Given the assumptions...
Posted by bobbapink on Mar 09, 2002 at 10:16
(207.172.209.190)Re: High school science problem (Amaranth Rose)
First, my only problem (i think) was this...
Satellites are mechanized so that they can redirect retransmissions in absolutely any direction.
That's different than omnidirectional but since you didn't give me the maximum possible coverage of the satellites, I’ll assume you meant omnidirectional. I’m not sure I could do it otherwise anyway.
First we’ll need three geosynchronous equatorial satellites separated by 120 degrees each. Then we’ll need three more polar satellites also separated by 120 degrees to reach the very small polar regions the equatorial satellites can’t quite see due to the planet’s curvature. That's 6 total. My reasoning is as follows.
Since the geosynchronous orbiting distance of this earth-like planet, ~22,000 miles, is greater than the diameter of the planet, 8000 miles, each of the six satellites will always an unobstructed line-of-sight view with the other five. At the given the latitude, and regardless of the longitudinal position with regards to the satellites, the Planet-based transmitting station will enjoy a line-of-sight view with at least two satellites; one on the equatorial course and one on the polar course. So now everybody can talk to everybody outward toward the universe and inward toward the planet.
If you had allowed me a lower frequency, one with a wavelength greater than the radius of the small polar area missed by the equatorial satellites, I could ‘a done it with three, or even two for that matter.