Angular size of the Moon at two positions (near horizon and high on the sky) lab 3

Experiment #3 Determining the Size of the Moon After completing this exercise, you should be able to estimate the angular size of celestial objects and calculate the approximate distance using the small angle formula. Angular size is the apparent size ofan object measured in degrees, with no information on the object's actual size (in kilometers or miles) or distance. Let's learn the skill by measuring the size of the Moon. You will be measuring the size twice in the interval of approximate three hours. You need to take one measurement when moon is very close to the horizon and the second measurement when moon is way above from the horizon because according to a folk -tale moon is larger when it is near the horizon. It is easiest to do it either early in the evening or very early in the morning when the Moon is either at the full or nearly full phase. You can do it when the Moon is on the other Gibbous or quarter phases as well, but you must measure the largest diameter of the Moon and find the moon near the horizon and way above the horizon. Let's get started. Angular size of the Moon at two positions (near horizon and high on the sky): When moon is near the horizon, hold a ruler (at least 1mm resolution or smallest division) at arm's length so that it is in front ofthe Moon. Use your thumb nails (or two index cards) to mark the edges of the Moon across the ruler as shown in Figure below. Denote it as 5. At the same time, have a friend measure the distance from your eye to the ruler. Denote it as d. Make sure you are measuring the size at the widest point of the Moon. There might be more accurate ways to do this measurement say, taping a dime to the inside ofthe window and step back until the dime just covers the moon or other variations on this theme. You are encouraged to be inventive. Now use the small angle approximation H S 9 : 206265E (both s and d should be in the same unit) The above formula gives you the angular size in arc seconds. Do you remember the size of the Moon in arc seconds? If not look at the book or intemet and calculate the percent difference using the formula below. difference between standard and measured values % difference X 100 standard value If your difference is more than 20 %, you should retake the data and calculate again. Repeat the process when moon is at the other position (high on the sky) after about three hours. Diameter of the Moon: Find the average of the two 6' measurements. Use the average value oftheta and the small angle formula to calculate S in the formula. It is the diameter ofthe moon. You need actual distance d, from Earth to Moon for it which is 3.8x105km. These measurements and calculations go to the data and calculations section of your lab report. Make sure to note down each measurement with proper notations (eg. d, 5 etc) and units. In the conclusion section discuss if the sizes of the moon measured at two positions about same. Test the tale that the size ofthe Moon in the sky is larger when it is near the horizon. How do your results compare? What do you think ofthe folk tale now? Don't forget to write possible sources of error in the measurements and how you tried to minimize them