Observation Assignment #1 Angles and Distances

Transcription

1 Observation Assignment #1 Angles and Distances Introduction The apparent positions and separations of objects in the sky are not determined by the linear distances between the two objects, but by their angular separation. For example, the angular distance from the horizon to the zenith (the point directly overhead) to 90 o. Not only can we measure the angular separation between two objects, but we can also measure the angular size of larger objects such as the Moon. Angles can be measured in a variety of ways. If the objects are located on a flat surface such as a piece of paper, or a block of wood, then you can use a protractor. Protractors are not very practical for use in measuring angles in the sky. The astronomers in Galileo s time, and ship captains who had to navigate by the stars used an instrument called a sextant. Since it is highly unlikely that you have a sextant to use, and since we are not concerned with a high degree of accuracy, we will estimate the angular measurements in this exercise with the use of our own

2 hands and fingers. As shown in class, you can estimate an angle by holding your hand at arm s length in front of your eyes. One finger width is about 1 o. A fist width is 10 o, and an outstretched hand is 20 o. The true linear size (d), the distance between the observer and the object (L) and the angular separation (θ) are related by the following geometry and equation: d = Lθ Equation 1 Where d and L are in the same units of distance (like inches, centimeters, meters, etc.) and the angle θ is in units called radians. There are 2π radians in 360. Therefore, if your angle is in degrees, the equation is d = L θ 3.14 = L θ 0.02 Equation Instructions: Complete the following 4 exercises, place your answers on the answer sheet. 1. Measuring a person s height. You will need a friend, a meter stick or measuring tape, and a long hallway or space outdoors. Dr. Wright will have meter sticks and measuring tapes available to borrow, and the hallway near her office is ideal for this experiment. Have your friend stand at one end of the hallway. The observer then moves to the other end of the hallway (about 50 feet away). The observer will measure the friend s angular height (θ in degrees) using the hand/finger method and the distance between the friend and the observation location (L) using the meter stick or tape measure. Calculate the height of the friend using Equation 2. Remember that the result will be in the same units as the distance L measurement. Measure the actual height of your friend. How did the calculated value compare to the measured value?

3 Place your values on the answer sheet. Before you put your measuring tools away, measure the length of one of your natural walking strides. 2. Measure the height of MC Reynolds. Now repeat the process, but instead of measuring a person s height, estimate the height of MC Reynolds building. Find a location where you can comfortably measure the angular height of the building using the hand/finger method. Count the number of natural strides between your viewing location and the building. Use Equation 2 to calculate the height of the building in units of stride lengths. Multiply this number by the number of feet in your natural stride to get an estimated height of the building in feet. Is your answer reasonable? Again, place your results on the answer sheet. 3. Pinhole Camera D H You will need a sunny day and something with a small hole or something in which you can punch a small hole (like an index card or thin piece of cardboard) to make a pinhole camera. You can even use something like a colander like I did at the Hendrix eclipse event. You will also need a ruler or tape measure, and a coin. A great introduction to how pinhole cameras work can be found at this website: (or search Hewwitt Drew it pinhole camera) Take your pinhole camera and measuring tool and coin outside on a h sunny day. It is best to do this around noon, when the Sun is high in the sky. Place your coin on a piece of paper on the ground. Place your pinhole camera so that the image of the Sun falls on the coin. Raise or lower the height of the pinhole camera until the Sun s image d is the same size as the coin. Measure the height of the pinhole camera when this happens. Hint: if you can t get that to work with the coin, position the Sun s image on a sheet of paper and have a friend draw a circle the size of the image on the paper or use a different object. Now use geometry to find the distance between the earth and the Sun. Show your work on the answer sheet. 4. Take it to the stars! The Big Dipper is an asterism (a pattern of stars) consisting of the seven brightest stars of the constellation Ursa Major. The Big Dipper, along with the constellation Cassiopeia, are both large bright features in our northern sky. Use a planetarium software such as Stellarium or Starry Night or the internet to label each star in the diagram. Head outdoors at night and look north. Find each object. You may need to go out at different times to see different parts of each. Using your hand/finger method, measure the angular distance between each bright star in each formation and add it to your diagrams.

4 Observation Assignment #1: Angles and Distances Answer Sheet Name: Exercise #1: Measured height of friend Angular height in degrees (θ) Distance between observer and friend (L) Calculated height of friend: d = L θ 0.02 Measured height of friend for comparison (degrees) Exercise #2: Estimated height of MC Reynolds building Angular height in degrees (θ) Distance between observer and building (L) Calculated height of building: d = L θ 0.02 Measured length of 1 stride (s) Estimated height of building in feet: d x s (degrees) (strides) (strides) (feet) (feet) Exercise 3: Pinhole Camera Distance between pinhole and image (h) Diameter of image (d) Ratio h/d Diameter of Sun (D) Distance between Earth and Sun = (h/d) x D (cm) (cm) 1.4 billion meters = (m)

5 Exercise #4: Take it to the Stars!