chapter 3 3-1 thru 3-4 gravity and the rise of modern astronomy earth seen from the moon courtesy of...

Chapter 3 3-1 thru 3-4

Gravity and the Rise of Modern

AstronomyEarth seen from the Moon

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© 2007 Jones and Bartlett Publishers

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


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.


Jupiter’s Moons

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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Figure 3.03c: Io and Europa in front of Jupiter

Courtesy of NASA, Voyager 2 photo/JPL


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.


Figure 3.05: Venus's motion according to Ptolemy


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.


Question 1

Why did seeing sunspots on the Sun support the idea of heliocentrism?


3-2 Isaac Newton’s Grand Synthesis

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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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.


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.


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.


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


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.


Question 2

Describe how Newton’s 3 laws of motion were important to those studying astronomy then and into present day.


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.


Figure 3.10: The string breaks as the rock is whirled in a circle. Which way does the rock go after the string breaks?


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.


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.


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.


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


Question 3

According to Newton’s law of universal gravitation are astronauts ever truly weightless? Explain your reasoning.

chapter 3 3-1 thru 3-4 gravity and the rise of modern astronomy earth seen from the moon courtesy of...

Documents

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bartlett publishers

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