LIED -size a star EXAMPLE 14-12 ESTIMATE Star radius. The giant star Betelgeuse emits radiant energy at a rate 104 times

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Lied Size A Star Example 14 12 Estimate Star Radius The Giant Star Betelgeuse Emits Radiant Energy At A Rate 104 Times 1 (49.54 KiB) Viewed 25 times

LIED -size a star EXAMPLE 14-12 ESTIMATE Star radius. The giant star Betelgeuse emits radiant energy at a rate 104 times greater than our Sun, whereas its surface temper- ature is only half (2900 K) that of our Sun. Estimate the radius of Betelgeuse, assuming e = 1. The Sun's radius is rs = 7 x 10 m. APPROACH We assume both stars are spherical, with surface area 4mr². SOLUTION We solve Eq. 14-6 for A: (Q/t) 4mr² = A= EOT Then (Q/1) B T (Q/t)s Ti (10¹) (2¹) = 16 x 10. r3 Hence 16 x 10¹ rs = (400) (7 × 108 m) 3 x 10¹ m. If Betelgeuse were our Sun, it would envelop us (Earth is 1.5 x 10¹ m from the Sun). =