In 2005 astronomers discovered a new object in the outer Solar System, which is now called the dwarf planet Eris. (Eris played a major role in Pluto's being demoted.) You are equipped to understand how Eris's size was first determined. a. Consider a planet with radius Rp at a distance D from the Sun. If L is the luminosity of the Sun, what is the total luminosity incident on the planet? Suppose the planet has albedoWhat is the luminosity Lp reflected from the planet? b. When astronomers first discovered Eris they found it to be D = 97 AU from the Sun and measured its reflected luminosity to be Lp = 5.8 Times 1018 erg s^-1. What does this imply for Eris's minimum and maximum possible size?c. More recently, astronomers measured the infrared light emitted by Eris and found that its spectrum peaks at a wavelength of 116 microns. Is this information sufficient to calculate an effective temperature? If yes, state any assumptions that you have to make, and calculate the temperature. d. Using your results from (b) and (c), is it possible to determine the size of Eris? If yes, how does it compare with Pluto (Rpluto = 1185 km)?