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Title: Chapter%202:%20The%20Copernican%20Revolution%20The%20Birth%20of%20Modern%20Science


1
Chapter 2 The Copernican Revolution The Birth of
Modern Science
  • Ancient Astronomy
  • Models of the Solar System
  • Laws of Planetary Motion
  • Newtons Laws
  • Laws of Motion
  • Law of Gravitation

2
Scientific Method
  • Gather data

Form theory
Test theory
3
Astronomy in Ancient Times
  • Ancient people had a better, clearer chance to
    study the sky and see the patterns of stars
    (constellations) than we do today.
  • Drew pictures of constellations
    created stories to account for the figures being
    in the sky.
  • Used stars and constellations for navigation.
  • Noticed changes in Moons shape and position
    against the stars.
  • Created accurate calendars of seasons.

4
Ancient Astronomy
  • Stonehenge on the summer solstice.
  • As seen from the center of the stone circle,
  • the Sun rises directly over the "heel stone" on
    the longest day of the year.

The Big Horn Medicine Wheel in Wyoming, built by
the Plains Indians. Its spokes and rock piles
are aligned with the rising and setting of the
Sun and other stars.
5
Astronomy in Early Americas
  • Maya Indians developed written language and
    number system.
  • Recorded motions of Sun, Moon, and planets --
    especially Venus.
  • Fragments of astronomical observations recorded
    in picture books made of tree bark show that
    Mayans had learned to predict solar and lunar
    eclipses and the path of Venus.
  • One Mayan calendar more accurate than those of
    Spanish.

6
Ancient Contributions to Astronomy
  • Egyptians
  • recorded interval of floods on Nile
  • every 365 days
  • noted Sirius rose with Sun when floods due
  • invented sundials to measure time of day from
    movement of the Sun.
  • Babylonians
  • first people to make detailed records of
    movements of Mercury, Venus, Mars, Jupiter,
    Saturn
  • only planets visible until telescope

7
Greek Astronomy
  • Probably based on knowledge from Babylonians.
  • Thales predicted eclipse of Sun that occurred in
    585 B.C.
  • Around 550 B.C., Pythagoras noted that the
    Evening Star and Morning Star were really the
    same body (actually planet Venus).
  • Some Greek astronomers thought the Earth might be
    in the shape of a ball and that moonlight was
    really reflected sunlight.

8
Time Line
  • Ancient Greeks
  • Pythagoras 6th century B.C.
  • Aristotle 348-322 B.C.
  • Aristarchus 310-230 B.C.
  • Hipparchus 130 B.C.
  • Ptolemy A.D. 140

9
Pythagorean Paradigm
  • The Pythagorean Paradigm had three key points
    about the movements of celestial objects
  • the planets, Sun, Moon and stars move in
    perfectly circular orbits
  • the speed of the planets, Sun, Moon and stars in
    the circular orbits is perfectly uniform
  • the Earth is at the exact center of the motion of
    the celestial bodies.

10
Aristotles Universe A Geocentric Model
  • Aristotle proposed that
  • the heavens were literally composed of
    concentric, crystalline spheres
  • to which the celestial objects were attached
  • and which rotated at different velocities,
  • with the Earth at the center (geocentric).

The figure illustrates the ordering of the
spheres to which the Sun, Moon, and visible
planets were attached.
11
Planetary Motion
  • From Earth, planets appear to move wrt fixed
    stars and vary greatly in brightness.
  • Most of the time, planets undergo direct motion -
    moving W to E relative to background stars.
  • Occasionally, they change direction and
    temporarily undergo retrograde motion - motion
    from E to W -before looping back.

(retrograde-move)
12
Planetary Motion Epicycles and
Deferents
  • Retrograde motion was first explained as follows
  • the planets were attached, not to the concentric
    spheres themselves, but to circles attached to
    the concentric spheres, as illustrated in the
    adjacent diagram.
  • These circles were called "Epicycles",and the
    concentric spheres to which they were attached
    were termed the "Deferents".
  • (epicycle-move)

13
Epicycle/Deferent Modifications
  • In actual models, the center of the epicycle
    moved with uniform circular motion, not around
    the center of the deferent, but around a point
    that was displaced by some distance from the
    center of the deferent.

This modification predicted planetary motions
that more closely matched the observed motions.
14
Further Modifiations
  • In practice, even this was not enough to account
    for the detailed motion of the planets on the
    celestial sphere!
  • In more sophisticated epicycle models further
    "refinements" were introduced

In some cases, epicycles were themselves placed
on epicycles, as illustrated in the adjacent
figure. The full Ptolemaic model required 80
different circles!!
15
Ptolemy
  • 127-151 A.D. in Alexandria
  • Accomplishments
  • completion of a geocentric model of solar
    system that accurately predicts motions of
    planets by using combinations of regular circular
    motions
  • invented latitude and longitude (gave
    coordinates for 8000 places)
  • first to orient maps with NORTH at top
    and EAST at right
  • developed magnitude system to describe brightness
    of stars that is still used today

16
Aristarchus
  • 310-230 B.C.
  • Applied geometry to find
  • distance to Moon
  • Directly measure angular diameter
  • Calculate linear diameter using lunar eclipse
  • relative distances and sizes of the Sun and Moon
  • ratio of distances to Sun and Moon by observing
    angle between the Sun and Moon at first or third
    quarter Moon.
  • Proposed that the Sun is stationary and that the
    Earth orbits the Sun and spins on its own axis
    once a day.

17
Hipparchus
  • 190-125 B.C.
  • Often called greatest astronomer of
    antiquity.
  • Contributions to astronomy
  • improved on Aristarchus method for calculating
    the distances to the Sun and Moon,
  • improved determination of the length of the year,
  • extensive observations and theories of motions of
    the Sun and Moon,
  • earliest systematic catalog of brighter stars ,
  • first estimate of precession shift in the vernal
    equinox.

18
Time Line
  • Ancient Greeks
  • Pythagoras 6th century B.C.
  • Aristotle 348-322 B.C.
  • Aristarchus 310-230 B.C.
  • Hipparchus 130 B.C.
  • Ptolemy A.D. 140
  • Dark Ages A.D. 5th - 10th century
  • Arabs translated books, planets positions
  • China 1054 A.D. supernova Crab Nebula

19
Heliocentric Model - Copernicus
  • In 1543, Copernicus proposed that the Sun,
    not the Earth, is the center of the solar system.
  • Such a model is called a heliocentric system.
  • Ordering of planets known to Copernicus in this
    new system is illustrated in the figure.
  • Represents modern ordering of planets.
  • (copernican-move)

20
Stellar Parallax
  • Stars should appear to change their position with
    the respect to the other background stars as the
    Earth moved about its orbit.
  • In Copernicus day, no stellar parallax was
    observed, so the Copernican model was considered
    to be only a convenient calculation tool for
    planetary motion.
  • In 1838, Friedrich Wilhelm Bessel succeeded in
    measuring the parallax of the nearby, faint star
    61 Cygni. ( penny at 4 miles)

21
Time Line
  • Ancient Greeks
    Pythagoras 6th century B.C.
    Aristotle 348-322
    B.C. Aristarchus 310-230
    B.C. Ptolemy
    A.D. 140
  • Dark Ages A.D. 5th - 10th century
  • Renaissance Copernicus
    (1473-1543) Tycho
    Brahe Kepler Galileo
    (1546-1601) (1571-1630)
    (1564-1642) Newton
    (1642-1727)

22
Galileo Galilei
  • Galileo used his telescope to show that Venus
    went through a complete set of phases, just like
    the Moon.
  • This observation was among the most important in
    human history, for it provided the first
    conclusive observational proof that was
    consistent with the Copernican system but not the
    Ptolemaic system.

23
Galileo and Jupiter
  • Galileo observed 4 points of light that changed
    their positions with time around the planet
    Jupiter.
  • He concluded that these were objects in orbit
    around Jupiter.
  • Galileo called them the Medicea Siderea-the
    Medician Stars in honor of Cosimo II de'Medici,
    who had become Grand Duke of Tuscany in 1609.

24
Time Line
  • Ancient Greeks
    Pythagoras 6th century B.C.
    Aristotle 348-322
    B.C. Aristarchus 310-230
    B.C. Ptolemy
    A.D. 140
  • Dark Ages A.D. 5th - 10th century
  • Renaissance Copernicus
    (1473-1543) Tycho
    Brahe Kepler Galileo
    (1546-1601) (1571-1630)
    (1564-1642) Newton
    (1642-1727)

25
Tycho Brahe
26
Tycho Brahe
  • Danish astronomer
  • Studied a bright new star in sky that faded
    over time.
  • In 1577, studied a comet
  • in trying to determine its distance from Earth by
    observing from different locations, noted that
    there was no change in apparent position
  • proposed comet must be farther from Earth than
    the Moon.
  • Built instrument to measure positions of planets
    and stars to within one arc minute (1).

27
Johannes Kepler Laws of Planetary Motion
28
Kepler Elliptical orbits
  • The amount of "flattening" of the ellipse is the
    eccentricity. In the following figure the
    ellipses become more eccentric from left to right.

A circle may be viewed as a special case of an
ellipse with zero eccentricity, while as the
ellipse becomes more flattened the eccentricity
approaches one.
(eccentricity-anim)
29
Elliptical Orbits and Keplers Laws
  • Some orbits in the Solar System cannot be
    approximated at all well by circles

- for example, Plutos separation from the Sun
varies by about 50 during its orbit!
According to Keplers First Law, closed orbits
around a central object under gravity are
ellipses.
30
As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse.
r
C
31
The line that connects the planets point of
closest approach to the Sun, the perihelion ...
As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse
perihelion
v
r
C
32
and its point of greatest separation from the
Sun, the aphelion
As a planet moves in an elliptical orbit, the Sun
is at one focus (F or F) of the ellipse
perihelion
is called the major axis of the ellipse.
v
r
C
aphelion
33
The only other thing we need to know about
ellipses is how to identify the length of the
semi-major axis, because that determines the
period of the orbit.
Semi means half, and so the semi-major axis a
is half the length of the major axis
v
r
C
34
Keplers 1st Law
  • The orbits of the planets are ellipses, with
    the Sun at one focus of the ellipse.

35
Keplers 2nd Law
  • The line joining the planet to the Sun sweeps out
    equal areas in equal times as the planet travels
    around the ellipse.

Orbit-anim
36
An object in a highly elliptical orbit travels
very slowly when it is far out in the Solar
System,
but speeds up as it passes the Sun.
37
According to Keplers Second Law,
the line joining the object and the Sun ...
38
sweeps out equal areas in equal intervals of
time.
equal areas
39
That is, Keplers Second Law states that
The line joining a planet and the Sun sweeps
out equal areas in equal intervals of time.
40
For circular orbits around one particular mass -
e.g. the Sun - we know that the period of the
orbit (the time for one complete revolution)
depended only on the radius r
- this is Keplers 3rd Law
M
For objects orbiting a common central body (e.g.
the Sun) in approximately circular orbits,
r
r
m
v
the orbital period squared is proportional to the
orbital radius cubed.
41
Lets see what determines the period for an
elliptical orbit
For elliptical orbits, the period depends not on
r, but on the semi-major axis a instead.
v
r
C
42
It turns out that Keplers 3rd Law applies to
all elliptical orbits, not just circles, if we
replace orbital radius by semi major axis
For objects orbiting a common central body (e.g.
the Sun)
the orbital period squared is proportional to
the orbital radius cubed.
the orbital period squared is proportional to
the semi major axis cubed.
43
So as all of these elliptical orbits have the
same semi-major axis a, so they have the same
period.
44
So if each of these orbits is around the same
massive object (e.g. the Sun),
45
So if each of these orbits is around the same
massive object (e.g. the Sun),
then as they all have the same semi-major axis
length a,
46
So if each of these orbits is around the same
massive object (e.g. the Sun),
then as they all have the same semi-major axis
length a,
then, by Keplers Third Law, they have the
same orbital period.
47
Ellipses and Orbits
  • Ellipse animation

48
Keplers 3rd Law
  • The ratio of the squares of the revolution
    periods (P) for two planets is equal to the ratio
    of the cubes of their semi-major axes (a).

P2 a3 or P2/a3 1 where P is the
planets sidereal orbital period
(in Earth years) and a is the length of
the semi-major axis (in astronomical
units)
49
Astronomical Unit
  • One astronomical unit is the semi-major
    axis of the Earths orbit around the Sun,
    essentially the average distance between Earth
    and the Sun.
  • abbreviation A.U.
  • one A.U. 150 x 106 km

50
Keplers 3rd Law for the Planets
P2 a3 or P2/a3 1
51
Planetary Motions
  • The planets orbits (except Mercury and Pluto)
    are nearly circular.
  • The further a planet is from the Sun, the greater
    its orbital period.
  • Although derived for the six innermost planets
    known at the time, Keplers Laws apply to all
    currently known planets.
  • Do Keplers laws apply to comets orbiting
    the Sun?
  • Do they apply to the moons of Jupiter?

52
Keplers Laws
  • 1st Law Each planet moves around the Sun in an
    orbit that is an ellipse, with the Sun at one
    focus of the ellipse.
  • 2nd Law The straight line joining a planet and
    the Sun sweeps out equal areas in equal intervals
    of time.
  • 3rd Law The squares of the periods of
    revolution of the planets are in direct
    proportion to the cubes of the semi-major axes of
    their orbits.

53
Whats important so far?
  • Through history, people have used the scientific
    method
  • observe and gather data,
  • form theory to explain observations and predict
    behavior
  • test theorys predictions.
  • Greeks produced first surviving, recorded models
    of universe
  • geocentric (Earth at center of universe),
  • other celestial objects in circular orbits about
    Earth, and
  • move with constant speed in those orbits.
  • Geocentric models require complicated
    combinations of deferents and epicycles to
    explain observed motion of planets. Ptolemaic
    model required 80 such combinations.
  • Copernicus revived heliocentric model of solar
    system, but kept circular, constant speed orbits.

54
Whats important so far? continued
  • Without use of a telescope, Tycho Brahe made very
    accurate measurements of the positions of
    celestial objects.
  • Johannes Kepler inherited Brahes data and
    determined three empirical laws governing the
    motion of orbiting celestial objects.
  • 1st Law Each planet moves around the Sun in an
    orbit that is an ellipse, with the Sun at
    one focus of the ellipse.
  • 2nd Law The straight line joining a planet and
    the Sun sweeps out equal areas in equal
    intervals of time.
  • 3rd Law The squares of the periods of revolution
    of the planets are in direct proportion to
    the cubes of the semi-major axes of their
    orbits.
  • Galileo used a telescope to observe the Moon and
    planets. The observed phases of Venus validated
    the heliocentric model proposed by Copernicus.
    Also discovered 4 moons orbiting Jupiter,
    Saturns rings, named lunar surface features,
    studied sunspots, noted visible disk of planets
    (stars - point sources).

55
Why do the planets move according to Keplers
laws? Or, more generally, why do objects move as
they do?
56
Historical Views of Motion
  • Aristotle two types of motion
  • natural motion
  • violent motion
  • Galileo
  • discredited Aristotelian view of motion

Animations Air resistance Free-fall
57
Galileo Why do objects move as they do?
speed increases.
speed decreases.
does speed change?
Without friction, NO, the speed is constant!
58
What is a natural state of motion for an
object?
Moving with constant velocity?
At rest?
59
Inertia and Mass
Inertia a bodys resistance to
a change in its motion.
Mass a measure of an
objects inertia or, loosely, a measure of
the total amount of matter contained within an
object.
60
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61
Newtons First Law
  • Called the law of inertia.
  • Since time of Aristotle, it was assumed that a
    body required some continual action on it to
    remain in motion, unless that motion were a part
    of natural motion of object.
  • Newtons first law simplifies concept of motion.

62
Animation collision-1st-law
63
FORCES and MOTION
  • An object will remain
  • (a) at rest or
  • (b) moving in a straight line at constant speed
    until
  • (c) some net external force acts on it.

64
What if there is an outside influence?
  • To answer this question, Newton invoked
    the concept of a FORCE acting on a body to cause
    a change in the motion of the body.

65
Forces can act
through contact
instantaneously (baseball bat
making contact with the baseball),

or at a distance.
or continuously (gravity
keeping the baseball from flying into space).
66
Velocity and Acceleration
Velocity describes the change in
position of a body divided by the time interval
over which that change occurs.
Velocity is a vector quantity, requiring
both the speed of the body and its direction.
Acceleration The rate of change of
the velocity of a body, any change in
the bodys velocity speeding up, slowing down,
changing direction.
Animation circularmotion
67
Newtons Second Law F ma
  • Relates
  • net external force F applied to object of
    mass m
  • to resulting change in motion of object,
    acceleration a.

68
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69
If there is a NET FORCE on an object, how much
will the object accelerate?
70
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71
Newton and Gravitation
  • Newtons three laws of motion enable calculation
    of the acceleration of a body and its motion,
    BUT must first calculate the forces.
  • Celestial bodies do not touch ------ do not
    exert forces on each other directly.
  • Newton proposed that celestial bodies exert an
    attractive force on each other at a distance,
    across empty space.
  • He called this force gravitation.

72
  • Isaac Newton discovered that two bodies share a
    gravitational attraction, where the force of
    attraction depends on both their masses

73
  • Both bodies feel the same force, but in opposite
    directions.

74
This is worth thinking about - for example, drop
a pen to the floor. Newtons laws say that the
force with which the pen is attracting the Earth
is equal and opposite to the force with which
the Earth is attracting the pen, even though the
pen is much lighter than the Earth!
75
  • Newton also worked out that if you keep the
    masses of the two bodies constant, the force of
    gravitational attraction depends on the distance
    between their centers

mutual force of attraction
76
  • For any two particular masses, the gravitational
    force between them depends on their separation
    as

as the separation between the masses is
increased, the gravitational force of
attraction between them decreases quickly.
77
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78
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79
Gravity and Weight
  • The weight of an object is a measure of the
    gravitational force the object feels in the
    presence of another object.
  • For example on Earth, two objects with different
    masses will have different weights.
  • Fg m(GmEarth/rEarth2) mg
  • What is the weight of the Earth on us?

80
Mass and Weight
  • Mass A measure of the total
    amount of matter contained within an object
    a measure of an objects
    inertia.
  • Weight The force due to gravity
    on an object.
  • Weight and mass are proportional.
  • Fg mg where m
    mass of the object and g acceleration
    of gravity acting on the object

81
Free Fall
  • If the only force acting on an object is force of
    gravity (weight), object is said to be in a state
    of free fall.
  • A heavier body is attracted to the Earth with
    more force than a light body.
  • Does the heavier object free fall faster?
  • NO, the acceleration of the body depends on both
  • the force applied to it and
  • the mass of the object, resisting the motion.
  • g F/m F/m

82
Newtons Law of Gravitation
  • We call the force which keeps the Moon in its
    orbit around the Earth gravity.

Sir Isaac Newtons conceptual leap in
understanding of the effects of gravity largely
involved his realization that the same force
governs the motion of a falling object on Earth -
for example, an apple - and the motion of the
Moon in its orbit around the Earth.
83
  • Your pen dropping to the floor and a satellite in
    orbit around the Earth have something in common -
    they are both in freefall.

84
Planets, Apples, and the Moon
  • Some type of force must act on planet otherwise
    it would move in a straight line.
  • Newton analyzed Keplers 2nd Law and saw that the
    Sun was the source of this force.
  • From Keplers 3rd Law, Newton deduced that the
    force varied as 1/r2.
  • The force must act through a distance, and
    Newton knew of such a force - the one that
    makes an apple accelerate downward from the tree
    to the Earth as the apple falls.
  • Could this force extend all the way to the Moon?

85
To see this, lets review Newtons thought
experiment Is it possible to throw an object
into orbit around the Earth?
86
On all these trajectories, the projectile is in
free fall under gravity. (If it were not, it
would travel in a straight line - thats
Newtons First Law of Motion.)
87
If the ball is not given enough sideways
velocity, its trajectory intercepts the Earth
...
that is, it falls to Earth eventually.
88
On the trajectories which make complete orbits,
the projectile is travelling sideways fast
enough ...
On all these trajectories, the projectile is in
free fall.
On all these trajectories, the projectile is in
free fall.
89
that as it falls, the Earth curves away
underneath it, and the projectile completes
entire orbits without ever hitting the Earth.
On all these trajectories, the projectile is in
free fall.
90
Gravity and Orbits
  • The Suns inward pull of gravity on the planet
    competes with the planets tendency to continue
    moving in a straight line.

91
Apparent Weightlessness in Orbit
This astronaut on a space walk is also in free
fall.
The astronauts sideways velocity is
sufficient to keep him or her in orbit around the
Earth.
92
Lets take a little time to answer the following
question
  • Why do astronauts in the Space Shuttle in Earth
    orbit feel weightless?

93
  • Some common misconceptions which become apparent
    in answers to this question are

(a) there is no gravity in space, (b) there is no
gravity outside the Earths atmosphere, or (c) at
the Shuttles altitude, the force of gravity is
very small.
94
In spacecraft (like the Shuttle) in Earth orbit,
astronauts are in free fall, at the same rate as
their spaceships.
On all these trajectories, the projectile is in
free fall.
That is why they experience weightlessness just
as a platform diver feels while diving down
towards a pool, or a sky diver feels while in
free fall.
95
Newtons Form of Keplers 3rd Law
  • Newton generalized Keplers 3rd Law to include
    sum of masses of the two objects in orbit about
    each other (in terms of the mass of the Sun).
  • (M1 M2) P2 a3
  • Observe orbital period and separation of a
    planets satellite, can compute the mass of the
    planet.
  • Observe size of a double stars orbit and its
    orbital period, deduce the masses of stars in
    binary system.
  • Planet and Sun orbit the common center of mass of
    the two bodies.
  • The Sun is not in precise center of orbit.

96
Mass of Planets, Stars, and Galaxies
  • By combining Newtons Laws of Motion and
    Gravitation Law, the masses of
    astronomical objects can be calculated.
  • a v2/r , for circular orbit of radius r
  • F ma mv2/r
  • mv2/r Fg GMm/ r2
  • v (GM/r)1/2
  • P 2?r/v 2? (r3/GM)1/2
  • M rv2/G
  • If the distance to an object and the orbital
    period of the object are known, the mass can be
    calculated.
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