In 1943, Antoine de Saint-Exupery wrote a children\'s novella called (in English
ID: 153109 • Letter: I
Question
In 1943, Antoine de Saint-Exupery wrote a children's novella called (in English) "The Little Prince," about a prince that lived on asteroid B612 and visited Earth. Asteroid B612 is now a real place, being an asteroid that was named after the fictional asteroid in the story. This asteroid is at times 2.3 times further from the sun than is the Earth from the sun. At this distance, the solar constant is W/m2 on Asteroid B612. (If you collaborate on this problem, be sure to answer your problem, not your collaborator's problem. They are likely to be subtly different)Explanation / Answer
The mathematical relation between Solar constant and Distance of any object from sun is given by
Solar constant = Esun / 4 * 3.14 * r2 , where Esun i.e total energy of sun's surface = 3.85 * 1026
[ Esun could be calculated by Stephan Boltzmann law i.e M = sigma * T4 Tsun = 5777 K and M = 5.67 * 10-8 W/ m2 K4 , Energy at an unit area = 5.67 * 10-8 * (5777)4 = 6.31 * 107 W/m2 Now multiply this with total surface area sun i.e Esun = 6.31 * 107 * 4 * 3.14 * Rsun2 = 3.85 * 1026 W]
Now distance of Asteroid B612 = 2.3 * A.U = 2.3 * 1.495 * 1011 = 3.438 * 1011 m
Therefore Solar constant = 3.85 * 1026 / 4 * 3.14 * (3.438 * 10 11)2 = 3.85 * 1026/ 148.46 * 1022
Solar ConstantB612 = 0.0259 * 104 = 259 W/m2