Transcript Geocentric model fails to account for phases of the inner planets

Astronomy Picture of the Day
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
Geocentric model fails to account
for phases of the inner planets
Heliocentric model easily accounts
for phases of the inner planets
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
The Scientific Method
• Geocentric model
abandoned because of
its failure, and to a
lesser extent because
of its complexity.
• Occam's razor
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?
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.
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Deduced three laws of
planetary motion.
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Took him the last 30 years
of his life.
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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
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.
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.
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
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- air track)
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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.
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.
(DEMO – Air Track, Jet Cart)
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
1/7 what it is on Earth.
Gravitational Force
• The gravitational force is
always attractive
• The strength of the
attraction decreases with
increasing distance
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
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