Transcript Galileo, Newton, and Einstein

25 pts of Extra Credit can be
done, 10 pts of these points must
be done before midterm (see page
41 of Student Handbook)
The Class Web Site:
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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
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Lecture 3c: Understanding Motion, Energy, and Gravity
Going Towards a Grand Synthesis

Galileo Galilei
Inclined
plane
• Credited with setting the standard for studying nature through
reliance on observation and experimentation to test hypotheses
• The heavens had similar features to the Earth (contrast
Aristotle)
• Galileo was the first to develop our modern ideas of motion –
made use of the inclined plane
– Demonstrated that all objects at the Earth’s surface fall at the same
rate regardless of mass
– Proposed the concept of inertia that was to overthrow Aristotle’s
notion that the natural motion of all earthly objects is to come to
rest.

René Descartes
• Extended Galileo’s notion of inertia along the Earth’s surface to
that of straight line motion
• Proposed three laws of motion which would inspire Newton to
create the now classical Three Laws of Motion
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Lecture 4: Newton
Isaac Newton’s Grand Synthesis
 Robert
Hooke
• Had ideas of planetary motion: a
central force is required to get
planet to move in a circular path
Kepler’s
Theory
 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.
© Sierra College Astronomy Department
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Lecture 4: Newton
Isaac Newton’s Accomplishments
Extended school holiday 1665-1666:
 invent reflecting telescope
 invent calculus
 develop particle theory of optics
 discover laws of motion
 discover universal gravitation
Lucasian Prof. of Math at Cambridge University
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Lecture 4: Newton
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
Here First:
Rock
around
Demo
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Lecture 4: Newton
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 4: Newton
Newton’s First Two Laws of Motion
Some more definitions:
 Mass (M or m): quantity of inertia
• An intrinsic property of an object
• Not volume or weight
• SI unit of measurement is a kilogram (kg)
 Weight
(W): gravitational force between
some object and a planetary body on which
the object rests
• On the Earth: 1 kilogram has an equivalent weight
of 2.2 lbs.
 Density:
Mass divided by Volume
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Lecture 4: Newton
Newton’s First Two Laws of Motion
Some more definitions:
mass times velocity  p=mv
 Angular momentum (or circular
momentum) : mass times velocity times
distance from center or axis of motion  mvr
 Torque: a “twisting” force which changes the
angular momentum
 Momentum:
© Sierra College Astronomy Department
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Lecture 4: Newton
Newton’s First Two Laws of Motion
Newton’s Second Law





Acceleration is inversely proportional to the mass
being accelerated.
Acceleration = net force / mass
Force = mass × acceleration, or F = ma
Demo
When the net force is zero, there is no acceleration.
Another way of stating the 2nd law: “When a net
2nd law
force acts on and object, it produces a change of
momentum of in the direction in which the force
acts”
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Lecture 4: Newton
Newton’s Third 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 physical forces.
 This law does not “feel” right – be careful
not to confuse force with acceleration
© Sierra College Astronomy Department
3rd Law
Demo
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Lecture 4: Newton
Motion in a Circle
Motion of an object in a circle at constant
speed (uniform circular motion) is an example
of acceleration by changing direction.
 Centripetal (“center-seeking”) force is the
force directed toward the center of the curve
along which the object is moving.
 What happens if the centripetal force is
removed?

board
Demo
© Sierra College Astronomy Department
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Lecture 4: Newton
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 of Law
the distance between the centers of the
objects (inverse square law).
 In equation form: F = GM1M2 / d 2
Another
where G is a constant, M and m are the form
masses, and r is the distance between
their centers.
F = GMm / r 2
© Sierra College Astronomy Department
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Weight of an object away from Earth
1/16
1/4
1/9
Grav
Law
Lecture 4: Newton
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
Grav
Law
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Lecture 4: Newton
The Law of Universal Gravitation
Grav
Law
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 4: Newton
Conservation Laws
Demo
• Under certain conditions, certain physical
quantities will not change in time
• These unchanging quantities are said to be
conserved
• Three important conservation laws for
astronomy
• (linear) momentum
• angular momentum
• energy
© Sierra College Astronomy Department
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Lecture 4: Newton
Conservation Laws

Demo
Momentum (Along a Line) and Conservation
• The momentum of an object with mass m and velocity v is
given as
p = mv
• The momentum of a system of objects is
P = p1 + p2 + … = m1v1 + m2v2 + …
• If the absence of external forces acting on the system, P
remains constant for all time - this is the Conservation of
Momentum
• Examples: Rockets and billiard balls
• For more than one direction, conservation of momentum
is applied in each direction separately
© Sierra College Astronomy Department
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Lecture 4: Newton
Demo
Conservation of Angular Momentum
• Angular Momentum and Conservation
– Spinning objects and objects in orbit are said to possess angular
momentum
– In the absence of a “twisting force” or torque, a spinning object will
maintain its angular momentum - this is the Conservation of Angular
Momentum
– Orbital angular momentum
• The orbital angular momentum, J, of an object is the product of that
object’s mass m, speed of rotation v, and distance from the center
of rotation r:
Skater
J = mvr
• The conservation of J means that (in the absence of an outside
torque) as the distance to the spin axis decreases (contraction), the
speed increases
• This is what Kepler really observed as his 2nd Law of Planetary
Motions (the Law of Equal Areas)
Orbit
© Sierra College Astronomy Department
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Lecture 4: Understanding Motion, Energy, and Gravity
Conservation of Angular Momentum
• Angular Momentum and Conservation (continued)
– Rotational angular momentum
• An object (like the Earth) will continue to spin at the
same rate as long as there is no net torque on it
– Precession is the result of an external torque
(observed for the Earth)
• In a system of objects, the total angular momentum can
be conserved (no outside torque), but the objects may
transfer rotational angular energy between themselves
– The slowing of the Earth’s day is due to the transfer
of rotational angular momentum of the Earth to
orbital angular momentum of the Moon
© Sierra College Astronomy Department
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Lecture 4: Newton
Energy is conserved too!
• Types of energy:
Demo
– Kinetic: the energy of moving objects (½ mv2)
• Ex: cars in motion, planets going around the sun,
molecules jostling in the air
• Thermal energy is a important subcategory (next slide)
Energy
cycle
– Radiative: energy carried by light (photons)
– Potential: stored energy which may be converted later
into kinetic or radiative energy
• Ex: A rock perched on a ledge, chemical (or nuclear)
bonds in an atom (or nucleus) (more later).
• MKS unit for energy: Joule
– 4,184 joules are in one food calorie
– Typical adult eats 2500 calories = 10 million joules
© Sierra College Astronomy Department
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Lecture 4: Newton
Temperatures

Temperature is the measure of the average kinetic
energy of a system of particles
• Thermal energy depends on temperature and density




Higher
Fahrenheit scale: freezing 32°F/boiling 212°F.
Lower
Kinetic
Celsius scale: freezing 0°C/boiling 100°C.
Kelvin scale:
0 K = absolute zero (-273°C)
273 K = freezing point of water (0 °C)
Thermal
dependence
373 K = boiling point of water (100 °C)
Note that Kelvin and Celsius degrees are the “same
size.”
© Sierra College Astronomy Department
Temperature
scales
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Lecture 4: Newton
Potential Energy in Astronomy
Of the many types of potential energy, two are of
particular importance in astronomy
 Gravitational potential energy: How much
energy would one get from motions due to
gravity? This energy get converted in kinetic
energy.
 Mass-energy: How much energy is stored in
the atom or nucleus?
E  mc
© Sierra College Astronomy Department
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Lecture 4: Newton
Conservation of Energy


Conservation of Energy states that in an isolated
system, although energy may change from one form
to another, the total amount of energy must remain
constant
Energy cannot be created nor destroyed, but can
be transferred between different types
• Ex: As a ball is dropped, its potential energy gets converted
to kinetic energy such that the sum of the kinetic and
potential energies remains constant

The ultimate source of all the energy in the
Universe is the Big Bang
© Sierra College Astronomy Department
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Lecture 4: Newton
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.

2
p =
3
Ka /(M
1
+ M2)
where K=4p2/G

Objects orbit their center of mass
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COM
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Lecture 4: Newton
Examples of Newton’s Laws

Orbits: Circular and Escape Speed
• Just how much speed does take to orbit the
Earth? To leave the Earth? See Mathematical
Insight 4.4
GM
Vc 
R
2GM
Ve 
R
• Notice that it requires only √2 times the circular
velocity to escape from the planet
• For the Earth Vc = 8 km/s and Ve = 11 km/s
Escape
• For comparisons, be careful with M and R
© Sierra College Astronomy Department
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Lecture 4: Newton
Examples of Newton’s Laws
Feather
Hammer
 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.
GM
 Acceleration due to gravity
at surface (See Mathematical g 
2
Insight 4.5):
R
• Note independence of g with respect to m
• For comparisons, be careful with M and R
2
• Notice Weight
(W)
=
mg
=
GMm/R
© Sierra College Astronomy Department
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Lecture 4: Newton
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
• People in orbit around the Earth feel weightless
because gravity is not countered by a surface
connected to the Earth

Changing Orbits
• Objects in orbit around each other do not spontaneously change
into other orbital configurations.
• The orbital energy of the system must change through:
– Gravitational encounters (encounters with a third object)
– Atmospheric drag (friction that diverts kinetic energy into other forms)
© Sierra College Astronomy Department
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Lecture 4: Newton
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 4: Newton
Tides
tides
 Moon
and Sun pull on Earth causing the water to
rise producing tides
• The Moon provides 2/3 of the tidal force, the Sun 1/3
 Earth’s
rotation provides daily rise and fall of tides
 Moon’s revolution about Earth cause half-monthly
rise and fall of tides
• Spring tide: Moon and Sun on same or opposite side of the Spring
Earth
Neap
• Neap tide: Moon and Sun at perpendicular angles to the Earth
© Sierra College Astronomy Department
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bulge
Lecture 4: Newton
Tides Effects of Tides on EarthMoon System
 Causes
Moon’s synchronous rotation
 Tidal forces make Moon recede
• Moon steals energy from Earth
 Tidal forces slow Earth’s rotation
• Moon steals energy from Earth
 Tidal forces create Roche Limit
• How close can something large be to planet/star until it
breaks apart?
© Sierra College Astronomy Department
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Other slides
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Lecture 4: Newton
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.
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Lecture 4: Newton
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
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D-14
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