The sun, like any star, can be treated as a black body emitter. the sun has a surface temperature of 5778°k and a radius of 6.963x105 km. the earth orbits at a radius or 1.496x 108 km from the sun (this distance is called one astronomical unit (au) (a) calculate for the sun the total irradiance at the sun's surface, total radiant flux, and light intensity at the earth's orbit (the intensity on the earth if there was no atmosphere). (3 marks) (b) from these values you can find the expected average surface temperature for the earth if there was no atmosphere by assuming the total energy landing on the earth is that received by the disk of the earth. assume that the earth has a reflectivity of 0.306 (called the albedo) so that only 0.694 of the light heats the earth. all this energy landing on the earth is radiated by the sphere of the earth acting as a black body emitter (emissivity is 1). the average temperature of the earth is when the energy landing from the sun equals the black body light radiated from the planet. calculate this for the earth. note this value is lower than the actual average earth temperature is 288 °k due to the green house effect of the earth's atmosphere stopping part of the black body radiation. how much warmer is the earth than the simple black body calculations says? (earth radius = 6371 km). (3 marks) (c) extrasolar planets are being discovered around other stars nearly every day. however what if observations showed that what they thought was a planet was really an alien megastructure - a huge planet sized rectangular block (maybe a borg ship) here is the actual data found but now treat it as a rectangular box. the star beta pic is a class a6v star with a surface temperature of 9790°k and a radius of 1.09 that of the sun's radius. the alien megastructure beta pic b orbits about this star at a distance of 8.38au (ie units of the earth orbital radius) and is a block with a square cross section on the ends with each side length l 13.07 times of that of earth diameter, while having a rectangular shape l by 3l on four of the sides. the square top face is aligned parallel to orbital plane, but one surface keeps an angle of 57.5° relative the light from the sun. the long faces are perpendicular to the orbital plane. you are to find out what are the following conditions for this star and rectangular box (i) repeat part (a) for this star and the alien structure. how much energy does the star radiate relative to the sun? how strong is the star light at that megastructure relative to that you calculated for the earth. (3 marks) (ii) repeat part (b) for this alien rectangular box. what do you expect the average surface temperature to be and how does this differs from earth's. in this case assume that the reflectivity of the cube material is 0.500 but the emissivity is effectively 1 over the entire spectrum.