2021USAAAO决赛第1题

1. (5 points) Jupiter emits more energy to space than it receives from the Sun. The internal heat flux of Jupiter can be quantified by the “intrinsic” temperature of the planet $$T_{int}$$. The effective temperature $$T_{eff}$$ of a planet is related to its intrinsic temperature and equilibrium temperature $$T_{eq}$$ by $$T_{eff}^{4} = T_{eq}^{4} + T_{int}^{4}$$. Given that Jupiter’s albedo is 0.5, its emissivity is 1, its average separation from the Sun is 5.2 AU, and its effective temperature is 134 K, estimate its intrinsic temperature in Kelvin. You may use the Sun’s surface temperature equal to 5777 K.