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The statistics of the gravitational field arising from an inhomogenous system of particles

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A. Del Popolo (1, 2) M. Gambera (1, 3) ((1) Istituto di Astronomia dell'Universita di Catania, Catania, ITALY (2) Facolta di Ingegeneria, Universita Statale di Bergamo, Bergamo, ITALY (3) Osservatorio Astrofisico di Catania
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CNR-GNA, Catania)x

Astrophysics · Submitted 27 Oct 1998

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction.

how it is stated · asserted 0.98 read the record →

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arXiv IDastro-ph/9810435 (version 1)
Pith ID5VCPWEGN, Pith's permanent record of this paper and its review
Citation2) M. Gambera (1, 3) ((1) Istituto di Astronomia dell'Universita di Catania, A. Del Popolo (1, Bergamo, Catania, Catania)x, CNR-GNA, ITALY (2) Facolta di Ingegeneria, ITALY (3) Osservatorio Astrofisico di Catania, Universita Statale di Bergamo. "The statistics of the gravitational field arising from an inhomogenous system of particles." arXiv:astro-ph/9810435 (1998). https://pith.science/paper/5VCPWEGN
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,992 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.37 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W({F},dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. contribution 0.87 0.80 0.07 asserted 0.95
s1 We derive a distribution function W({F},dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. contribution 0.67 0.97 0.20 asserted 1.00
s2 We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction. contribution 0.72 0.96 0.18 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we extend Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W({F},dF/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by dF/dt. We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction.

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References
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1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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