On the Errors of spherical Harmonic Developments of Gravity at the Surface of the Earth.

Abstract

The spherical harmonic expansion of the external gravity field of the earth is divergent at the surface of the earth. From the practical point of view a truncated series can be used if the errors are small. The errors are of two types: the truncation error and the downward continuation error. This report investigates the latter, which is caused by the disturbing topography above the point where the series is developed. This error is studied for potentials, gravity anomalies and for the vertical gradient of gravity. It is shown that the usual relation between the spherical harmonics of T and del(Delta (g) del(r) is also valid for their errors, while the relation between T sub n and Delta (g sub n) does not hold for the downward continuation errors. The relative errors of Delta (g) are found to be more serious than those for T.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1977
Accession Number
ADA052713

Entities

People

  • Lars Sjoeberg

Organizations

  • Ohio State University

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Boundary Value Problems
  • Coefficients
  • Computations
  • Continents
  • Convergence
  • Earth Models
  • Elevation
  • Ellipsoids
  • Geodesy
  • Gravity
  • Gravity Anomalies
  • Models
  • New York
  • Sea Level
  • Spherical Harmonics
  • United States

Fields of Study

  • Physics

Readers

  • Approximation Theory.
  • Space Exploration and Orbital Mechanics.