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Mother body problem

  • Anton Savin
  • Boris Sternin
Chapter
  • 869 Downloads
Part of the Frontiers in Mathematics book series (FM)

Abstract

This chapter is devoted to the following problem. Given an external gravitational field, produced by some body, there arises the question of determining the form and mass density of this body. Similar problems appear in geoprospecting, where one measures the gravitational field on the ground surface and wants to determine the source of this gravitational field located inside the earth. Clearly, the solution of this problem is not unique. For example, it has been well known since the time of Newton that a ball with constant mass density produces the same gravitational field as the same mass concentrated at the center of the ball.

Keywords

Singular Point Mass Density Integral Curve Integral Curf Real Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Anton Savin
    • 1
    • 2
  • Boris Sternin
    • 1
    • 2
  1. 1.Department of Applied MathematicsRUDN UniversityMoscowRussia
  2. 2.Institut für AnalysisLeibniz Universität HannoverHannoverGermany

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