Appendix 4

# Pentagram of Venus

This is the diagram on the zodiac that Venus makes in eight years. After that period, Venus, the Sun, the Earth and the stars are again in the same relative positions. It means that Venus, seen from the Earth, is in the same position with respect not only to the Sun, but also to the stars. This happens because five periods of Venus take eight years (When we round Venus' synodic period to a whole number 584, we can calculate that 584x5=2920 days, 2920/365 = 8 years). Take a particular point in a synodic revolution of Venus, for instance the greatest elongation east which places it in one zodiacal constellation. After an interval of 584 days (or nearly 19 months) later, greatest elongation east will take place again, this time almost seven constellations away. These events repeat every nineteen months and the result is that in eight years the eastern elongation point will return close to the point where it started - only about two degrees less - making a pentagram on the zodiac .

Dynamic "human" models of the pentagram of Venus
This situation can be modelled with a simulation activity in a large outdoor area. The focus is on the position of Venus with respect to the Sun and the zodiacal constellations. (pentagram picture No. 3) Two students move simultaneously along the orbits of Venus and the Earth (large concentric circles divided into 7 and into 12) for 19 steps or months (= 1 cycle), repeated five times. At each cycle, the Earth goes 7 steps ahead (19 steps modulo 12); Venus goes 5 steps (19 steps modulo 7). For an observer on the Earth, after five cycles (5 by 19 months = 8 years), Venus has the same position with respect to the Sun and the zodiacal constellations. In eight years Venus has made 13 revolutions around the Sun (8 years/224 days = 13 times) and the Earth eight. The pentagram can be highlighted with coloured string (link picture No. 4)

Back to the Educational sheet 1.