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 . Determine the rate at which the sun is losing its mass.

Step-by-step solution

The intensity of solar radiation at the earth's distance is I = 1400 W m ⁻² . The total power radiated by the sun is distributed over a spherical surface of radius R = 1.5 10¹¹ m . Total power P = I 4 R^2 Substituting the given values: P = 1400 4 (1.5 10¹¹)^2 P = 1400 4 2.25 10²² = 12600 10²² J s ⁻¹ According to the mass-energy equivalence principle, E = mc^2 , the rate of mass loss is: dm dt = P c^2 Using c = 3 10^8 m s ⁻¹ : dm dt = 12600 10²² (3 10^8)^2 dm dt = 12600 10²² 9 10¹⁶ = 1400 10^6 kg s ⁻¹ Taking = 22 7