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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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