ABSTRACT THE Earth's gravitational potential is usually expressed as a double infinite series of spherical harmonics. Analysis of thousands of photographic and laser observations of

satellites, together with gravity measurements has yielded global models of the geoid1–3 accurate to about 3 m on average. The harmonic coefficients have been evaluated complete up to degree

and order 16 in the Goddard Earth Models (GEM) 4 and 6 (refs 1 and 2), and up to degree and order 18 in the Smithsonian Standard Earth III(SSE)3. Models currently being evaluated will

extend to degree 25 (D. E. Smith, personal communication). Although these comprehensive global solutions give the overall geoid shape or gravitational field quite accurately, the individual

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Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS MULTIPOLE EXPANSION OF INTEGRAL POWERS OF COSINE THETA Article Open access 18 November 2020 STABILITY ANALYSIS,

\(\:{\VARVEC{\PHI\:}}^{6}\) MODEL EXPANSION METHOD, AND DIVERSE CHAOS-DETECTING TOOLS FOR THE DSKP MODEL Article Open access 21 April 2025 HIGH-ORDER ASYMPTOTIC METHODS PROVIDE ACCURATE,

ANALYTIC SOLUTIONS TO INTRACTABLE POTENTIAL PROBLEMS Article Open access 20 February 2024 REFERENCES * Lerch, F. J., Wagner, C. A., Putney, B. H., Sandson, M. L., Brownd, J. E., Richardson,

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Report_, 73170 (1973). * Wagner, C. A., and Klosko, S. M., _Goddard Space Flight Center Report_, X-592-73-279 (1973). Download references AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Royal

Aircraft Establishment Farnborough Hampshire, UK D. G. KING-HELE, DOREEN M. C. WALKER & R. H. GOODING Authors * D. G. KING-HELE View author publications You can also search for this

author inPubMed Google Scholar * DOREEN M. C. WALKER View author publications You can also search for this author inPubMed Google Scholar * R. H. GOODING View author publications You can

also search for this author inPubMed Google Scholar RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE KING-HELE, D., WALKER, D. & GOODING, R.

Fifteenth-order harmonics in the geopotential. _Nature_ 249, 748–750 (1974). https://doi.org/10.1038/249748a0 Download citation * Received: 04 March 1974 * Issue Date: 21 June 1974 * DOI:

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