Venus is currently in the western sky in the evenings.  It had a close encounter with Mercury.  Here Mercury is just over a degree above Venus, photographed on August 17th, 2016.

VenusMercury07172016

I followed Venus through its Eastern elongation at the end of 2016 and into 2017.  I already have results for two Eastern and two Western elongations, and they contain enough information for me to take a stab at finding the eccentricity of its orbit.  The four previous distances from the Sun that I have measured are 0.7277, 0.7188, 0.7225, and 0.7203, all in astronomical units.  I am hoping the uncertainties are a few in the last decimal place.  What I would really like to do is to measure the distance of Venus from the Sun at perihelion or aphelion, but I have no control over this.  All I can do it keep on measuring the distances at maximum elongations and hope that sooner or later one of them falls close to aphelion of perihelion.  Obviously, the numbers to look at are the largest and smallest values. My best estimate (see chapter 16 of the book) for the semi-major axis, a, is 0.72333 ± 0.00006.  If I combine this with the first of my values, assuming Venus was at aphelion, I calculate an eccentricity of 0.0060.  The smallest of my values is 0.7188.  If I suppose Venus was at perihelion for this elongation, I calculate an eccentricity of 0.0063.  These are encouragingly close and I can certainly treat 0.0063 as a lower bound on the eccentricity.  What I am hoping to do this time is to continue the measurements until Venus goes into its retrograde motion.  I have never done that previously.