Abstract
Isaac Newton’s notable success in providing a theoretical explanation for the motion of planets around the sun was followed quickly by his realization that the gravitational problem involving three bodies was immensely more difficult than the two-body problem. Where the two-body problem, as we have seen in Chapter 2, can be solved exactly, Newton’s attempts to provide a concise mathematical description of the earth-sun-moon system were not successful.
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Notes
- 1.
Newton’s colleague Edmond Halley remarked that Newton claimed the problem “made his head ache, and kept him awake so often, that he would think of it no more.”
- 2.
The methods due to the Italian/French mathematician Joseph-Louis Lagrange (originally Giuseppe Luigi Lagrangia) and the Irish physicist William Rowan Hamilton form the basis of the next class in mechanics.
- 3.
As we have seen previously, the historical record cannot be deduced from the current attribution. While it is important to understand the historical circumstances of discoveries, science is never conducted in isolation. There are generally several individuals who deserve some credit for each discovery.
- 4.
It is common practice to define the specific impulse \(I_{sp} = v_{e}/g\), where g is the gravitational acceleration at the earth surface. Then the rocket equation is written in terms of I sp in place of v e . This practice led to the loss of the Mars Climate Orbiter in 1999 due to a units conversion issue: NASA presumed I sp to be defined in SI units but the vendor utilized British units.
- 5.
Actually, we will utilize a model system in which we take GM 1 = 1 and do not deal with the earth’s mass explicitly. This will provide us with a test system that embodies many of the issues we wish to study but without the complexity associated with more realistic calculations.
- 6.
Hohmann’s Die Erreichbarkeit der Himmelskörper was published in 1925.
- 7.
Minovitch was a graduate student at the University of California Los Angeles who spent a summer internship working at the Jet Propulsion Laboratory. His work on exploiting gravitational interactions to change spacecraft velocities were detailed in a series of JPL technical reports in 1961.
- 8.
We have consistently used this representation throughout the text. Astronomers historically utilize a different set of coordinates for their measurements that we shall not describe here.
- 9.
The word derives from the Latin resonantia meaning echo.
- 10.
Kirkwood’s “On the theory of meteors” was published in the Proceedings of the American Association for the Advancement of Science in 1866.
- 11.
Gerald Sussmann and Jack Wisdom demonstrated that Pluto’s orbit was chaotic in 1988.
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© 2015 Mark A. Cunningham
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Cunningham, M.A. (2015). VII Celestial Mechanics. In: Neoclassical Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-10647-2_7
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