# Lab report of Geology

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Lab 02 Worksheet – The Earth and It’s Sun Name: Earth Science Online

Earth Science Online Lab 03 Worksheet Page 1

What can the length of a shadow tell us about the seasons and our location on earth?

Physical Lab Required Materials:

A Pencil or wooden dowel (approx. 6in/15cm), A paper plate, a Ruler (with millimeters), A pen

(fine point), Clock, GPS receiver.

Background: As you have read in the text our earth rotates around the Sun one full rotation

each year. The earth has a constant parallel axis during it’s orbit around the sun. We know that

the amount of daily solar radiation at any latitude that the earth receives is spread evenly (or

consistent) around all of the earth. This is due to the earths rotation (spinning) on its axis. The

axial tilt is approximately 23.5 degrees. The length of daylight at any given point on earth is

determined by (1) The latitude of the location and (2) the location of earth in the annual orbit

around the sun. Ie. The axial tilt relative to the orbit. he angle of insolation is the angle at

which the sun’s rays strike a particular location on Earth.

Part 1. Angles of Insolation vary across the hemispheres

Review an animation about the Earth-Sun Relations.

Stop the animation at 2:13.

(A) The June Solstice (June 21st) is when the earth’s northern hemisphere has maximum tilt

toward the sun (23.5 degrees). What is angle of insolation at the tropic of cancer during

the June Solstice?________

(B) Use the GPS receiver to identify at which latitude you are currently located. What is it?

Latitude___________Where are you? City__________State____________

(C) Calculate the angel of insolation of your current location.

Latitude of subsolar point

(angle of declination) -

Latitude of current

location

=

Change in angle from

subsolar point

(a) - (b) = (c)

Angle of Insolation at

subsolar point +

Change in angle from

subsolar point =

Angle of insolation at

current location

90° + (c) = (d)

A basic formula for the angle of declination is

sin δ = 0.39795 ⋅ cos [ 0.98563 ⋅ ( N – 173 ) ] where the argument of the cosine here is in degrees and N denotes the number of days since January 1.

Lab 02 Worksheet – The Earth and It’s Sun Name: Earth Science Online

Earth Science Online Lab 03 Worksheet Page 2

Seeing as you may not have had trigonometry we are going to use the analemma diagram to

determine the angle of declination at the subsolar point (see figure 1 below).

Figure 1. An Analemma diagram.

How to use the Analemma

Find the current date located on the dashed figure 8 line in the analemma diagram from figure 1. Use

the grid lines to move to the left axis. Each date on the analemma corresponds to an angle of

declination.

Lab 02 Worksheet – The Earth and It’s Sun Name: Earth Science Online

Earth Science Online Lab 03 Worksheet Page 3

Part 2. Compare your Theoretical Angle to a Measured Angle

Build a measuring device (a crude sun dial base).

Place a small hole in the center of the paper plate with the pencil. Push the pencil nearly all the

way through the plate. Make sure that it can stand vertically the closer to straight up the better.

If you have access to a grassy area you can press the pencil into the ground to make it more

sturdy.

Figure 2. Diagram of pencil in a paper plate.

Collect Data

Figure 3 Diagram of what to measure on insolation shadow device.

Lab 02 Worksheet – The Earth and It’s Sun Name: Earth Science Online

Earth Science Online Lab 03 Worksheet Page 4

(A) Measure the height of the pencil relative to the plate.

a= _________mm

(B) At noon (12:00PM) measure the distance of the tip of the shadow of the pencil to the

base 90° directly below the tip of the pencil. Use a protractor or a book to get a right

angle.

b=_______mm

(C) Calculate the angle of insolation using the following formulas:

𝑎2 + 𝑏2 = 𝑐2

c = ___________mm

∠𝐴 = arccos( 𝑏2 + 𝑐2 − 𝑎2

2𝑏𝑐 )

(D) What angle did you calculate for the angle of insolation?

∠A= ____________

(E) Insert a picture of your insolation angle measuring device and add graphics and labels

to show which distance equals which variable in the equation

(F) What is the angle from Part 1 Q3d? ______________

(G) Are the two angles of insolation the same? If not, what might account for the

differences?

Lab 02 Worksheet – The Earth and It’s Sun Name: Earth Science Online

Earth Science Online Lab 03 Worksheet Page 5

(H) If you used the same device to collect a shadow length at noon in a latitude north of

your location, what would you expect to see?

(I) If you used the same device to collect a shadow length at noon in a latitude south of

your location, what would you expect to see?

(J) If you used the same device to collect a shadow length at noon in a latitude east of your

location, what would you expect to see?

(K) If you used the same device to collect a shadow length at noon in a latitude west of your

location, what would you expect to see?

(L) If you used the same device to collect a shadow length at noon on July 24th, at the same

location, what would you expect to see?