By Neil., . Ashby
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Additional resources for AN EARTH-BASED COORDINATE CLOCK NETWORK
Weber, General Relativity and Gravitational Waves, Interscience Publishers, Inc. New York (1961). 42,  R. Schlegel, h e r . J. Phys. [ 51 Schlegel's expression for this discontinuity contains an error.  C. W. Misner, K. S. Thorne, and J. A . Wheeler, Gravitation, W. H. , San Francisco, p . 596 (1973).  F. K. Manasse and C. W. Misner, J. Math. Phys. [81 B. Hoffman, Phys. Rev. [ 91 M. Caputo, The Gravity Field of the Earth, Academic Press, New York, p. 32 (1Y67). [lo) G. D. Garland, The Earth's Shape and Gravity, Pergamon Press, New York (1Y65); R.
H. , San Francisco, p . 596 (1973).  F. K. Manasse and C. W. Misner, J. Math. Phys. [81 B. Hoffman, Phys. Rev. [ 91 M. Caputo, The Gravity Field of the Earth, Academic Press, New York, p. 32 (1Y67). [lo) G. D. Garland, The Earth's Shape and Gravity, Pergamon Press, New York (1Y65); R. H. Rapp, Geophys. Res. Letters 1, 35 (1Y74). Ll] W. J. Cocke, Phys. Rev. Letters 16,662 (1966); 779 (1966); 1233 (1966). , 32nd Edition, p. 2508 (1954). 121,337 p. 183 (1974). 4, p . J35 (1963). (1961). b31 Note that this equation does not take account of the redefinition o t coordinateclock rates mentioned in connection with Equation (77).
Then . on the surface which is +. Write + and c$ C . We have so and hence s . = (1-f)'C Since the equation of the ellipsoid is 2 2 X + E = l 2 2 al a3 we obtain 2 2 C cos 9 2 a 1 4 2 2 (1-f) C sin Q = 2 a3 + or Now we may write the coordinates of P as Then r 2 = x2 + Y 2 and after some algebra, we find that retaining only first-order corrections to in flattening and altitude, r 2 al - alf sin2 4 30 + h a 1 Also, neglecting altitude corrections which can be shown to be of order and hence negligible, we find for t h e polar angle COS 2 0 = Y2 7 2 2 2 sin $I (1-4f cos $1.