A certain stellar body has radius 50 R s and temperature 2 T s and is at a distance of 2 × 10 10   AU from the earth. Here, AU refers to the earth-sun distance and R s and T s refer to the sun's radius and temperature, respectively. Take, both star and sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

Step-by-step solution

Intensity of radiation of sun on earth or solar constant, S 1 = P 4 π R 0 2 = 4 π R s 2 . σ . T s 4 4 π R 0 2 = σ R s 2 R 0 2 . T s 4 where, R s = radius of sun, R o = radius of orbit σ = Stefan-Boltzmann constant and T s = temperature of sun. Now, intensity of radiation received from steller body on earth's surface, S 2 = σ 50 R s 2 2 × 10 10 R 0 2 . 2 T s 4 ⇒ S 2 = 2500 × 16 4 × 10 20 × σ . R s 2 R 0 2 . T s 4 ⇒ S 2 = 10 - 16 S 1 (from Eq. ( i ) ) ⇒ S 2 S 1 = 10 - 16