The mystery associated with the Venusian Dichotomy was probably first termed by Patrick Moore in 1956, though the problem was realised almost one-and-a-half centuries before this. It is also known as the Schröter Effect, being based on the visual discrepancy of the exact observed time of planet’s visual half-phase or dichotomy.
In August 1793, Johann Schröter (1748-1816) had discovered that the observed time of the 50% phase with Venus did not correspond to the predicted time. Schröter saw some phase deformity of the southern limb, which remaining concave, he said, until about eight days before or after each solar conjunction, but later thought this average difference was six days. (Some popular references even still wrongly state eight days.) Modern apparent values, based on several dozen amateur observed dichotomies, now suggest perhaps four days early or later. Differences depend on which side of the particular elongation occurs.
Some strongly suggest that this effect is merely an optical illusion, yet it is odd that the effect is neither aperture, field orientation nor magnification dependant. A possible proof of this optical effect, in what seems a partly unconvincing argument, was presented in Sky and Telescope on August 1994 — exactly 201 years later after the effect was first observed. This suggested this was due to the composition of the Venusian atmosphere. However, any proper causal explanation of this odd effect has yet to be satisfactorily determined.
How dichotomy occurs is very easy to understand using simple geometry. It happens at the time when the planet’s position lies at right angles to the Earth and Sun. This is approximately during the time of maximum elongation, which happens somewhere between elongations of 45° and 47°. One very common misconception is that dichotomy corresponds exactly with the greatest elongation East (or West) of the Sun. This is not quite true, whose simple reason is that the observed disparity is caused by the slightly dissimilar eccentricities of the two independent planetary orbits of Venus and Earth. When Venus has its greatest elongation wither east or west of the Sun, predicted times of the true dichotomy can be either slightly early or later than expected. Often these variations never exceed more than one day, but this is independent of the four-day difference between the observed and predicted dichotomies.
For reasons, which are still uncertain, predicted times of the Dichotomy of Venus or Schröter Effect are never the same as the observed event. Differences average about four to six days earlier or later than expected, depending on the Sun’s side that the morning or evening elongation of Venus (or Mercury) takes placed. For example, an eastern elongation was predicted for the afternoon of 10th June 1999, and this suggests the observed 50% phase will be more like occur on the 4th or 6th June.
HOW to OBSERVE and FIND the DICHOTOMY of VENUS
Finding dichotomy times requires a series of visual observations made during the the middle of the day when the planet is near as possible to the local meridian. If Venus is east of the Sun, this will be around three hours after midday, If Venus is west of the Sun, it is three hours before midday. I.e. At 3pm. or 9am.
Observations must also be made well before and after the predicted date through apertures above 10.5cm or so is required. A summary below is generally useful for amateur astronomers by using the ‘standard’ methodologies when finding the precise time of this event — and this equally applies to Mercury.
PREDICTED DICHOTOMY of VENUS (2003-2023)
Source: J. Meeus, J.B.A.A., 110, 2 (2000)
OTHER DICHOTOMY VARIATIONS
There are also slight differences in the time between the greatest elongation east or west of Venus and the exact moment of the half-phase. These are to do with the orbital eccentricities of both Earth and Venus around the Sun. In some instances the differences can be up to two days. Although this is significant for determining the differences in the time of the observed dichotomy, it does affect the predicted time.
OBSERVED PHASE CALCULATIONS
After finishing each individual or series of observations, move well away from the telescope — preferably in the shade — and measure the width of the brighter and darker parts of the terminator perpendicular to the poles of your drawn disk. Often the terminators are uneven, so draw a very faint line of best fit and measure this width in millimetres. As the disk is 50mm in diameter, calculate the observed phase by;
% Phase = Length of Bright Phase Distance (in mm.) × 2
I.e. If the width is 23.5mm then the phase is 47.0%. If 26.5mm then the phase is 53%, etc. Repeat this procedure each day for several weeks around the time of maximum elongation, and for as many days as possible (Weather permitting.)
OBSERVED DICHOTOMY CALCULATIONS
To calculate the observed time of dichotomy, simply graph the measured phase versus the date expressed in decimal days. This should produce a rough straight line of points. Estimate (or calculate) the “line of best fit” and then draw a thin straight line. Where the axis cuts the 50% line, measure the time from the alternate axis. This is the time of dichotomy, and should be accurate to several tenths of a day — as long as at least eighteen to twenty observations have been made. Naturally, if several different observers do this, the result will be far more precise and will find much better better estimations of the statistical variances.
Differences from dichotomy times (Δt) from the graph is simply;
Δt = Dval − Pval