Paul Christopher PFC Associates, Leesburg, VA
Congratulations to the staff of Wolfram Research on your 25th anniversary.
We were fortunate to see the editorial in the New York Times on the values of Mathematica in 1992.
The symbolic math capabilities caught our eye because we realized how important the MIT symbolic math service was.
We used Mathematica for satellite communication analysis. Unlike another software package which does satellite orbits very well, Mathematica can be used for many kinds of communication analysis: orbit representation and visualization, antenna pattern representation, signal loss in the atmosphere, and frequency optimization.
Mathematica allowed a large-scale view of signal loss in the atmosphere. We saw that key Italian experiments (Barbaliscia, Ka Band Conference, Italy, 1998) produced worldwide attenuation maps at 22.2 GHz and at 49.5 GHz. The former attenuation was largely a function of water vapor attenuation, and the latter a function of cloud attenuation. Mathematica solved the functions simultaneously at all points on the map, to allow attenuation to be closely estimated for all frequencies in the 6 GHz to 94 GHz region (Ka Conference, Taormina Sicily, October 1999). Mathematica later allowed solutions for optimum satellite communications frequencies (Virginia Tech Wireless Symposium, June 2009; Ka Conference Ottawa, October 2012).
With close analysis of Molniya orbits, we were able to see a particular eccentricity that gave effectively stationary orbits over Norway for 6 hours at a time. This analysis yielded a new and useful satellite constellation (a Brandon4 Constellation) at the International Communications Satellite Systems Conference (Proc ICSSC, Edinburgh, Scotland, June 2009).