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The inverse planetary problem: a numerical treatment

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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.

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

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

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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

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