The Sun’s Motion in our Sky

The Sun’s Motion in our Sky

ONLINE PHYSICAL SCIENCE II   

 Lab Activity


The Sun’s Motion in our Sky”

Equipment

For this activity you will need:

A level

Three rulers

A yardstick or a tape measure

A pencil

Tape

A half piece of posterboard

Scissors

A smartphone with a compass application (or an actual compass)

 

The Sun’s Motion in our Sky Learning Outcomes

After this activity you will be able to identify:

  1. how the altitude of the sun in the sky is changing with each day.
  2. the relationship between the sun’s altitude and the time of year.
  3. the heading (direction) to the rising or setting sun.
  4. the relationship between the heading of the rising (or setting) sun, and the time of year.
  5. the relationship between the sun’s altitude and the level of insolation (i.e. the degree to which the sun’s energy is spread out across the ground).

 

Introduction

Tracking the movements of the sun in the sky is one of the oldest astronomical activities.  Some of the earliest monuments built by humans (such as Stonehenge, Carnac, or Newgrange in the British Isles) have astronomical significance, and mark the locations of the sun along the horizon at key times of the year (such as the summer solstice, or the spring equinox).  Others capitalize on knowledge of the sun’s path through the sky to create spectacular optical effects (such as the “snake” that slithers down the main staircase of the pyramid at Chichen Itza on the spring equinox).

 

 

In this activity, you will track the motions of the sun in the sky over the course of several weeks, and use the data you collect to make and test predictions about how the sun’s position in our sky changes, along with the relationship between the sun’s altitude in the sky, and how efficiently it heats the ground.

 

Getting Started

Before you can begin gathering your data, you will need to make sure you’ve gathered all of your supplies, done a few “startup” activities (to get your equipment ready), and practiced how you will take your measurements.  A few notes:

  1. It is highly recommended that you dedicate a day or two to getting everything set up and ready to go (and to practice taking measurements) before you actually begin taking data.
  2. Likewise, once you’ve started taking data, you will need to commit to taking data regularly for the next four weeks. Failing to do so will affect your results and could potentially affect your grade.  You should carefully check your schedule, and make sure you can reasonably fit in these activities for the next four weeks.  (Remember, once you are practiced in taking these measurements, it should take you less than ten minutes each day to gather your data.)
  3. Several of these activities will go a lot more smoothly if you have a partner to help you – a friend, spouse, co-worker, child, etc. As part of your preparation, you should carefully read through the entire activity so that you know exactly what to expect and can explain to a partner (if any) how they can help you with your measurements (i.e. what they need to hold, what they need to help you measure, and so forth).
  4. For one day (and one day only) you’ll be making several measurements at regular intervals. A weekend (or a day you don’t have to be at work) will work best here, and you should check the weather report before setting the day – it will need to be a clear, sunny day.

 

A typical piece of poster board is about 20” by 30” (often they are 22” by 28”).  To make your half piece, cut parallel to the short side of the board, so your half piece should be about 20” by 15.”  In the center of your half piece of poster board, use a ruler to measure out a 10 cm by 10 cm square, and cut out the square.  This half piece of poster board with the square cut out of it is what you’ll use to measure how direct the sun’s rays are.  Let’s call it your Insolation Tool (or IT for short).

 

Once IT is ready, your next preparation task will be figuring out a time when you can (consistently) measure the sun’s altitude in the sky every day for the next four weeks.  It is best to choose a time that is as close to noon as possible – if you’ve got a consistent lunch break, that will work well.  Try to choose a time between 10 am and 2 pm in the early spring, winter or late fall, or between 10 am and 4 pm in the summer, fall, or late spring.  Be sure you can set aside around three to five minutes each day at your chosen time to make your measurement.  As part of your preparation, you might want to consider setting an alarm or reminder to go off a few minutes before you need to make your measurement each day.

 

 

The start or end of Daylight Saving Time can really mess up your results.  For this reason, you should try very hard to schedule this activity so it can be entirely done either before or after Daylight Saving Time starts (or ends).  In other words, make sure a Daylight Saving Time change doesn’t occur during the four weeks you are making measurements. If you have no choice, and have to conduct measurement both before and after a Daylight Saving Time change, there are instructions as to what to do later in the activity – but it is best to avoid this if possible.

 

You will also need to choose either sunrise or sunset to make a measurement (in addition to the one you make at the same time every day).  You need to choose one or the other: if you choose sunrise, you’ll need to do a measurement at sunrise every day.  If you choose sunset, you’ll need to always do a measurement at sunset.  Choose whichever one you can consistently measure.

 

For the sunrise/sunset measurement you’ll need take your smart phone (or whatever portable device your compass application is on), and tape a pencil (or something else that will act as a pointer) to the back of the device so that it points in whatever direction the smart phone is pointing.  The idea is you want to be able to point the pencil and have the compass heading be whatever direction the pencil is pointing.  Obviously you’re not expect to go around all day with a pencil taped to your phone – you can “set up” your pointer shortly before each time you need to make your measurement.

 

 

How to Make Measurements (Procedures for the Activity The Sun’s Motion in our Sky )

Here’s how you will make your measurements.

The Sun’s Altitude:  At the time you’ve decided on, go to flat, level ground (use the level to make sure the ground is level).  Make sure the ground is in sunlight.  With the help of the level, stand one of your rulers vertically on the ground.  With the other one or two rulers, measure the length of the shadow (in centimeters).  Record your results in Table 1.1 (the tables are all in the Data Collection part of the activity).

The first column of the table is the “day” of your measurement (i.e. Day 1, Day 3, etc.).  The second column is where you will write in the actual date (e.g. March 10th, October 14th, etc.).  The third column is where you will write in the shadow length.

 

For the fourth column, you will need to divide the ruler length (in cm) by the length of the shadow. (Hint: since it’s a ruler, you only have to look at its markings to figure out how long it is in cm.)

 

For the fifth column, look up your shadow length to ruler length ratio (the fourth column) in the table given below.  From that ratio, you can read off the sun’s altitude in the sky.

Ratio Sun Altitude Ratio Sun Altitude Ratio Sun Altitude
.268 15° .839 40° 2.246 66°
.287 16° .869 41° 2.356 67°
.306 17° .900 42° 2.475 68°
.325 18° .933 43° 2.605 69°
.344 19° .966 44° 2.747 70°
.364 20° 1.000 45° 2.904 71°
.384 21° 1.036 46° 3.078 72°
.404 22° 1.072 47° 3.271 73°
.424 23° 1.111 48° 3.487 74°
.445 24° 1.150 49° 3.732 75°
.466 25° 1.192 50° 4.011 76°
.488 26° 1.235 51° 4.331 77°
.510 27° 1.280 52° 4.705 78°
.532 28° 1.327 53° 5.145 79°
.554 29° 1.376 54° 5.671 80°
.577 30° 1.428 55° 6.314 81°
.601 31° 1.483 56° 7.115 82°
.625 32° 1.540 57° 8.144 83°
.649 33° 1.600 58° 9.514 84°
.675 34° 1.664 59° 11.43 85°
.700 35° 1.732 60° 14.30 86°
.727 36° 1.804 61° 19.08 87°
.754 37° 1.881 62° 28.64 88°
.781 38° 1.963 63° 57.29 89°
.810 39° 2.050 64° No shadow 90°

 

If your ratio is between a ratio listed here, then use the altitude whose ratio is closest to yours.  For example, if your ratio is 1.477, then you’d record an altitude of 56°, because 1.477 is closest to 1.483, the ratio corresponding to 56°.

The Insolation:  The insolation is a measure of how much solar energy is striking a given surface area.  Normally it would be expressed as an amount of energy per unit time per surface area (Watts per square centimeter, for example), but we’re actually going to measure it as a ratio of current insolation to what it would be if the sun were directly overhead. Once you’ve recorded the sun’s altitude, it will be time to make your insolation measurement.  You’ll measure this with your

Insolation Tool (IT).  Using a yardstick (or tape measure), hold the IT 1 yard off the ground.  Use the level to make sure it is parallel to the ground.  The IT will cast a shadow on the ground, but the sun’s light will shine through the square you cut into the IT.  So the shadow will have an illuminated rectangle in the middle of it (it will only be a perfect square if the sun is directly overhead).  You will want to measure the length and width of this rectangle (in cm).  Figure out the area of this rectangle (the area is length times width and will have units of cm2) and record the length, width, and area in Table 1.2.  Then, divide the area into 100 cm2 (the area of the square you cut into your IT) – you’ll get a decimal less than 1 but higher than 0.  Record that number in the last column in Table 1.2 (the one labeled insolation).

The insolation you’ve recorded is the fraction of solar energy striking the ground compared to how much would be striking the ground if the sun were directly overhead.  For example, if your insolation was 0.83, that would mean the ground is absorbing 83% as much solar energy as it would if the sun were directly overhead (at an altitude of 90°).  An insolation of 0.31 would mean the ground is getting only 31% of the solar energy it would be getting if the sun were directly overhead.  The closer your insolation is to 1, the more direct the sun’s rays are – the closer it is to 0 the more indirect its rays are.

The Sun’s Heading:

For this measurement, you will need to measure the heading to the sun at either sunrise or sunset (whichever one you chose when preparing for this activity).  The measurement itself is easy.  Turn on the compass application on your smart phone.  Using the pencil you taped pointing out of your smart phone, point the phone toward the rising (or setting sun) and record the compass heading in Table 1.3.  If the sun is

rising, you’ll most likely get a heading between 70° and 110° (less

than 90° means the sun is rising north of east; more than 90° means it is rising south of east).  If it is setting, you’ll get a heading between 250° and 290° (more than 270° means it’s setting north of east; less than 270° means it’s setting south of east).  Record the direction your heading corresponds to (NE, NW, SE, SW, or due E or due W) in the Table.

 

Dealing with Daylight Saving Time:

If you were unable to schedule your observations so that they are all before or after a Daylight Saving Time change, you’ll need to take the time change into account.  When we “spring forward” we set our clocks one hour ahead.  So that means you’ll need to make your observations of the sun one hour later than before the time change (e.g. if you were recording the sun’s altitude at 2:30 pm every day before the change, you’ll need to record the altitude at 3:30 pm every day after the change).  When we “fall back” we set our clocks one hour back, so you’ll need to make your observations of the sun one hour earlier than before the time change.

 

What to do if it is cloudy:

Clouds can potentially spoil one or more days of your observations.  As long as the cloud cover isn’t heavy enough to keep the sun from casting shadows, you can make your measurement.  If the clouds keep the sun from casting shadows, however, you’ll need to make a note of it in the Tables.  To document the fact that you tried to take data, but was clouded out, take a picture of yourself (make it so that the picture makes it obvious it is cloudy), and include the picture with this activity when you e-mail it to you instructor.

 

 

Making your Predictions:

You’ll notice Tables 1.1, 1.2, and 1.3 cover the first four weeks of your observations.  At the end of the four weeks, you’ve collected enough data on the sun’s motions to attempt to predict what the sun will do over the next two weeks.

 

Tables 2.1, 2.2, and 2.3 all have an extra column for data: “predicted altitude”, “predicted insolation”, and “predicted heading.”  Carefully review your last four weeks of data, and use it to predict what you think the altitude, insolation, and heading of the sun will be over the next two weeks.  Also, in the space provided (under the three tables), explain in detail how you made your predictions.  You don’t have to explain every single predicted number – just explain the steps and assumptions you made in coming up with your predictions.

 

The steps and assumptions you are using to predict the sun’s altitude, insolation, and heading for the next two weeks is your hypothesis.  The predictions themselves are the testable predictions that you will use to test the validity of your hypothesis.

 

You won’t (necessarily) be graded on how well your predictions match what you will later record as the real values for the sun’s altitude, insolation, and heading.  If the reasoning behind your predictions is logical and sound, you won’t be penalized even if your predictions don’t match your later measurements.

 

It is extremely important that your predictions be “honest” – for this reason, on the day you make all of your predictions (writing them into Tables 2.1, 2.2, and 2.3) take a picture of these Tables with your predictions entered into them (but without any actual measurements – which you won’t have made yet.)

 

The Single Day Measurements:  At some point during the six weeks of the activity you will track the sun’s altitude and insolation (but not its heading) over a single day.  The reason you are doing this is to see if there is a consistent relationship between altitude and insolation – if the sun is at a particular altitude, will the insolation always be the same?  The measurements are exactly as described under The Sun’s Altitude and Insolation, but you’ll be recording your data in Table 3.1.

 

I Missed A Measurement!  If you forgot to take a measurement on a day (or had a schedule conflict), make your measurements on the next day (and continue normally from there).  Be sure the dates in Table 1.1 (and 2.1) reflect the actual dates you made the measurements (so that your instructor can check the accuracy of your measurements)!

 

Analyzing Your Data. Your Results:  Once you’ve completed your six weeks of observations, and have filled out the tables, you will analyze your results by answering the questions in the Analysis and Conclusions sections of the activity.  When the questions are answered, you’ll be ready to submit the activity to your instructor (don’t forget to include the requested pictures)!

 

Data Collection for The Sun’s Motion in our Sky

Don’t forget to answer any questions in this section in addition to filling out the tables!  To type in information or question answers simply click on the text box provided.  For tables, click on the cell and type in the appropriate information.  Remember to save frequently.  When you are finished, e-mail your completed activity to your instructor, along with any attachments specified in the activity description.  While you are doing the activity you are certainly welcome to print out a hard copy of this activity and write in answers in pen or pencil – but remember that the activity you submit to your instructor will need to be filled out using your computer.

 

Part One: The Four Weeks Before Your Predictions

 

What time (each day) were your observations?                                                   .

 

Table 1.1: The Sun’s Altitude (Weeks 1 through 4)

 

Day Date Shadow Length Ratio Altitude
Day 1        
Day 3        
Day 5        
Day 7        
Day 9        
Day 11        
Day 13        
Day 15        
Day 17        
Day 19        
Day 21        
Day 23        
Day 25        
Day 27        

 

Table 1.2: The Insolation (Weeks 1 through 4)

 

Day Length Width Area Insolation
Day 1        
Day 3        
Day 5        
Day 7        
Day 9        
Day 11        
Day 13        
Day 15        
Day 17        
Day 19        
Day 21        
Day 23        
Day 25        
Day 27        

 

 

Table 1.3:  The Heading (Weeks 1 through 4)

 

Day Heading
Day 1  
Day 3  
Day 5  
Day 7  
Day 9  
Day 11  
Day 13  
Day 15  
Day 17  
Day 19  
Day 21  
Day 23  
Day 25  
Day 27  

 

Part Two:  Weeks Five and Six

Don’t forget to make your predictions.

In the space below, explain in detail how you arrived at your predictions.  Be as specific as possible in detailing the steps of your reasoning and explaining where your numbers came from.  Remember to photograph the tables with your predictions filled in (but before you’ve taken any actual readings for weeks five and six).

 

.

Table 2.1: The Sun’s Altitude (Weeks 5 and 6)

 

Day Date Shadow Length Ratio Predicted Altitude Altitude
Day 29          
Day 31          
Day 33          
Day 35          
Day 37          
Day 39          
Day 41          

 

Table 2.2: The Insolation (Weeks 5 and 6)

 

Day Length Width Area Predicted Insolation Insolation
Day 29          
Day 31          
Day 33          
Day 35          
Day 37          
Day 39          
Day 41          

 

Table 2.3:  The Heading (Weeks 5 and 6)

 

Day Predicted Heading Heading
Day 29    
Day 31    
Day 33    
Day 35    
Day 37    
Day 39    
Day 41    

 

 

Part Three: Your Measurements of the Sun’s Motion Over a Single Day

Date:                                                        .

 

Table 3.1: Single Day Measurements

If any times listed here are while the sun isn’t up (or if “Ratio” would be less than .268, leave the whole row blank.)

Time Shadow Length Ratio Altitude Length Width Area Insolation
7:00 am              
8:00 am              
9:00 am              
10:00 am              
11:00 am              
12:00 pm              
1:00 pm              
2:00 pm              
3:00 pm              
4:00 pm              
5:00 pm              
6:00 pm              
7:00 pm              

 

The Sun’s Motion in our Sky Analysis and Conclusions

All of your answers to questions posed in this section should be detailed and well thought out.  Use complete sentences, proper spelling and grammar, and cite specific numbers from your data to support your conclusions.

 

Discuss how the general altitude of the sun in the sky changed over your six weeks of observation.  In your discussion, relate the current season to the changing altitude of the sun, and state, based on your data, what you expect the relationship to be between the sun’s general altitude in the sky, and the seasons of the year.

 

.

Discuss how the heading of the sun at sunrise or sunset changed over the six weeks of your observations.  In your discussion, relate the current season to the heading of the sun, and state what you expect the relationship between the sun’s heading and the seasons to be.  In particular, be sure to mention during which seasons you expect the sun to be on the northern side of east (or west), and which seasons you expect it to be south of east (or west).  Also relate how the sun’s altitude related to its heading (i.e. if the altitude is currently increasing, is the heading becoming increasingly north or south – and vice versa).

 

.

Discuss how the insolation relates to the altitude of the sun in the sky.  Be sure to specifically mention if your data supports if the insolation is specific to the altitude, or if it can vary (i.e. is the insolation when the sun is at a particular altitude always the same, or can it vary even for the same altitude in the sky?).  Because the insolation is directly related to the amount of solar energy being absorbed by the ground, explain how the level of insolation relates to the typical temperatures of the seasons.

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Be sure to take a few photos of your measuring equipment in use and attach or paste below!

The Sun’s Motion in our Sky

 

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