Transcript File - Mr. Catt`s Class

Chapter 3
3-1 thru 3-4
Courtesy of NASA, JSC Digital Image Collection
Gravity and the
Rise of Modern
Astronomy
Earth seen from the Moon
3-1 Galileo Galilei and the Telescope
1. Galileo was born in 1564 and was a contemporary of
Kepler. He built his first telescope in 1609.
2. Galileo was the first to use a telescope to study the
sky. He made five important observations that
affected the comparison between the geocentric and
heliocentric theories.
(a) Mountains and valleys on the Moon
(b) Sunspots
(c) More stars than can be observed with the naked eye
(d) Four moons of Jupiter
(e) Complete cycle of phases of Venus
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Observing the Moon, the Sun, and the Stars
1. Though Galileo’s first three observations do not
disprove the geocentric model, they cast doubt
on its basic assumption of perfection in the
heavens.
2. The existence of stars too dim to be seen with
the naked eye also cast doubt on the literal
interpretation of some Biblical passages.
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1. In 1610 Galileo discovered that Jupiter
had four satellites of its own, now known
as the Galilean moons of Jupiter.
2. The motion of Jupiter and its orbiting
moons contradicted the Ptolemaic
notions that the Earth is the center of all
things and that if the Earth moved
through space it would leave behind the
Moon.
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© Stock Montage, Inc./Alamy Images
Jupiter’s Moons
Figure 3.03c: Io and Europa in front of Jupiter
Courtesy of NASA, Voyager 2 photo/JPL
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The Phases of Venus
1. Galileo observed that Venus goes through a full
set of phases: full, gibbous, quarter, crescent.
2. Venus’s full set of phases cannot be explained by
the Ptolemaic model but can be explained by the
heliocentric model.
3. The Ptolemaic model predicts that Venus will
always appear in a crescent phase, which is not
borne out by the observations.
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Figure 3.05: Venus's motion according to Ptolemy
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4. Also, the heliocentric model explains the
correlation between Venus’ phases and its
corresponding observed sizes.
5. Galileo is credited with setting the standard for
studying nature through reliance on observation
and experimentation to test hypotheses.
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Question 1
Why did seeing sunspots on the Sun support the idea
of heliocentrism?
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Newton’s First Two Laws of Motion
1. The year Galileo died—1642—is the year Isaac
Newton was born. Newton took the work of
Galileo and Kepler and created a new theory
of motion.
2. Newton’s First Law (Law of Inertia): Unless a
net, outside force, acts upon an object, the
object will maintain a constant speed in a
straight line (if initially moving), or remain at
rest (if initially at rest).
3. Inertia is the tendency of an object to resist a
change in its motion.
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© North Wind Picture Archives/Alamy Images
3-2 Isaac Newton’s Grand Synthesis
4. The first law indicates that a net force is
necessary for an object to change its speed
and/or its direction of motion (i.e., to accelerate).
5. Newton’s second law quantifies and extends the
first law. It tells us how much force is necessary
to produce a certain acceleration of an object.
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An Important Digression—Mass and Weight
1. Mass is the quantifiable property of an object
that is a measure of its inertia. It is an intrinsic
property of an object and independent of
location.
2. Mass is NOT volume or weight. (The weight of an
object on Earth is simply the downward force
experienced by the object due to its gravitational
interaction with the Earth.)
3. The international (SI) unit of mass is the
kilogram. A kilogram weighs about 2.2 pounds
on Earth.
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Back to Newton’s Second Law
1. Newton’s Second Law
A net external force applied to an object causes it
to accelerate at a rate that is inversely proportional
to its mass:
Acceleration = net force / mass, or F = m a.
2. When the net force is zero, there is no acceleration.
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Figure 3.07: The brick will accelerate if a
force is exerted on it. If twice as much
force is exerted on it, it will accelerate at
twice the rate.
Figure 3.08: The same amount of
force will give twice as much mass
only half the acceleration
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Newton’s Third Law
1. Newton’s Third Law: When object X exerts a force
on object Y, object Y exerts an equal and
opposite force back on X.
2. The Third Law is sometimes stated as “For every
action there is an equal and opposite reaction,”
but the first statement is more precise in terms
of physical forces.
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Question 2
Describe how Newton’s 3 laws of motion were
important to those studying astronomy then and
into present day.
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3-3 Motion in a Circle
1. Motion of an object in a circle at constant speed
(uniform circular motion) is an example of
acceleration causing a change in direction.
2. Centripetal (“center-seeking”) force is the force
directed toward the center of the curve along which
the object is moving. Centripetal force is simply a
label we apply to a net force that causes an object
to move in a curve.
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Figure 3.10: The string breaks as the rock is whirled in a circle. Which way
does the rock go after the string breaks?
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3-4 The Law of Universal Gravitation
1. The law of universal gravitation states that
between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the
distance between the centers of the objects.
2. In equation form:
F = Gm1m2 / d2,
where G is a constant, m1 and m2 are the masses,
and d is the distance between their centers.
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3. Weight is the gravitational force between an
object and the planetary/stellar body where the
object is located.
4. 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. His laws could explain the
planets’ motions and why Kepler’s laws worked.
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Arriving at the Law of Universal Gravitation
1. Whether or not force is proportional to mass can be
tested by showing that weight is proportional to
mass here on Earth.
2. To test the dependence of force on distance, Newton
compared accelerations of objects near the Earth’s
surface to the Moon’s acceleration in orbit around
the Earth.
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3. 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 (1/60)2
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.
Figure 3.12: Weight decreases with distance from Earth
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Question 3
According to Newton’s law of universal gravitation are
astronauts ever truly weightless? Explain your
reasoning.
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