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Lecture 5
ASTR 111 – Section 002
Outline
1. Quiz Discussion
2. The Moon in its orbit review
3. Gravitation and the Waltz of the Planets
– through section 4.3 of text.
The great debate
• Geocentric – Earth is fixed and everything
rotates around it.
• Heliocentric – The sun is fixed and
everything rotates around it.
The resolution of this question is one
of the great examples of the scientific
method
The great debate
• Geocentric – Earth is fixed and everything
rotates around it.
• Heliocentric – The sun is fixed and
everything rotates around it.
The resolution of this question is one
of the great examples of the scientific
method
Parallax
• Apparent
change in an
objects position
due to a change
in the line of
sight
• In astronomy we use
Apparent and Actual
in many contexts.
Parallax is one
example.
Side note: What is wrong with this picture
(from text)?
• What if the nearby object is moving too?
• That is, moving at a speed comparable to
the speed of Earth in its orbit?
Typical observations
Projection
(in context of celestial sphere)
• Connect point on celestial sphere with
a line to the center of Earth. Where
line intersects Earth’s surface is
where celestial point projects onto
Earth’s surface.
• Need two points + a projection point
P
U
Top View
If U is fixed and P rotates CCW, what
does U see on the wall?
1. Beam traces a line from left to right
2. Beam does not move
3. Beam traces a line from right to left
Will U ever see P reverse directions
with respect to the distance stars?
1. Yes
2. No
If U is fixed and P rotates 90o CCW,
what does U see on the wall?
1. Beam traces a line from left to right
2. Beam does not move
3. Beam traces a line from right to left
If P is fixed and U rotates 90o CCW,
what does U see on the wall?
1. Beam traces a line from left to right
2. Beam does not move
3. Beam traces a line from right to left
Distant “stars”
5 4 3
2
6
1
7
8
9
•
•
In this diagram, are the Republicans to the East or West?
At points 1-8, an observer on Earth will see the planet in
front of a different “star”. Label them below:
1.
2.
3.
4.
5.
6.
7.
8.
•
Rush Limbaugh
During which intervals was the planet moving “to the
right” and which “to the left”? When was the planet in
retrograde motion?
Typical observations
4-5-6 = retrograde motion (westward
against background stars)
1-2-3-4 and 6-7=8-9 = protograde (direct) motion
(eastward against background stars)
Occam’s Razor
Occam’s Razor
• Law of parsimony
• When all things are equal, choose the
theory or model that is simpler or requires
fewer assumptions
• As a group, write down two theories for a
given phenomena. One theory should not
be parsimonious.
Copernicus devised the first
comprehensive heliocentric model
• Copernicus’s heliocentric
(Sun-centered) theory
simplified the general
explanation of planetary
motions
• In a heliocentric system,
the Earth is one of the
planets orbiting the Sun
• The sidereal period of a
planet, its true orbital
period, is measured with
respect to the stars
Copernicus devised the first
comprehensive heliocentric model
• Some planets always
observed near Sun while
looking in the sky.
• Some planets are
sometimes observed at
night and sometimes
opposite the Sun.
Inferior planets
superior planets
A planet’s
synodic period
is measured
with respect to
the Earth and
the Sun (for
example, from
one opposition
to the next)
Copernicus’ heliocentric model
was not widely accepted. Why?
• Predictions
• Occam’s razor
Theme
• Need. More. Data.
• Need. “Satisfactory”. Mathematical. Theory.
If the Earth was in motion
(heliocentric), parallax of
nearby stars should appear
to shift throughout the year
If the Earth was in motion
(heliocentric), parallax of
nearby stars should appear
to shift throughout the year
If Earth is fixed
(geocentric), parallax
does not change)
• I measure the angular separation of two dots on
the screen from the four corner chairs in this
room. Describe what happens to my
measurement of the angular separation.
• I sit in the middle of the room and measure the
angular separation of two dots on the screen.
Someone rotates the walls of the building by 90
degrees. What happens to my measurement of
the angular separation?
If Earth is fixed,
then parallax
angle of stars
does not change
throughout the
year
a
Earth rotates around Sun;
stars and Sun are fixed
The
heliocentric
model
a
If Earth is fixed,
then parallax
angle a of stars
changes
throughout the
year
• Brache did not find a difference in the
parallax angle. Did he prove the
heliocentric model was incorrect?
One more problem with the
geocentric model
• One of Galileo’s most important discoveries with the telescope was
that Venus exhibits phases like those of the Moon
• Galileo also noticed that the apparent size of Venus as seen through
his telescope was related to the planet’s phase
• Venus appears small at gibbous phase and largest at crescent
phase
There is a correlation between the phases of Venus and
the planet’s angular distance from the Sun
Galileo’s discoveries with a telescope strongly
supported a heliocentric model
• The invention of the
telescope led Galileo
to new discoveries
that supported a
heliocentric model
• These included his
observations of the
phases of Venus and
of the motions of four
moons around Jupiter