[Grand Lodge]
The history of the use of the pentagram clearly shows that this astronomical curiosity is not the source of its perceived occult value.
Venus and the pentagram
The synodic period of Venus, the time required for it to return to the same position relative to the Sun as seen by an observer on Earth, is 583.9211 days. There is a 0.0789 day slippage every 584 days, totalling a one day slippage each 12.67 synodic periods. This means that the pentagram figure is slowly revolving within an oval in a clockwise direction, alternating either one or two points ascendant roughly every 160 years. There is no observation point on Earth that would present a regular pentagram. Moving further north elongates the figure while on the equator the figure is an irregular pentagon.

Compiled by Trevor W. McKeown. Calculations and text reviewed by Dr. Leigh Hunt Palmer.
Above: Plotting the apparent position of Venus in altitude and azimuth as observed from Uruk (Lat. 31°19'00") at the moment of sunrise for consecutive apparitions separated by intervals of 584 days, starting at sunrise, 06:12:07 am, March 23, 716BCE, during the reign of Tiglath-pileser III, near the times of greatest westward elongation of the planet (46.070° - 46.3620°). The Julian Period is noted. The moving light on the horizon is the sun as east is fixed and the seasons vary.
A plotting taken for similar periods running from, or to, January 13, 2003 would show a pentagram with one point down. These figures are not readily available in published form but can be created using software applications such as Starry Night.
Note that Venus is not travelling in a straight line from point to point. The lines are a construct determined by the observer. Any running set of observation times other than those tied to the synodic period of Venus would create a recursive pattern such as that shown below.
Detail from James Ferguson’s, Astronomy Explained Upon Sir Isaac Newton’s Principles, 1799 ed., plate III, opp. p. 67.

