Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

The inverse planetary problem: a numerical treatment

  • 15 Accesses

  • 2 Citations

Abstract

The so-called “inverse planetary problem” can be stated as follows: given the distances from the centre, masses, and radii of (say) three planets of a planetary system, find the optimum polytropic index, mass, and radius of their star, and also other quantities of interest, which depend either explicitly or implicitly on the foregoing ones (e.g., central and mean density, central and mean pressure, central and mean temperature, etc.). It is hereafter tacitly assumed that the system is opaque with respect to observations concerning periods of planetary otbits; hence, we cannot have any relevant estimates due to the well-known period laws. In the present paper, the inverse planetary problem is treated numerically on the basis of the so-called “global polytropic model”, developed recently by the first author.

This is a preview of subscription content, log in to check access.

References

  1. Chandrasekhar, S.: 1939,Stellar Structure (New York: Dover).

  2. Geroyannis, V. S.: 1993,Earth, Moon, and Planets,61, 131–139.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Geroyannis, V.S., Valvi, F.N. The inverse planetary problem: a numerical treatment. Earth, Moon, and Planets 63, 15–21 (1993). https://doi.org/10.1007/BF00572135

Download citation

Keywords

  • Numerical Treatment
  • Planetary System
  • Polytropic Index
  • Relevant Estimate
  • Polytropic Model