Chapter 2- QP

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9th Edition: 53) Arcminutes and Arcseconds. There are 360° in a full circle. a. How many arcminutes are in a full circle? 360° * 60 minutes/ 1° = 21,600 arcminutes b. How many arcseconds are in a full circle? 360° * 60 minutes/ 1° * 60 seconds/ 1 minutes = 1,296,000 arcseconds c. The Moon’s angular size is about ½°. What is this in arcminutes? In arcseconds? 1/2° * 60 minutes/ 1° = 30 arcminutes 30 arcminutes * 60 seconds/ 1 min = 1800 arcseconds 55) Angular Conversions I. The following angles are given in degrees and fractions of degrees. Rewrite them in degrees, arcminutes, and arcseconds. a. 24.3° 0.3*60 24° 18’ b. 1.59° 0.59*60=35.4 → 0.4*60=24 1° 35’ 24’’ c. 0.1° 0.1*60 6’ d. 0.01° 0.01*60*60 36’’ e. 0.001° 0.001*60*60 3.6’’ 56) Angular Conversions II. The following angles are given in degrees, arcminutes, and arcseconds. Rewrite them in degrees and fractions of degrees. a. 7° 38’ 42’’ 7° 38/60 +42/3600 = 7.642 degrees b. 12’ 54’’ 12/60+ 54/3600 = 0.215 degrees c. 1° 59’ 59’’ 1° 59/60+59/3600= 1.9997 degrees
d. 1’ 1/60 = 0.017 degrees e. 1’’ 1/3600 = 0.000278 degrees 57) Sun Diameter. Use the Sun’s approximate distance of 150 million km and angular diameter of about 0.5° to calculate the Sun’s physical diameter. Compare your answer to the actual value of 1,390,000 km. 2*pi*d * angular diameter/360°= physical diameter 2*pi*(150,000,000) * 0.5°/360° = 1,308,996.939 ≈ 1,309,000 Δ physical diameter = 1,390,000 - 1,309,000 = 81000 58) Betelgeuse Diameter. Estimate the diameter of the supergiant star Betelgeuse from its angular diameter of 0.05 arcsecond and distance of about 600 light-years. Compare your answer to the size of our Sun and the Earth-Sun distance. 0.05 arcsec= 0.00001389 degrees 2*pi*(600) * (0.00001389°/360°) = 0.000145 light years Size of the sun: 1.47* 10^ -7 light years D B /D S = 0.000145/1.47*10^-7 = 986.39 light years Earth-Sun distance: 0.00001581 0.000145/0.00001581= 9.17 light years
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