Transcript lecture4

Astronomy Picture of the Day
Windows on the Universe Simulation:
Comets and Retrograde Motion
Testing - the key to science
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Greeks
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Rational thought was sufficient
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Inconsistencies blamed on faulty perception
Modern Science
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Models make predictions
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Verification provides support for model
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A “Theory” is a generally accepted model
Geocentric model fails to account for
phases of the inner planets
The Scientific Method
• Geocentric model
abandoned because of
its failure, and to a
lesser extent because
of its complexity.
The scientific method is used to develop new scientific theories.
Scientific theories are accepted when they make testable
predictions that can be verified using new observations and
experiments.
Heliocentric model easily accounts
for phases of the inner planets
Geocentric vs. Heliocentric
Predicted Phases of Venus
Observations show both!
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Geocentric:
only crescent phases
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Heliocentric:
both full and crescent
phases
Tycho Brahe
• Collected vast
amounts of
astronomical data
(positions of different
bodies at certain
times)
• Had a gold nose and a
moose that couldn’t
hold his liquor.
Kepler (1571-1630)
• Used Tycho Brahe's
precise data on apparent
planet motions and
relative distances.
• Deduced three laws of
planetary motion.
• Took him the last 30
years of his life.
Kepler’s Laws
• What are the shapes and important properties of
the planetary orbits?
• How does the speed of a planet vary as it orbits
the sun?
• How does the period of a planet's orbit depend
on its distance from the Sun?
Kepler’s First Law
• The orbits of the planets
are elliptical (not
circular) with the Sun at
one focus of the ellipse.
• 'a' = semi-major axis:
Avg. distance between
sun and planet
• video
The amount of elongation in a planet’s orbit is defined as its
orbital eccentricity. An orbital eccentricity of 0 is a perfect circle
while an eccentricity close to 1.0 is nearly a straight line.
In an elliptical orbit, the distance from a planet to the Sun
varies. The point in a planet’s orbit closest to the Sun is
called perihelion, and the point farthest from the Sun is called
aphelion.
Kepler's Second Law
A line connecting the Sun and a planet sweeps out equal areas
in equal times.
slower
faster
Translation: planets move faster when closer to the Sun.
video
Kepler's Third Law
The square of a planet's orbital period is proportional to the
cube of its semi-major axis.
P2
is proportional to a3
or
P2 (in Earth years) = a3 (in A.U.)
1 A.U. = 1.5 x 108 km
Translation: The further the planet is from the
sun, the longer the period.
Summary video
CPS Question
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Which of the following is not a stage in the
cyclical representation of the scientific method.
A) Observation
B) Argumentation
C) Theory
D) Prediction
CPS Question
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A circular orbit has an eccentricity of _____.
A) exactly 0
B) between 0 and 0.5
C) exactly 1
D) infinity
CPS Question
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In Ptolemy's geocentric model, the normal
(non-retrograde) motion of the planets was
attributed to actual motion along what circle?
A) deferent
B) epicycle
C) retrograde loop
D) equant
Galileo was the first to use a telescope to
examine celestial objects. His discoveries
supported a heliocentric model of the solar
system.
Galileo discovered that Venus, like the Moon, undergoes a series of phases as
seen from Earth. In the Ptolemaic (geocentric) model, Venus would be seen in
only new or crescent phases. However, as Galileo observed, Venus is seen in
all phases, which agrees with the Copernican model as shown.
Galileo also discovered moons
in orbit around the planet
Jupiter. This was further
evidence that the Earth was not
the center of the universe.
Newton (1642-1727)
Newton’s laws are fundamental principles
that govern the motions of all astronomical
bodies!
What is the natural state of motion of a
body with no forces acting on it?
Newton's First Law of Motion
Every object continues in a state of rest or a state of uniform
motion in a straight line unless acted on by a force.
● Inertia - resistance to change in motion of object - is related
to its mass.
(Demo- coin/ egg)/$ video
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Newton's Second Law of Motion
When a force, F, acts on an object with a mass, m, it produces
an acceleration (a) equal to the force divided by the mass.
a=
F
m
or F = ma
Acceleration is a change in velocity or a change in direction of
velocity.
Newton’s laws classify objects as accelerating or nonaccelerating, not as moving or stationary.
video
Newton's Third Law of Motion
To every action there is an equal and opposite reaction.
Or, when one object exerts a force on a second object,
the second exerts an equal and opposite force on first.
(Video1, video2)
What force governs the motions of astronomical
objects, and what factors determine how strong the
force is?
Newton's Law of Gravity
For two objects of mass m1 and m2, separated by a
distance R, the force of their gravitational attraction
is given by:
F=
G m1 m2
R2
Your "weight" is just the gravitational force between the
Earth and you. On the moon your “weight” would be about
1/6 what it is on Earth.
Isaac Newton formulated three laws to describe
the fundamental properties of physical reality.
NEWTON’S THREE LAWS OF MOTION
LAW #1: A body remains at rest or moves in a
straight line at constant speed unless acted upon
by a net outside force.
LAW #2: The acceleration of an object is
proportional to the force acting on it.
LAW #3: Whenever one body exerts a force on
a second body, the second body exerts an equal
and opposite force on the first body.
Newton also discovered that gravity, the force that causes
objects to fall to the ground on Earth, is the same force
that keeps the Moon in its orbit around the Earth.
NEWTON’S LAW OF UNIVERSAL GRAVITATION
Two objects attract each other with a force that is directly
proportional to the product of their masses and inversely
proportional to the square of the distance between them.
With his laws, Newton was
able to derive Kepler’s
three laws, as well as
predict other possible
orbits.
Gravitational Force
• The gravitational force is
always attractive
• The strength of the
attraction decreases with
increasing distance
• F=Gm1m2
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r2
CPS Question
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The force that holds you to the Earth is the same
force that keeps the Earth in orbit around the sun
and the moon in orbit around the Earth.
A) True
B) False
Orbit of Earth around Sun
(Demo - Ball on String)
Gravity and Orbits
• Throwing an object
fast enough will put
the object into orbit!
(Neglecting air
resistance)
• Moon is continually
“falling” towards the
Earth in its orbit
(Gravity vs. inertia)
Correction to Kepler’s Third Law
• Earth and sun
actually rotate about
their common center
of mass
• Corresponds to a
point inside sun
• Used to detect
extrasolar planets