Abstract
The three-body problem is Sir Isaac Newton’s problem. It is not only an academic problem, but a serious problem, affecting the whole existence of mankind. Nobody before Newton had thought of it, but as soon as it dawned on Newton, he started to work on it feverishly, even though it gave him a head ache (Fig. 2.1).
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Notes
- 1.
You may think that the Earth exerts greater attraction to the Moon than the distant Sun. Actually, the reverse is the case—Sun’s gravitational influence on the Moon is more than double the influence of the Earth. So the question appears: Why doesn’t the Moon fall into the Sun?
We should remark on the beautiful coincidence of sizes and distances: diameter of the Moon is approximately 1/400 of the Sun’s, the Moon’s mean distance is 1/389 of the Sun’s. Thus the Moon and Sun are nearly same size as seen from the Earth. Because of the ellipticity of the Moon’s and Earth’s orbits, during the solar eclipse the Moon can be seen a little bigger than the Sun (in this case we observe a total eclipse), or a little smaller (in this case we see an annular eclipse). Total eclipses occur slightly less often than annular.
- 2.
Quantum mechanics was a new formulation of mechanics which was developed to explain phenomena at the atomic level where Planck’s constant is the suitable measure of action. The development was initiated by the Dane Niels Bohr (1885–1962), who created a model for an atom where light electrons orbit around heavy atomic nuclei. The model had resemblance to the Solar System with the heavy Sun at the center and light planets going around it. However, it soon became obvious that Newton’s rules did not apply. The new rules were generated in a rush around 1925 by Germans Werner Heisenberg (1901–1976) and Max Born (1882–1970) as well as Austrian Erwin Schrödinger (1887–1961) and others. One of the essential features of this model is that bodies are represented by probability waves. These waves can interfere with each other, sometimes amplifying each other, sometimes cancelling each other. Where the wave is strong, there the particle is likely to be. The statement where the body actually is loses significance, except when its position is actually measured. Thus a particle going from point A to point B is not located anywhere in particular until it comes to B where it is found by a detector
- 3.
The story of the 1905 miracle is told in many places, e.g., in Walter Isaacson “Einstein. His Life and the Universe.” (Simon & Schuster, New York 2007).
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Valtonen, M., Anosova, J., Kholshevnikov, K., Mylläri, A., Orlov, V., Tanikawa, K. (2016). From Newton to Einstein: The Discovery of Laws of Motion and Gravity. In: The Three-body Problem from Pythagoras to Hawking. Springer, Cham. https://doi.org/10.1007/978-3-319-22726-9_2
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DOI: https://doi.org/10.1007/978-3-319-22726-9_2
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