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Advance of perihelion
1. R. Resnick, D. Halliday, and K. S. Krane, Physics, 4th ed. (Wiley, New York, 1992), Vol. 1.
2. R. Resnick, D. Halliday, and K. S. Krane, Physics, 5th ed. (Wiley, New York, 2002), Vol. 1.
3. R. Wolfson and J. M. Pasachoff, Physics for Scientists and Engineers, 2nd ed. (HarperCollins, New York, 1995).
4. J. R. Taylor, C. D. Zafiratos, and M. A. Dubson, Modern Physics for Scientists and Engineers, 2nd ed. (Pearson Prentice-Hall, Upper Saddle River, NJ, 2004).
5. J. A. Coleman, Relativity for the Layman: A Simplified Account of the History, Theory, and Proofs of Relativity (Macmillan, New York, 1959).
6. A. S. Eddington, Space, Time, and Gravitation: An Outline of the General Relativity Theory (Harper, New York, 1959).
7. L. Brillouin, Relativity Reexamined (Academic Press, New York, 1970).
8. L. Fang and Y. Chu, From Newton's Laws to Einstein's Theory of Relativity, translated by H. Huang (Science Press, Beijing, 1987).
9. C. M. Will, Was Einstein Right?: Putting General Relativity to the Test (Oxford U.P., Oxford, U.K., 1988).
10. R. Wolfson, Simply Einstein: Relativity Demystified (Norton, New York, 2003).
11. R. Stannard, Relativity: A Very Short Introduction (Oxford U.P., Oxford, U.K., 2008).
12. W. Isaacson, Einstein: His Life and Universe (Simon and Schuster, New York, 2007).
13. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).
14. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
15. B. F. Schutz, A First Course in General Relativity (Cambridge U.P., Cambridge, U.K., 1985).
16. T. L. Chow, General Relativity and Cosmology: A First Course (Wuerz Publishing, Winnipeg, 1994).
17. J. B. Hartle, Gravity: An Introduction to Einstein's General Relativity (Addsion-Wesley, San Francisco, 2003).
18. M. P. Hobson, G. P. Efstathiou, and A. N. Lasenby, General Relativity: An Introduction for Physicists (Cambridge U.P., Cambridge, U.K., 2006).
19. T. P. Cheng, Relativity, Gravitation and Cosmology: A Basic Introduction (Oxford U.P., Oxford, U.K., 2010).
21. M. P. Price and W. F. Rush, “ Nonrelativistic contribution to Mercury's perihelion precession,” Am. J. Phys. 47, 531–534 (1979).
26. N. T. Roseveare, Mercury's Perihelion: From Le Verrier to Einstein (Clarendon Press, Oxford, U.K., 1982).
27. R. Baum and W. Sheehaan, In Search of Planet Vulcan: The Ghost in Newton's Clockwork Universe (Plenum, New York, 1997).
31.This is analogous to a simple harmonic oscillator with natural frequency 1 and responding at the driving frequency m.
32.This is analogous to a simple harmonic oscillator driven at resonance, and responding with secular terms.
33.It will be seen below that as , so is finite.
35. T. M. Brown et al., “ Inferring the sun's internal angular velocity from observed p-mode frequency splittings,” Ap. J. 343, 526–546 (1989), cited by Hartle (Ref. 17).
36.Whether Pluto is regarded as a planet is irrelevant.
37. I. S. Gradyshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York and London, 1965).
38.This is evidenced by the first-order expansion in in arriving at their Eq. (10).
39.In our formalism and in that of Stewart,22 it does not matter whether the expansion is carried out around or , since all terms are kept.
40.When only one planet is discussed, there is the freedom to change , , so only enters but not . But when is already defined by the orbit of one planet, this freedom is no longer available to change the sign of for another planet, so corrections will enter to .
41.A sum over different planets i is understood.
42.See, e.g., J. D. Jackosn, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 92, Eq. (3.38) and p. 102, Eq. (3.70).
43.Heliocentric longitudes on 1 January 1960 are found from <http://cohoweb.gsfc.nasa.gov/helios/planet.html>: for the perihelion of Mercury, and , respectively for the longitudes of Uranus and Neptune. Within the approximation of circular orbits for the perturbing planets, the latter two are calculated at other times by assuming a uniform rate of change according to the known periods.
44.This situation is not axiomatic. One can imagine a hypothetical system where for Venus.
45.Replacing the finite difference by a derivative in N is justified only for those terms with .
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