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Renaissance Astronomy
Astronomy 1-1
Lecture 04-1
Cast of Characters
Nicolaus Copernicus (1473-1543) Galileo Galilei (1564-1642)
Telescopic observations
Circular motion of planets
supporting Copernicus
around sun
Isaac Newton (1642-1727)
Tycho Brahe (1546-1601)
Laws of gravity
Recorded planets' positions
Explained elliptical orbits
Johannes Kepler (1571-1630)
Deduced elliptical motions
Laws of planetary motion
Astronomy 1-1
Lecture 04-2
Nicolaus Copernicus
Discrepancies between observed and predicted
positions
Sun at the center and the planets moved about
the Sun
Suggested that
Earth rotated about its own axis (day, night cycle)
Earth's axis of rotation titled with respect to orbit
(seasons), and
Earth's axis of rotation wobbled (precession)
Astronomy 1-1
Lecture 04-3
Nicolaus Copernicus
Problems still
Used circular orbits
Only privately circulated ideas at first
Tried to publish a larger volume
Publisher afraid of Church - Inserted a disclaimer
stating that what was being presented was only a
mathematical tool and not reality
Copernicus missed all the controversy because he died
just after receiving the first printed copy on his
death bed
Astronomy 1-1
Lecture 04-4
Giordano Bruno
Expanded on Copernicus' work
Stellar region was not finite
Earth and Sun were just like other heavenly
bodies
Universe was homogeneous
Space and time - infinite
Burned at the stake
Astronomy 1-1
Lecture 04-5
Tycho Brahe
1546 - 1601
Danish nobleman noted for his
detailed and accurate observations
Developed a geo-heliocentric system
Johannes Kepler was his assistant
Astronomy 1-1
Lecture 04-6
Tycho Brahe
In 1572 Brahe made two observations
1) Observed a supernova - an exploding star
Showed no evidence for parallax – therefore very
far away
2) Detailed observations concerning a comet Its orbit was not circular
Brought notoriety and money
Astronomy 1-1
Lecture 04-7
Johannes Kepler (1571-1630)
Believed in heliocentric system
Distances of planets from Sun were based on regular
geometric solids imbedded within each other
Appropriated data from Brahe
Orbit of Mars
Mars did not move at constant rate along orbit
Therefore could not be on circular path
Concluded it must be an ellipse with the Sun at one of
the focii
If orbit had been that of Jupiter or Saturn, doubtful he
would have seen this
So long as the mother, Ignorance, lives, it is not safe for Science, the offspring,
to divulge the hidden causes of things.
Astronomy 1-1
Lecture 04-8
Kepler's Laws of Planetary Motion
1) Each planet moves around the sun in an orbit whose
shape is that of an ellipse, with the sun at one focal
point
2) A straight line joining the planet and the sun sweeps
out equal areas in space in equal intervals in time
3) The squares of the periods of any two planets have the
same ratio as the cubes of their semi-major axes
If P is the period and R is the semi-major axis, this can
be expressed in equation form as
P12
P22
Astronomy 1-1
=
R13
R23
Lecture 04-9
Kepler’s 2nd Law
Kepler's Laws Demonstrations
Astronomy 1-1
Lecture 04-10
Heliocentric view not accepted
No observable stellar parallax
Stellar parallax too small for equipment of the day
Why do we not feel movement?
How does the Earth drag the Moon with it?
Astronomy 1-1
Lecture 04-11
Galileo Galilei (1564-1642)
Built telescope based on work by a Dutchman, Hans
Lippershey
Saw:
Thousands of stars in what was thought to be diffuse band in the
Milky Way
Craters on the Moon
Not the perfect object it was thought to be
Sun spots and solar rotation
Again an imperfect object.
Moons orbiting Jupiter
That Venus went through phases just as the Moon does
Can only happen if Venus orbits the Sun!
Otherwise impossible to see Venus in its full phase
Astronomy 1-1
Lecture 04-12
Galileo Galilei
Concluded that the Earth is not the center of everything!
Reminiscent of Copernican theory of solar system
Galileo ran into problems with the Church, which still
held to the geocentric point of view, despite the
accumulating evidence that it was not correct
Galileo was forced to refute his belief in the Copernican
theory and was sentenced in effect to house arrest
Astronomy 1-1
Lecture 04-13
Physical Underpinnings
What was still missing was the why of the
Copernican system
Models of anything should have
underpinnings in theory
Unless new ground is being broken
Astronomy 1-1
Lecture 04-14
Isaac Newton (1642-1727)
Responsible for many ideas concerning
how things work
The Calculus
Nature of light and its properties
Cohesive picture of how objects move
Astronomy 1-1
Lecture 04-15
Mass
Each object has something inherent to it - MASS
This is a measure of the amount of matter within it
Mass is not the same as weight!
Weight is related to mass
The mass of an object is the same no matter where it is in
the universe
Weight is dependent upon where the object is
It is the mass of an object that determines how it responds
to the various influences acting upon it
The more massive an object, the more difficult it is to change the
state of its motion
Astronomy 1-1
Lecture 04-16
First Law of Motion
Newton summarized this in his First law which states
A body at rest remains at rest and a body in motion moves
at constant speed in a straight line unless acted upon by
an outside force
An implication of this statement is that circular motion is
not a natural motion
Astronomy 1-1
Lecture 04-17
Second Law of Motion
How does an object, of a certain mass, respond to
an external force?
The object will undergo an acceleration that is
directly proportional to the force exerted on the
object and inversely proportional to the mass of
the object
This can be expressed mathematically as
F = ma
Acceleration is defined to be either a change in
the speed of an object and/or a change in its
direction
Astronomy 1-1
Lecture 04-18
Third Law of Motion
Newton also realized that when two objects
interact with each other that each exerts the
same force on the other
This is often stated as follows:
For every force (action) on one body, there is an
equal and opposite force (reaction) acting on
another body
It must be remembered that these forces are
acting on different bodies
Astronomy 1-1
Lecture 04-19
Newton's work showed that linear motion is the
natural motion
Circular motion therefore is not a natural motion,
thus a force is required to produce it
Newton deduced that the object at the center of
the motion must be responsible for the force
that keeps the second object in motion about
the center
Newton concluded that the Sun must exert such a
force on each planet, otherwise they would fly off in
a straight line
By using Kepler's third law and other
observations Newton formulated his Universal
Law of Gravitation
Astronomy 1-1
Lecture 04-20
Law of Universal Gravitation
Every particle in the universe attracts every other
particle with a force proportional to the
product of their masses and inversely
proportional to the square of the distance
between them
F =G
Astronomy 1-1
m1m 2
r
2
Lecture 04-21
Gravity
Gravity is the interaction of two objects with each other.
For objects that are separated from each other, the objects
act as if all of the mass were concentrated at the center
of the objects
All objects on Earth experience the same gravitational
acceleration g which is given by
g=
GM
R2
Where G is the gravitational constant, M is the mass of the
Earth, and R is the radius of the Earth
Astronomy 1-1
Lecture 04-22
Energy
The energy that we will deal with comes in two
basic varieties:
Kinetic Energy
This is the energy due to either linear or rotational motion
Potential Energy
This is stored energy that can be converted into kinetic
energy
Nature's processes often convert one form of
energy into the other
Astronomy 1-1
Lecture 04-23
Total Energy
In the relative motion of one body with respect to
another, an important quantity is the total
energy
If the potential energy of one body with respect to
the other is larger than its kinetic energy, the
body is bound to the other
This is the case for all the planets orbiting the Sun and
for the moons orbiting their respective planets
If the kinetic energy of the body is larger than its
potential energy with respect to the other body,
the body is free
Astronomy 1-1
Lecture 04-24
Escape Velocity
For one body to be able to escape from another body, its
kinetic energy must be greater than or equal to its
potential energy
Kinetic Energy ≥ Potential Energy
The necessary velocity for this to occur is called the
escape velocity
The escape velocity from a planet is given by
v=
GM
R
This will be of concern for planets with "weak" gravity as
far as their atmospheres are concerned
Astronomy 1-1
Lecture 04-25
Center of Mass
With respect to the motion of one body moving about
another, both objects are in fact in motion about a
common point
A point known as the center of mass
If one body is much larger than the other one, this point is
often contained within the large one, giving the
appearance of the smaller one just moving about the
larger one with the large one being at rest
Astronomy 1-1
Lecture 04-26
Center of Mass
Two identical masses
Slightly differing masses
Major difference in mass
Very large difference in mass
Astronomy 1-1
Lecture 04-27