PAER: Tarleton Observatory: Dr. Goderya Phys1411/1403 Lab: Making a Cross Staff

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1 Phys1411/1403 Lab: Making a Cross Staff Instructions: This Lab activity is designed for you to build an instrument and go outside at night and collect data to test the instrument. I will discuss and show you an example in class on Monday October 9 th. Policies. 1. You must make your own Cross Staff (see making instructions below) and show it when you submit the worksheet. 2. You are allowed to work with a partner and do the activity together but submit your own individual work. 3. After the activity keep your Cross staff because you will use it for another lab activity to be assigned on the week of October 16 th. 4. I am assigning this lab during the week of October 9 th. To allow you to complete the activity, we will not have lab during this week and the week of October 16 th. 5. For Monday Lab Section the Due Date is and for Wednesday Lab Section th. So, you have roughly two weeks to finish this lab activity. We will have Lab in the planetarium on the week of October 23 rd and I will assign a new lab activity using the Cross Staff. Introduction The role of instruments is crucial to gathering astronomical data. Astronomer s measure distance between two stars in the sky as angles. This lab activity is about building a simple instrument called cross staff to measure the angles in the sky or the planetarium. Making the Cross Staff 1. Build a Cross Staff: Visit the following web-link for basic instructions on how to make the Cross Staff or you can also google making an astronomical Cross Staff. This link expects that you know the tangent function from trigonometry. Well you have learned this in middle or high school math class otherwise you would not pass the SAT and be in college. If you have forgotten it, follow the link in the document to refresh your memory. 1

2 2. My Design: No workshop tools Needed Tools This is all I needed to use. 1 scoring knife, 1 Medium size scissors, 1-foot ruler (any kind), you may already have these or you can buy it from dollar store or Walmart for cheap. 1-yard ruler (optional). Something to press the thumb tacks. Materials one furring strip 1.5 x 3/4 x 96 inches. Can be found at most hardware or lumber store. Cut the furring strip in the following lengths. Two 3.5-inch pieces, one 8.5-inch piece, one 22-inch pieces and one 40-inch piece (36 inch will do also). Most hardware/lumber stores will do it for free if you give them the measurements. I used furring strip only because I had one, but you can substitute with what you like. You can also choose a lighter wood (say 1 x ½ x 96 inches). Supplies I roll of Duct Tape 2-inch-wide, a few thumb tacks with flat top. Sharpie, Coarse sand paper, glow in the dark paint (small bottle). You can buy these also at dollar store or Walmart for cheap. You will also need a shoe box cover or something similar. This will be needed to make to right angle cardboard strips for sight notches. Tools, materials and supplies: Obtaining the cut wood pieces is the hardest part. Make sure when you buy it the store can cut it for you unless you have a wood saw or a friend who can help. The wood should cost about $2-4. There is no need to buy very expensive highgrade wood. The supplies may cost a few dollars, but you can cut down the cost if you share with a partner or borrow the tools from a friend or a roommate who has them. 2

3 Brief assembly instructions: 1. Sandpaper all the wood pieces and remove any rough spots and splinters. 2. On the 22-inch wood piece mark the center on both sides and 5 inches and 10-inch pencil mark on both sides from the center on one side. 3. Assemble the 22-inch, the two 3.5- inch and the 8.5-inch wood pieces as shown below. 3

4 4. tape it with duct tape. I have not used any nails or screws. 5. Cut out the right-angle strips from shoe box cover and put them on the 22- inch wood piece. Use thumb tack and Duct Tape to secure it to the 22-inch wood piece. 6. Cut out the sight notches with scissors as shown by arrows 7. Put Glow paint on the 5-inch and 10- inch marks and on the sight notches. 8. Mark and label the 40-inch wood piece as shown. Mine are in inches, but you can use centimeters if you wish. Slide the 22-inch wood piece on 40-inch wood piece and complete the assembly of Cross Staff. Do not put Glow in the dark paint on 40- inch wood stick or else it will make it difficult to line up the stars. 9. Once I had the wood pieces and supplies it took me about 3 hours to make my Cross staff. 4

5 3. Alternatives: You don t have to follow the two designs given above. You can make your own or make modifications to the ones above to your hearts content. You can also use any tools or materials and supplies if you have access to them and use more elaborate designs from google. My designs show you can do this project without needing workshop tools. 4. The math behind the Cross Staff: Refer to the following diagram from the web-link given above and study the equation in relation to this diagram the angle A is what we are interested in finding and to do that we need the lengths BC and AC. tan AA = BBBB AAAA oooo AA = tan 1 BBBB AAAA 5. Using and testing your Cross Staff: Test your Cross Staff by going outside on a clear night, find Big Dipper and collect the data on BC and AC for the angles shown and enter it in table given below. Complete the calculations and submit your worksheet Love the Night Sky 5

6 Worksheet for Cross Staff Making and Testing Name: Part I Take a snapshot of your Cross Staff with a smart phone or digital camera and attach (staple) a picture of your Cross Staff here: Your Cross Staff should be labelled with your name on it with a permanent black ink (say Sharpie). When you hand in your worksheet, I will verify the picture with your Cross Staff, so bring the Cross Staff with you for verification. Instructors verification: Part II Enter the relevant data for Big Dipper in the table below. Do the calculation for column D using equation given above. Then complete column E with the equations for %Difference. A B C D E Angle indicated in BC AC A % Difference Big Dipper in degrees cccccccccccc EE cccccccccccc AA % DDDDDDDDDDDDDDDDDDDD = 1 2 (cccccccccccc AA + cccccccccccc BB) If your %difference are very high (more than 10%), you need to figure out what s wrong with your cross staff. Take help from other class mates who have gotten better results. Questions: Explain why it does not matter whether the measurement of BC and AC are in inches or centimes. 6

7 Part III Find the height of a flag pole near the admin building (or another place that has a US or Texas flag). Do it from three different angles for three separate reading so you can compute the average. Obtain A from cross staff and h is your height. Use average value for A and d in calculations. A y h d Your height h = A B C D E Measurement BC AC A Distance from Flag Pole Average FFFFFFFF PPPPPPPP HHHHHHHHhtt = yy + h = dd tttttt(aa) + h = cccccccccccc EE tan(cccccccccccc AA) + h 7