Can the eccentricity of a planet's orbit be found just from the analemma of its star? We can draw an analemma given the axial tilt and eccentricity, but how do we find the reverse?
Note: I already know that the highest and lowest points indicate the amount of axial tilt

  • $\begingroup$ In theory, yes, assuming things like precession and tidal friction are ignorably small. Quoting en.wikipedia.org/wiki/Equation_of_time, "The equation of time is the east or west component of the analemma", so using the east/west change in the analemma, you could find the equation of time. The equation of time itself depends on two factors: eccentricity and orbital tilt. Since you already know orbital tilt from the analemma's height, you can factor it out and thus find the eccentricity. $\endgroup$ – user21 Jun 30 '19 at 3:41
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    $\begingroup$ This is a really interesting question! It may be easier if the analemma is really produced as a series of photographs at the same mean solar time each day, then the spacing between each solar position and the next will give some information about the speed of the orbit. For a highly eccentric orbit, you will have a large number of overalpping sun exposures near aphelion, and much wider spacing near perihelion. $\endgroup$ – uhoh Jun 30 '19 at 8:50
  • $\begingroup$ @uhoh how do I process that information into something numerical? $\endgroup$ – Arnab Chowdhury Jul 1 '19 at 16:08
  • $\begingroup$ @barrycarter could you please elaborate your process $\endgroup$ – Arnab Chowdhury Jul 1 '19 at 16:09

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