Just outside the earth's atmosphere, energy from the sun arrives at a rate of 1400 W m ⁻² . The distance separating the sun and the earth is 1.5 10¹¹ m . If the present mass of the sun is 2 10³⁰ kg , determine how long the sun will last assuming a constant decay at this rate.

Step-by-step solution

Total power radiated by the sun is given by P = S 4 R^2 , where S is the solar constant and R is the distance between the sun and the earth. P = 1400 4 (1.5 10¹¹)^2 P = 1400 4 2.25 10²² = 1.26 10²⁶ W The rate of mass decay of the sun is obtained using Einstein's mass-energy equivalence, dm dt = P c^2 . dm dt = 1.26 10²⁶ (3 10^8)^2 = 1.26 10²⁶ 9 10¹⁶ = 1.4 10^9 kg s ⁻¹ The time the sun will last is t = M dm/dt , where M is the present mass of the sun. t = 2 10³⁰ 1.4 10^9 = 1 0.7 10²¹ s 4.55 10²⁰ s Converting the tim