positions for
celestial objects had become less
accurate over time.
 The Ptolemaic model was not
aesthetically pleasing enough.
© Sierra College Astronomy Department
Ptolemy’s System
D-8, Sun-centered
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Lecture 3a: A Sun-Centered System
The Copernican System
 His
system revived many of the ideas of
the ancient Greek Aristarchus.
 The Earth rotates under a stationary sky
(which gives the same observations as a
rotating celestial sphere and a stationary
Earth).
 The Earth revolves around a stationary
Sun, which appears to move among the
background stars.
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
The Copernican System
Motions of the Planets
 His model explains the generally west to
east motion of the planets.
 Observed retrograde motion of planets
beyond Earth (such as Mars) is explained
more simply and conclusively.
02_07c
© Sierra College Astronomy Department
Fig 1-25
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Real Retrograde
Lecture 3a: A Sun-Centered System
The Copernican System
 Copernicus
had the Moon revolving around
the Earth. All others circled the Sun.
 The Sun’s apparent motion north and south
of the equator is explained by having the
Earth’s equator tilted with respect to the
planet’s orbit around the Sun.
 The tilt of Earth’s axis causes the ecliptic to
be sometimes above and sometimes below
the celestial equator.
© Sierra College Astronomy Department
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tilt
Lecture 3a: A Sun-Centered System
Comparing The Two Models
1. Accuracy in Fitting the Data
 A good model accurately fits all observed
data.
 Copernicus’s model, though more aesthetic
than Ptolemy’s, still was no more accurate in
predicting all observed planetary motions.
 Copernicus was forced to add small epicycles
of his own to improve accuracy.
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
Comparing The Two Models
2. Predictive Power
 Using the Astronomical Unit (AU) - the
average distance between Earth and Sun Copernicus predicted with amazing accuracy
the Sun-to-planet distances for the 5 planets
visible from Earth in the 1500s.
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
Comparing The Two Models
3. Aesthetics: Mercury and Venus
 The Copernican model was more
aesthetic since it could explain the
motions of Mercury and Venus without
resorting to special rules needed by the
Ptolemaic model.
 Copernicus offered a simpler explanation
for retrograde motion that required no
use of epicycles.
© Sierra College Astronomy Department
D-8, Sun-centered
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Lecture 3a: A Sun-Centered System
Tycho Brahe (1546 – 1601)
 Tycho was born 3 years after
Copernicus died.
 Tycho built the largest and most
accurate naked-eye instruments
yet constructed.
 He could measure angles to within
0.1º, close to the limit the human
eye can observe.
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
Johannes Kepler (1571 – 1630)
In 1600, a year before Tycho died, Kepler
accepted a position as Tycho’s assistant,
working on models of planetary motion.
 Tycho’s best data had been gathered for Mars.
 Based on circles and epicycles Kepler’s best
model for Mars matched Tycho’s data to an
accuracy of 0.13º (8 arcminutes).
 Yet, this error exceeded the error in Tycho’s
measurements, which bothered Kepler.
 Kepler’s persistence led him to abandon circles and
try other shapes. The shape that worked for Mars
and all other planets
ellipse.
© Sierrawas
College the
Astronomy
Department
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
Lecture 3a: A Sun-Centered System
Johannes
Kepler
The Ellipse
 The
Ellipse
ellipse is a geometrical shape every
point of which is the same total distance
from two fixed points (the foci, one is called
focus).
 Eccentricity is the distance between the
foci divided by the longest distance across
(major axis).
 Astronomers refer to the semi-major axis
distance and
eccentricity.
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
Kepler’s First Two Laws of Planetary
Motion
Law: Each planet’s path around the
Sun is an ellipse, with the Sun at one
focus of the ellipse (the other focus is
empty). [Note: perihelion vs aphelion]
 2nd Law: A planet moves along its
elliptical path with a speed that changes
in such a way that a line from the planet
to the Sun sweeps out equal areas in
equal intervals of time.
 1st
3 laws
02_20c
© Sierra College Astronomy Department
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Lecture 3a: A Sun-Centered System
Kepler’s Third Law
 3rd
Law: The ratio of the cube of a
planet’s average distance a from the Sun
to the square of its orbital period p is the
same for each planet: a³/p² = C
 Example: Mars’s period is 1.88 year. Its
distance from the sun is calculated as:
a³/(1.88 yr)² = 1 AU³/yr²
a³ = 3.53 AU³
a = 1.52 AU
© Sierra College Astronomy Department
D-9
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Lecture 3a: A Sun-Centered System
 Kepler’s
Kepler’s Contribution
modification to the Copernican
model brought it into conformity with the
data. Finally, the heliocentric theory
worked better than the old geocentric
theory.
 Kepler’s breakthrough choice of ellipses to
explain planetary motion was empirical ellipses worked but he did not know why
they worked.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Galileo Galilei (1564 – 1642) and the
Telescope (1609 – )
 Galileo
was born in 1564 and
was a contemporary of Kepler.
 Galileo built his first telescope
in 1609, shortly after hearing
about telescopes being
constructed in the Netherlands.
 Galileo was the first person to
use a telescope to study the
sky (and publish the results!).
poor Thomas Harriot (1560-1621)
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Galileo Galilei and the Telescope

Galileo made 5 important observations:
Mountains and valleys on the Moon
Sunspots
More stars than can be
observed with the naked eye
The nature of Earthshine
Four moons of Jupiter
Complete cycle of phases of
Venus
© Sierra College Astronomy Department
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The
TheMoon
Moon
11-Sep-2006
13-Sep-2006
http://umbra.nascom.nasa.gov/images/latest.html
Stars seen with just your eyes
Pleiades
Aldebaran
TAURUS
More seen stars through
telescope than with just your eye
Pleiades
Aldebaran
TAURUS
Earthshine
Earthshine
Lecture 3b: Galileo, Newton, and Einstein
Galileo Galilei and the Telescope
The Moon, the Sun, and the Stars
 Though Galileo’s first three observations
do not disprove the geocentric theory,
they cast doubt on the the assumption of
perfection in the heavens.
 The existence of stars too dim to be
seen with the naked eye also cast doubt
on the literal interpretation of some Bible
passages.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Galileo Galilei and the Telescope
Satellites of Jupiter
Galileo Jup
http://www.webpersonal.net/parabolix/castro/satgali.en.html
 In
1610 Galileo discovered that Jupiter had
four satellites of its own, now known as the
Galilean moons of Jupiter.
 Jupiter and its orbiting moons contradicted
the Ptolemaic notions that the Earth is the
center of all things and if the Earth moved it
would leave behind the Moon.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Galileo Galilei and the Telescope
The Phases of Venus
 Galileo observed that Venus goes
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through a full set of phases: full,
gibbous, quarter, crescent.
 Venus’s full set of phases can be
explained by the heliocentric theory.
 The Ptolemaic theory predicts that Venus
will always appear in a crescent phase,
which is not borne out by the
03-07C
observations.
03-05C
03-06C
© Sierra College Astronomy Department
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Lecture 3c: Galileo
Galileo Galilei’s Major Works
 The
Starry Messenger (Sidereus Nuncius, 1610)
• First telescopic discoveries
 Letters
on Sunspots (1613)
• Correspondence with German amateur
• Realized the general nature of sunspots
 Letter
to the Grand Duchess Cristina (1615)
• The Bible and Science
 The Assayer
(1623)
• Opinions on Comets (dismissed as atmospheric [!])
© Sierra College Astronomy Department
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Lecture 3c: Galileo
Galileo Galilei’s Major Works
 The
Dialogue Concerning the Two Chief World
Systems (1632)
• Discourse between three characters (Salviati,
Sagredo, Simplicio) about the geocentric and
heliocentric theories of the universe
• Led to his condemnation
• This wasn’t his first controversy …
© Sierra College Astronomy Department
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Lecture 3c: Galileo
Galileo Galilei’s Controversy
Sunspots (1613) irked some Jesuits
 Copernicus’ book banned by Catholic Church
• Led to decree of 1616 about the heliocentric universe
 Jesuit Orazio Grassi wrote book about Comets in 1619
• Had correct view of extraterrestrial nature of comets
 Urban VIII becomes Pope in 1623
• Good friend and supporter of Galileo
• Assayer written in response to Jesuit book

– Dedicated to Urban VIII

Dialogue met with ire of some Jesuits and Pope Urban VIII
• Thought to be personal attack (SimplicioPope’s view)
• Book banned and led to heresy trial and conviction in 1633
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Isaac Newton’s Grand Synthesis
 Galileo
is credited with setting
the standard for studying nature
through reliance on observation
and experimentation to test
hypotheses.
 The year Galileo died - 1642 - is
the year Isaac Newton was born.
 Newton took the work of Galileo
and Kepler and created an
expansive theory of motion. Rock
© Sierra College Astronomy Department
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Motion of whirling rock when string breaks
A
X
C
B
D
Lecture 3b: Galileo, Newton, and Einstein
Newton’s First Two Laws of Motion
 Inertia
is the property of an object
whereby it tends to maintain whatever
velocity it has.
 Newton’s First Law (Law of Inertia):
Unless an object is acted upon by a
net, outside force, the object will
maintain a constant speed in a
straight line.
 Note: Speed and direction = velocity
© Sierra College Astronomy Department
Demo
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Lecture 3b: Galileo, Newton, and Einstein
Newton’s First Two Laws of Motion
 Acceleration
is a measure of how
rapidly the speed or direction of motion
of an object is changing.
 An object at rest has a speed of zero.
 Newton’s first law says that a force is
needed to change the speed and/or
direction of an object’s motion.
Demo
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Newton’s First Two Laws of Motion
An Important Digression - Mass & Weight
 Mass is the quantity of inertia an object has.
 Mass is NOT volume or weight.
 Weight is the gravitational force between an
object and the planetary body on which the
object is located.
 The international (SI) unit of mass is the
kilogram.
 A kilogram on Earth weighs about 2.2 pounds.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Newton’s First Two Laws of Motion
Newton’s Second Law
 Acceleration is inversely proportional to
the mass being accelerated.
 Acceleration = net force / mass
Demo
= mass X acceleration, or F = ma
 When the net force is zero, there is no
acceleration.
2
 Force
© Sierra College Astronomy Department
nd
Law
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Lecture 3b: Galileo, Newton, and Einstein
Newton’s Third Law
3 Law
Newton’s Third Law:
 When object X exerts a force on object Y,
object Y exerts and equal and opposite
force back on X.
 The Third Law is sometimes stated as
“For every action there is an opposite
and equal reaction,” but the first
statement is more precise in terms of
Demo
physical forces.
rd
© Sierra College Astronomy Department
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The End, for now
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Motion in a Circle
board
 Motion
of an object in a circle at constant
speed (uniform circular motion) is an
example of acceleration by changing
Demo
direction.
 Centripetal (“center-seeking”) force is
the force directed toward the center of
the curve along which the object is
moving.
Cannon
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
The Law of Universal Gravitation
 This
law states that between every two
objects there is an attractive force,
the magnitude of which is directly
proportional to the mass of each object Grav
and inversely proportional to the square Law
of the distance between the centers of
the objects (inverse square law).
Another
 In equation form: F = GMm / r 2
where G is a constant, M and m are the
masses, and r is the distance between
their centers.
form
F = G m1 m2 / d 2
© Sierra College Astronomy Department
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Weight of an object away from Earth
1/16
1/4
1/9
Grav
Law
Arny
Lecture 3b: Galileo, Newton, and Einstein
The Law of Universal Gravitation
 According
to Newton, gravity not
only makes objects fall to Earth but
keeps the Moon in orbit around the
Earth and keeps the planets in orbit
around the Sun. He could therefore
explain the planets’ motions and
why Kepler’s laws worked.
© Sierra College Astronomy Department
Cannon
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Lecture 3b: Galileo, Newton, and Einstein
The Law of Universal Gravitation
Testing the Law of Universal Gravitation
 Because the distance from the center of the
Earth to the Moon is about 60 times the
distance from the center of the Earth to its
surface, the centripetal acceleration of the
Moon should be (1/60²) or 1/3600 of the
acceleration of gravity on Earth. Newton’s
calculations showed this to be the case and
confirmed the validity of his theory of
gravitation. © Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Newton’s Laws and Kepler’s Laws
 Newton
showed mathematically (using
calculus) that Kepler’s laws derive from
the inverse square law for gravitation
and the equation of motion (F = ma).
 Newton modified Kepler’s third law,
showing that the masses are an
important factor.
a³/p² = K(M + m)
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Examples of Newton’s Laws
 Surface
Gravity is the gravitational attraction at
the surface of a planet or star. It is the
acceleration on a mass created by the local
gravitational force.
 Acceleration due to gravity
GM
at surface:
g
R
2
• Note independence of g with respect to m
• For comparisons, be careful with M and R
• Notice Weight = mg = GMm/R2
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Examples of Newton’s Laws
 Weightlessness
• Weight is the force that counters
gravity creating a zero net force
• Weightlessness is the absence of the
countering force
 Orbits:
Circular and Escape Velocity
• Found from the conservation of energy
2GM
GM
Vesc 
Vcirc 
Escape
R
R
• For comparisons, be careful with M and R
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
The Importance of Newton’s Laws
 Kepler’s
laws can be derived from them.
 They explain tides and precession.
 Their use predicted the existence of the
planet Neptune.
 They provide a way to measure things
quantitatively and predict the motion of
things.
 Newton laid the foundation for our notion of
the Universe.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Beyond Newton to Einstein
Newton assumed time was
absolute. Einstein’s Special
Theory of Relativity showed this
was not true.
 Newton proposed that inertial mass
was equivalent to gravitational
mass. Subsequent measurements
confirmed this coincidence.


Einstein in his General Theory of Relativity
showed mathematically that the two types of
masses are indeed equivalent.
© Sierra College Astronomy Department
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Lecture 3b: Galileo, Newton, and Einstein
Beyond Newton to Einstein
 Principle
of equivalence states that
the effects of the force of gravity are
indistinguishable from those of
acceleration.
 The general theory predicts that light
will curve in the presence of a
massive object. This prediction,
made in 1907, was first confirmed
during a solar eclipse in 1919.
© Sierra College Astronomy Department
D-13
D-14
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Lectures 3 and 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light
 Digression:
Temperature scales

Fahrenheit scale: freezing 32°F/boiling
212°F.
 Celsius scale: freezing 0°C/boiling 100°C.
 Kelvin scale:
0 K = absolute zero (-273°C)
273 K = freezing point of water (0 °C)
373 K = boiling point of water (100 °C)
 Note that Kelvin and Celsius degrees are
the “same size.”
© Sierra College Astronomy Department
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Lectures 3 and 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light

Spectrum is the order of color or
wavelengths produced when light
dispersed, such as by a prism.
is
Wave Motion in General
 Wavelength (l) is the distance from a point on a wave
to the next corresponding point.
 Frequency (f or n) is the number of repetitions per unit
time and often is given in cycles/second or hertz (Hz).
 There IS a relationship between f and l!
Wavelength
© Sierra College Astronomy Department
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Astronomy Club
Meets every Tuesday at
2 PM in S-202
(Planetarium)
Fall 2005