Calculate the solar constant 1. [10 points.] Please calculate the solar constant for the Earth (i.e., the intensity of solar radiation in W/m?) given that the sun emits 3.87 x 1026 W and the Earth's average distance from the sun of 148 million km. Hint: think about spreading the radiation that far out in all directions from the sun (you'll need to calculate the surface area of a sphere, 4nr?). Earth's equilibrium temperature without an atmosphere 2. [15 points.] Using this solar constant, please calculate Sunlight Earthlight what the Earth's equilibrium surface temperature would be if we didn't have an atmosphere. Remember that to be in energy balance the Earth has to emit as much radiation to space as it absorbs from the sun, and the amount of Tenilab Mice da radiation an object emits = F = of' (where 7 = temperature in kelvin and o = 5.67 x 10-8 (W/m?)/K*). Remember, you'll need to account for (1) the fact that the sun shines on the Earth as if it were a disc (with the area of a circle = mr?), but that the solar energy is distributed around the planet's entire surface area (which has the area of a sphere = 4nr?), and (2) that the Earth has an albedo of 0.306 (i.e., it reflects 30.6% of the sunlight that hits it). One-layer atmosphere model 3. [15 points.] Now, let's add a one-layer atmosphere to this ......... Poundery to "pros. . .... model that is transparent to incoming sunlight (solar radiation)- but that absorbs all of the longwave radiation (the "earthlight") emitted by the Earth's surface. Please write equations that define the energy balance for the Earth's surface and for the Earth's single-layer atmosphere and use them to calculate the equilibrium temperature of each. (Hint: please give names to the arrows on the figure at right-such as "up," "down," "in," or "out"-and write equations using these names/terms for the energy balances of the Earth and its atmosphere). 4. [5 point.] The Earth's surface temperature is actually 288 K. What assumptions/simplifications are there in this model?5. [15 points.] Imagine that during a war, Visible Infrared a large number of nuclear weapons are exploded, which kicks up enormous amounts of dust and smoke into the atmosphere. The net result is that the atmosphere now absorbs all visible Dusty atmosphere radiation - so all the solar energy the Earth's absorbs is now absorbed in the atmosphere while the atmosphere also retains its ability to absorb all longwave infrared radiation. Once again, please name the arrows and write equations that define the energy balance for the Earth's surface and for the single-layer atmosphere and then calculate the equilibrium temperature of each. Please assume that Earth's solar constant and albedo remain unchanged. 6. [10 points.] Please explain in words why the temperature changes the way it does after the nuclear war [1-2 sentences]. Is describing this as "nuclear winter" appropriate [1 sentence]? Venus 7. [10 points.] Please calculate Venus's equilibrium surface temperature assuming that it has no atmosphere. Venus is 108 million km from the sun and has an albedo of 0.76. Mars 8. [2 points.] Please calculate Mar's equilibrium surface temperature assuming that it has no atmosphere. Mars is 228 million km from the sun and has an albedo of 0.25. The Greenhouse Effects on Mars and Venus 9. [10 points.] Venus's and Mars's observed surface temperatures are 737 K and 213 K, respectively. What do your calculated temperatures suggest about the strength of their respective greenhouse effects