*Sigh* A Picture is Worth a Thousand Wor(l)ds
Posted by Amaranth Rose on Mar 13, 2002 at 17:45
Re: Well, the answers are in (bobbapink)
The planet wants to transmit messages away from itself, to the entire universe. The only messages of interest in this problem are ones that are being sent, as in away.
There is one, and only one, land mass on the planet, located at roughly 45 degrees north latitude. The rest of the world is ocean. There is no stable ice pack, no other surface, no nothing on which to base another transmitter anywhere on the planet itself.
There is one, and only one, transmitter on that land mass.
Amazing how different people have seemingly taken the same question and changed it in such different ways.
The geosynchronous requirement was stipulated in an effort to simplify the problem by allowing the assumption that the satellites stay above the same positions on the surface, thus removing the necessity of calculating perpetually moving targets, a skill well above most High School student without a supercomputer.
Full marks were given for any reasonable, logical answer with adequate supporting logic. My student and I concluded that 2 was too few, and 3 might work adequately. Four in a tetrahedral arrangement with a vertex near the land mass was deemed the most dependable arrangement, because of the equal angles of separation allowing for some redundancy. This was suggested, in part, by the tetrahedral symmetry of the carbon atom, and by the displacement of the land mass from the equator. A land mass nearer the equator might have allowed complete coverage with only three.