Prologue

Charles HakesFort Lewis College 1


Prologue

Parallax


Logistics

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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.


Lab Notes

• Binocular lab Monday, Thursday (?)• http://faculty.fortlewis.edu/hakes_c

http://faculty.fortlewis.edu/hakes_c


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


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



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



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



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


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


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.


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.


Measuring Distances

• Question for discussion - How can you find the distance to an object? Come up with three methods.


Measuring Distances

• Question for discussion - How can you find the distance to a distant object without traveling to it?


Measuring Distances

• Measuring angles• Parallax


More Precisely P-1Angular Measure


Trigonometry


Trigonometry

• sin() = opposite/hypotenuse• cos() = adjacent/hypotenuse• tan() = opposite/adjacent


Figure P.10Triangulation


Figure P.11Parallax


Figure P.12Parallax Geometry


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


More Precisely P-2aMeasuring Distances with Geometry

x distance


Radians

• Not just an extra button on your calculator

• 2 radians in a circle• Conversion formula

2 rad = 360°


Small Angle Approximation

• Angle must be in radians• Angle must be small

• (opposite << adjacent)

• Then: sin() tan()



• For small angles in radians:

angle = baseline/distance



• For small angles in radians:

angle = baseline/distance

or

distance = baseline/angle

or

baseline = angle*distance


Distance of your thumb

• Group exercise - use parallax to calculate the distance to your thumb.


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.


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 3: 25000cm


More Precisely P-2bMeasuring Distances with Geometry



• 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.


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.


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?






D) The celestial equator has a maximum height of 25° above the horizon.






D) The celestial equator appears about 35° south of the zenith point.






D) The celestial equator appears about 35° south of the zenith point.


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?

Documents

Prologue