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<p>We construct an estimator for gravitational potential on an irregular closed surface as a finite spherical polynomial, based on a finite number of sample observations. This estimator is a natural discrete adaptation of an approximation for gravitational potential suggested by Sanso and Sideris. We consider the following discrete analogue of their conjecture: that the error in our estimator is a contraction operator, implying that the estimation process can be iterated to approximate gravitational potential to arbitrarily levels of accuracy. We then offer evidence for the conjecture through a series of numerical simulations and conclude with a simulation using a model of the Earth’s topography and real-world data.</p>

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A discrete contraction conjecture for estimating gravity fields on irregular closed surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Crichton Ogle,
  • Michael Bevis,
  • Dena Asta,
  • Dean Ogle,
  • Jim Fowler

摘要

We construct an estimator for gravitational potential on an irregular closed surface as a finite spherical polynomial, based on a finite number of sample observations. This estimator is a natural discrete adaptation of an approximation for gravitational potential suggested by Sanso and Sideris. We consider the following discrete analogue of their conjecture: that the error in our estimator is a contraction operator, implying that the estimation process can be iterated to approximate gravitational potential to arbitrarily levels of accuracy. We then offer evidence for the conjecture through a series of numerical simulations and conclude with a simulation using a model of the Earth’s topography and real-world data.