The invisible area
There are 12 fully spherical planets all of same radius 6000km in any random configuration in some gifted stellar system. Let be the solid angle contained by the part of the planet ,which is not been seen from any other planet or fully hidden from all other 11 planets. Then find out the value of
.
The answer is 12.566.
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1 solution
This is only a partial solution, because it assumes that the problem statement is correct. We are not given any information about the configuration of the solar system, so assume that all the planets are in a straight line. Planet 1 and Planet 12 are each half invisible, and planets 2-11 are entirely visible. So a full planetary surface is invisible, in total. This corresponds to 4 π steradians.