Angular Measurement When measuring positions, distances, or sizes in the sky, it is helpful to think of ourselves as inside a large sphere. When we measure the distance between two celestial objects – like stars – or the size of a celestial object – like a planet – it is measured as an angle (see figure below). Angular distance and size is measured in “degrees of arc” with the vertex of the angle at the center of the sphere. Fractional values of “degrees of arc” are measured in arcminutes and arcseconds. One arcminute (written 1’) is equivalent to 1/60 of a degree and one arcsecond (written 1”) is equivalent to 1/60 of an arcminute or 1/3600 of a degree. Angular Distance/Size Angular Angular Distance Size Angular measurement can be used to describe the distance between two celestial objects such as stars or the size of a celestial object like a planet. Prepared by the Center for History of Physics at AIP 1 Name: ________________________________ Date: _______________ Measuring the Big Dipper In the field, you can use your hand to estimate the angular distance between and size of celestial objects like the Big Dipper! The North Star (Polaris) The Pointer Stars in the Big Dipper always point to the North Star 7 Dubhe 4 2 Merak 3 Megrez 6 Mizar Alioth 1 Phecda Alkaid The Big Dipper (Ursa Major) 5 Prepared by the Center for History of Physics at AIP 2 1. Find the Big Dipper in the sky using the North Star. Remember that the two stars at the edge of the Big Dipper always point to the North Star (see above illustration). 2. Hold your arm outstretched to the sky. Your eyes will be the center of the celestial sphere. As a guide, the angular size (diameter) of the moon is approximately 30° (see below). Use the following chart to estimate the distance between the different stars in the Big Dipper: Pinky finger width 1 degree of arc Three middle fingers together (Ring 5 degrees of arc finger, middle finger, and pointer finger) Back of your fist 10 degrees of arc Pinky and pointer finger in a “Y” shape 15 degrees of arc Pinky and thumb in a “Y” shape (Hang 25 degrees of arc Loose sign) Fill in the different distances on the above illustration of the Big Dipper. Fill in the following distances in degrees, arcminutes, and arcseconds. Remember the following conversion: 1° (Degree of arc) = 60 Arcminutes = 3600 Arcseconds Alkaid Dubhe = ________ Degrees = ________ Arcminutes = __________ Arcseconds Merak Polaris = ________ Degrees = ________ Arcminutes = __________ Arcseconds Alkaid Polaris = ________ Degrees = ________ Arcminutes = __________ Arcseconds Check how accurate you are with the below diagram. Remember, these are just estimates, so if you are off by a few degrees, don’t worry. ~30 arcminutes ~5° or 1/2° Prepared by the Center for History of Physics at AIP 3 .