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I have created a celestial mechanical data set for exoplanets with density values (https://github.com/tslever/Tom_Levers_Git_Repository/blob/main/UVA/2--Linear_Models_For_Data_Science/Project_2/Data_For_Exoplanets_With_Density.csv) based on the NASA Exoplanets Archive's Planetary Systems data set (https://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=PS&constraint=default_flag%20%3E0) and Exoplanet Catalog (https://exoplanets.nasa.gov/discovery/exoplanet-catalog/).

Below is a graph of Density vs. Orbital Semimajor Axis. What are your thoughts of normalizing orbital semimajor axis by stellar surface gravity, for example, for the purpose of mathematically aligning a planetary system with Earth's solar system? What insights do you glean from this graph?

What simple and multiple regressions would be valuable with number of stars, number of planets, number of moons, circumbinary status, orbital semimajor axis, radius, mass, density, eccentricity, insolation flux, equilibrium temperature, spectral type, stellar mass, stellar luminosity, stellar surface gravity, and/or type (terrestrial / non-terrestrial)?

enter image description here

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  • $\begingroup$ A cursory visual inspection suggests a relationship of the type y ∝ 1/x might be applicable, but it also depends on how much influence you want to give to the outliers. $\endgroup$
    – Fred
    Nov 11, 2022 at 9:41
  • $\begingroup$ Plot it as log-log... $\endgroup$
    – AtmosphericPrisonEscape
    Nov 11, 2022 at 10:06
  • $\begingroup$ scale it by the power of the surface density of the protoplanetary disc model you prefer. That said, this question does IMHO not allow a right or wrong answer, but would be opinion-based as asked. It's basically a survey question which are not suitable for this site. $\endgroup$
    – planetmaker
    Nov 11, 2022 at 11:16
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    $\begingroup$ Welcome to Astronomy SE! "What are your thoughts...?" questions don't work well in Stack Exchange, and "What insights do you glean...?" should be replaced with "What can be learned...?" to make sure readers understand you're asking for fact-based answers. Can you clarify just what "for the purpose of mathematically aligning a planetary system with Earth's solar system" means? Thanks! $\endgroup$
    – uhoh
    Nov 11, 2022 at 13:34

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