Question

Temperatures on planets. To a good approximation, stars and planets emit their energy like a black body, which means the energy flux (energy per unit area and per unit time) at the solar surface (radius R_s = 7 times 10^8 m) is given by F = sigma_SBT^4, where sigma_SB = 5.67 times 10^8 W m^-2 K^-41 is the Stefan-Boltzmann constant. [Remember, energy per unit time is power and it- is measured in watts (1 Js^-1 - 1 W).] (i) Using T = 5778 K for the Sun, compute the energy flux at the solar surface and at a distance r = 1AU 1.5 times 10^11 m. (ii) The cross-sectional area of the Earth is pi R_E^2, where R_E 6 times 10^6 m is tin- Earth radius. (Don't worry about more than just the first or second significant, digit.) How much power does the Earth receive from the Sun? How much more is this than tin; average consumption in the world, which is 10^13 W? (iii) Next, lake into account that 30% is reflected (e.g., by clouds and ice). What is now the power received by the Earth? (iv) How much power does the Earth emit on average at its surface, assuming an average temperature T = 300 K? (v) Compare your answers from parts (ii) and (iv). Explain why the Earth appears to release more power than it receives from the Sun. (vi) Apply the formula derived in Lecture 9 (page 51 of Lectures 8+9) to estimate the average temperatures on Venus, Earth, Mars, and Titan, assuming A = 0 for the albedo (nothing is reflected). (vii) Using the equation from page 48 of the lecture slides, repeat your temperature calculation for the Earth using 0.3 as a value for the albedo, A. Compare your answer to the value of 300 K assumed in part (vi) by what factor is your temperature enhanced/diminished? (viii) Finally, let's look at Venus. Compare your calculated temperature for Venus in part (vi) to the actual surface temperature of 730 K. By what, factor is your estimate for the Venusian surface temperature enhanced/diminished compared to the real world Venusian temperature?

Answer all parts except the ones refering to lecture slides.

Answer 1

1) af a distante ao (jっ