VENUS : Part 3

The DICHOTOMY of VENUS

The mystery associated with the Venusian Dichotomy was 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 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 did not correspond to what was predicted, stating he saw some phase deformity of the southern limb that remaining concave for up till eight days before or after conjunction with the Sun. He thought the average difference in dichotomy was six days, and some references still wrongly states eight days, though modern values - based on several dichotomies - suggested perhaps four days early or late, depending on the side of the particular elongation. Some suggest that this is merely an optical illusion, yet it is odd that the effect is neither aperture, field orientation nor magnification dependant. A proof, in a partly unconvincing argument of this optical effect was presented in Sky and Telescope August 1994 exactly 201 years later. However, the proper explanation of the cause of the effect has yet to be determined.

The general geometry of how the dichotomy occurs is easy to understand. It is where the inferior planet’s position is at right angles to the Earth and Sun near the time of maximum elongation, and somewhere between 45^o and 47^o. One common misconception is that dichotomy exactly corresponds with the greatest elongation East (or West) of the Sun. This is not true, and the reasons for this disparity are the different eccentricities of the two independent orbits of Venus and Earth. When Venus has its greatest elongation east or west of the Sun, the predicted time of dichotomy can be either slightly early or later. Often these differences 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, the predicted time of the Dichotomy of Venus or Schr#246;ter Effect is never the same as the observed event. This difference averages about four to six days earlier or later than expected, depending on the Sun’s side that Venus (or Mercury) is placed. For example, the eastern elongation was predicted for the afternoon of 10th June 1999, this suggests the observed 50% phase will be more like the 4th or 6th June.

To find the time when the dichotomy occurs, a series of visual observations through apertures above 10.5cm or so is required both before and after the predicted date. Below is a useful summary useful for amateur astronomers by using the ‘standard’ methodologies in 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 eccentricities of the orbits 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. As the disk is 50mm in diameter, calculate the phase by; % Phase = Measured Bright Phase Distance (in mm.) x 2 Ie. If the width is 23.5mm then the phase is 47.0%. If 26.5mm then 53% etc. Repeat this procedure each day for a few weeks around the time of maximum elongation, and for as many days as possible.

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 have been made. Naturally, if several different observers do this, the result will be far more precise and will find better estimations of the variances.

The difference in the time of dichotomy (Δt) from the graph is simply;

Δt = Dval - Pval

Where;
Dval = Date of Observed Dichotomy. (in Decimal days)
Pval = Date of Predicted Dichotomy. (in Decimal days)

** The values for Pval see Table “Predicted Dichotomy 2003-2023“.

NOTE: I am willing to collate any observations to figure out the next dichotomy. Please do not hesitate to contact me if you require any further detailed information or would like to participate in a suitable observing programme.

Last Update : 29 October 2005

Southern Astronomical Delights © (2005)

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