Venus years - An explanatory note
                                       
   by

Michael G. Reade

   Modern practice is to analyse planetary motions in terms of
   conjunctions and oppositions with the sun but these are seldom
   directly observable, due to the glare of the sun, and the ancients
   substituted observable 'heliacal risings' for 'conjunctions'. Heliacal
   rising implies simultaneous rising of the sun and a planet (or star).
   By definition, if two celestial bodies are in perfect conjunction,
   they must also rise and set simultaneously.

   There are complications which slightly modify this idealised equation.
   Firstly, the modern convention is that conjunction occurs when two
   bodies have the same celestial longitude but 'perfect conjunction'
   requires them also to have the same declination (or ecliptic
   latitude), which is seldom the case in practice. In practice, eclipses
   of the sun by the moon are the only directly observable conjunctions
   of a planet with the sun. A total eclipse occurs when both have the
   same longitude and declination. A partial eclipse can occur if the
   moon's declination is marginally different from the sun's; the moon is
   also close enough to the earth for its apparent declination to vary
   slightly when viewed from different locations.

   Conjunctions of Venus (and Mercury) with the sun can occasionally be
   observed directly but only with the help of observing equipment to
   reduce the glare of the sun. This may have been unknown to the
   ancients (although it is surprising that finds of tinted glass, or an
   equivalent glare suppressing device, appear never to have been
   reported at archaeological observatory sites - close observation of
   the sun is frequently all but impossible without the help of this).
   The ancients could have observed such planetary conjunctions (or
   eclipses) on occasion but they might not have recognised them for what
   they are, as the observations would not be easily distinguishable from
   sunspot observations.

   The ancients do not appear to have appreciated that an eclipse of the
   sun, whether by the moon or a planet, is really only a special case of
   the heliacal rise phenomenon. Secondly, 'imperfect conjunctions' at
   which there is a difference of declination between the planet and the
   sun are much more common than 'perfect' ones, occasionally even
   causing heliacal rising to occur before conjunction instead of after
   it, as is more usual. Event 1 of the Ninsianna tablet record is one of
   those at which conjunction (= equality of longitudes) occurred after
   heliacal rising and thus at a time when Venus was recorded as being
   visible.

   It appears to have been common in ancient times to date the start of
   the year by the heliacal rising of Sirius, which occurs once per year
   (at a time of distinctly different declinations of the Sun and
   Sirius). When Venus became noticeably more conspicuous than Sirius,
   however, it seems some people substituted the heliacal rising of Venus
   for that of Sirius as the marker of the start of the year. The
   interval between successive heliacal risings of Venus averages about
   292 days (very close to 10 months of 29.5 days) but it varies widely
   from year to year; it is affected not only by the brightness and the
   declination of Venus but also by the orbital eccentricities of Earth
   and Venus.

   In short, heliacal rising was the ancients' equivalent of our modern
   concept of conjunction; Venus years were those in which heliacal
   rising of Venus was seen as the marker of the start of the year.