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Orbital Motion of an Artificial Earth-Satellite. Robert Sprague

The mathematical-physicist C.Lanczos in his book on mechanics prefaces the chapter on the Hamilton-Jacobi Equation by quoting from the Bible, Exodus 3, 5. The equation is so beautiful and profound that it evokes an emotional response to all who use it.

Some months prior to Sputnik I had been contacted by a graduate student in physics working towards his M.S. He was Robert S.Sprague, and I found out later that he had formerly been an infantryman (S/Sgt mortar section leader) in Patton's army and fought in the Battle of the Bulge. He said that he had devised a promising way to determine in analytic form the orbit of an artificial earth satellite, taking the bulge at the earth's equator into account, and that Dr.Dresden had recommended for him to get Storer or me to serve as his thesis adviser. The primary motivation for this work was that during the forthcoming International Geophysical Year 1957-8 there would be attempts to launch an artificial earth-satellite. If successful, then by comparing actual orbital positions (a network of observing stations would be required; indeed, later a K.U. astronomy student actually manned one of these stations) with theoretical ones it would be possible to determine the shape of the geoid with more accuracy than had been achieved previously. Sprague and I discussed his thesis problem in my office, and his suggested approach seemed reasonable, though difficult, to me. A meeting with Dresden was arranged, during which Dresden asked how long it would probably take to work out the solution. Since it involved the Hamilton-Jacobi equation, I would have guessed a few months at least, but to my surprise Sprague answered without hesitation "about two weeks." In any event I was still willing to go along, though with reservations (I was aware of Delaunay's lengthy study of the motion of the moon published in 1860 and 1867), so Dresden approved of the arrangement.

Clearly my rôle was going to be more like a spectator than a participant, though I worked through and checked most of the mathematics. In any event Sprague's derivations went quite smoothly, but simultaneously he had deadlines connected with his final exams in physics. Somehow he finished everything on time (July, 1957), and the next month he presented his thesis results, An Analytical Determination of the Orbital Motion of an Artificial Earth Satellite, at a meeting of the American Astronomical Society held at the University of Illinois (I went along ). In my opinion his thesis easily merited a Ph.D., but he decided against continuing in graduate school.

He obtained a teaching position at Foothill College, CA, and after a successful teaching career is now retired. He applied much modern technology to his teaching, for example, he invented a cosmic ray "telescope" consisting of a muon "filter cube" of lead bricks with scintillation paddles on opposite sides and from which he was able to determine the mean lifetime of the muon (around two micro-secs; a student Ron Sufred assisted in this work). He has acquired several patents for his inventions, and has done much consulting work; for example, even before coming to K.U. he had already developed the design philosophy and bombing systems used in the world's first supersonic bomber (Convair B-58). More recently he modulated a light beam and transmitted a TV-program on a beam of light.

He and his wife, Joan, have developed a unique linguistics system for teaching the American-English language. This project has been twenty years in development, and is called Phonics Plus; the part called "Learning by Association" is original and explains the different depths of learning and paths toward motivation. The two live in Los Altos, CA., and they have one adult son.


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