Download Slide - Fort Lewis College

Charles Hakes
Fort Lewis College
1
Prologue
Parallax
Charles Hakes
Fort Lewis College
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Charles Hakes
Fort Lewis College
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Charles Hakes
Fort Lewis College
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Review
• What was the most important thing
you learned?
• Elliptical orbit does not create our
seasons.
• The Earth is on a wobble, but it takes
26,000 years.
• You cannot “prove” something, but you
can disprove it.
Charles Hakes
Fort Lewis College
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Where along the horizon does the Sun rise on
June 21 in Durango, Colorado?
A) North of east
B) Due east
C) South of east
D) Can’t tell with information given
Charles Hakes
Fort Lewis College
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Where along the horizon does the Sun rise on
June 21 in Durango, Colorado?
A) North of east
B) Due east
C) South of east
D) Can’t tell with information given
Charles Hakes
Fort Lewis College
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Where along the horizon does the Sun rise on
June 21 in Sydney, Australia?
A) North of east
B) Due east
C) South of east
D) Can’t tell with information given
Charles Hakes
Fort Lewis College
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Where along the horizon does the Sun rise on
June 21 in Sydney, Australia?
A) North of east
B) Due east
C) South of east
D) Can’t tell with information given
Charles Hakes
Fort Lewis College
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You carefully measure the height of Polaris from
Durango and from Grand Junction to the north.
A) Polaris appears higher in Durango
B) Polaris appears higher in Grand Junction
C) Polaris is the same height in both places
D) not enough information
Charles Hakes
Fort Lewis College
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You carefully measure the height of Polaris from
Durango and from Grand Junction to the north.
A) Polaris appears higher in Durango
B) Polaris appears higher in Grand Junction
C) Polaris is the same height in both places
D) not enough information
Charles Hakes
Fort Lewis College
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You carefully measure the height of the noon Sun
from Durango and from Grand Junction.
A) The Sun is higher in Durango
B) The Sun is higher in Grand Junction
C) Which is higher depends on the season.
D) Not enough information.
Charles Hakes
Fort Lewis College
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You carefully measure the height of the noon Sun
from Durango and from Grand Junction.
A) The Sun is higher in Durango
B) The Sun is higher in Grand Junction
C) Which is higher depends on the season.
D) Not enough information.
Charles Hakes
Fort Lewis College
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Measuring Distances
• Question for discussion - How can
you find the distance to an object?
Come up with three methods.
Charles Hakes
Fort Lewis College
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Measuring Distances
• Question for discussion - How can
you find the distance to a distant
object without traveling to it?
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Fort Lewis College
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Measuring Distances
• Measuring angles
• Parallax
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Fort Lewis College
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More Precisely P-1
Angular Measure
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Fort Lewis College
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Trigonometry
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Fort Lewis College
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Trigonometry
• sin(q) = opposite/hypotenuse
• cos(q) = adjacent/hypotenuse
• tan(q) = opposite/adjacent
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Fort Lewis College
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Figure P.10
Triangulation
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Fort Lewis College
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Figure P.11
Parallax
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Fort Lewis College
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Figure P.12
Parallax Geometry
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Fort Lewis College
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Star A has a parallax shift of 0.2 arc second
Star B has a parallax shift of 0.5 arc seconds
A) Star B is more than twice as far as star A
B) Star B is a little farther than star A
C) Star A is more than twice as far as star B
D) Star A is a little farther than star B
E) Not enough information
Charles Hakes
Fort Lewis College
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More Precisely P-2a
Measuring Distances with Geometry
x distance
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Fort Lewis College
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Radians
• Not just an extra button on your
calculator
• 2 radians in a circle
• Conversion formula
2 rad = 360°
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Fort Lewis College
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Small Angle Approximation
• Angle must be in radians
• Angle must be small
• (opposite << adjacent)
• Then:
q  sin(q)  tan(q)
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Fort Lewis College
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Small Angle Approximation
• For small angles in radians:
angle = baseline/distance
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Fort Lewis College
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Small Angle Approximation
• For small angles in radians:
angle = baseline/distance
or
distance = baseline/angle
or
baseline = angle*distance
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Fort Lewis College
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Distance of your thumb
• Group exercise - use parallax to
calculate the distance to your thumb.
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Fort Lewis College
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Distance of your thumb
• If your baseline is 5cm, (about the
width of your eyes) and
• You observe a parallax shift of 0.1
radian (about 5.7 degrees) then
• Use
distance = baseline/angle
• Your thumb is about 50cm away.
Charles Hakes
Fort Lewis College
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If your baseline is 25cm, and you observe a
parallax shift of 0.01 rad.
• The distance to the object is:
1: 2.5cm
2: 2500cm
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Fort Lewis College
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3: 25000cm
More Precisely P-2b
Measuring Distances with Geometry
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Fort Lewis College
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Small Angle Approximation
• If you know the size of an object, you can
determine it’s distance using the same
triangle formulas
distance = baseline/angle
• This time the “baseline” is the known
diameter of the object and the angle is the
observed apparent “size” of the object.
Charles Hakes
Fort Lewis College
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Observing from a latitude of 25° North
A) The star Polaris appears about 65° above the horizon.
B) The celestial equator has a maximum height of 65° above
the horizon.
C) The star Polaris appears about 25° north of the zenith point.
D) The celestial equator has a maximum height of 25° above
the horizon.
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Fort Lewis College
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Discussion
• Where does Polaris appear when standing
on the equator?
• Where does Polaris appear when standing
on the pole?
• How high does the celestial equator appear
when standing on the equator?
• How high does the celestial equator appear
when standing on the pole?
Charles Hakes
Fort Lewis College
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Observing from a latitude of 25° North
A) The star Polaris appears about 65° above the horizon.
B) The celestial equator has a maximum height of 65° above
the horizon.
C) The star Polaris appears about 25° north of the zenith point.
D) The celestial equator has a maximum height of 25° above
the horizon.
Charles Hakes
Fort Lewis College
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Observing from a latitude of 55° North
A) The star Polaris appears about 35° above the horizon.
B) The celestial equator has a maximum height of 55° above
the horizon.
C) The star Polaris appears about 35° north of the zenith point.
D) The celestial equator appears about 35° south of the zenith
point.
Charles Hakes
Fort Lewis College
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Observing from a latitude of 55° North
A) The star Polaris appears about 35° above the horizon.
B) The celestial equator has a maximum height of 55° above
the horizon.
C) The star Polaris appears about 35° north of the zenith point.
D) The celestial equator appears about 35° south of the zenith
point.
Charles Hakes
Fort Lewis College
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Three Minute Paper
• Write 1-3 sentences.
• What was the most important thing
you learned today?
• What questions do you still have
about today’s topics?
Charles Hakes
Fort Lewis College
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