My name is Merrick Sims and I come from a long line of hotelkeepers on my father’s sideof the family and on an equally long line of farmers on my mother’s side. So there is not much in my family history to indicate why I want to publish a paper on “The Dynamics of a Two Mass System”.
Why then, do I want to publish one?
Well, I first became interested in this matter, when by chance I realised that Newton ’s inverse square law, when applied to his theory of gravitation did not correctly predict the measured heights of tides in the ocean. I wanted to get to the bottom of this apparent anomaly.
I had studied science at Sydney University in the years immediately after the war but I then went home and ran my family ’s hotel, because my father had been killed in an accident and I was the only one of my siblings even marginally old enough to legally run such a business. However,this did not prevent me from continuing my studies, andwhile running the hotel, I obtained a diploma in “Advanced Engineering Mathematics” from International Correspondent Schools.
Thus, I was not totally bereft of the mathematical knowledge necessary for an attack on the above problem, which I commenced in my spare time at night, about 50 years ago.
I noted that Newton had based his gravitational theories on Kepler’s three laws of planetary motion, which that great man had developed about 70 years before hand, by studying the con-focally related elliptic motions of the sun with the three planets:-Venus, Mars and Jupiter. Here Kepler implicitly made two of what I consider to be, the most serendipitous discoveries in science. These were: [1] The paths of the planets are ellipses with the sun at one focus and [2] The planets’ rotational KEs are inversely proportional to their radius of rotation. My conclusions are largely derived from these two discoveries, taken as working hypotheses.
I Soon realised, that to get anywhere with my problem, I would need to greatly increase my already considerable, knowledge in the discipline of conics and I was surprised to find that there was little in the literature of that field that I did not already know. I therefore decided that my first job was to begin investigation in the realm of conics myself and the result of these extra investigations greatly facilitated the production of the work to be published.
In this, I have attempted to establish the principles by which two masses react and move relative to each other, when they are in the same vicinity. I have found that even when only two masses are being considered, the problems to be solved are quite considerable, so this paper has been limited to examination of the case of two masses. Another paper analysing more complicated situations is anticipated for the future.