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October 2013 Feature: Venus Cycles, the Golden Triangle & the Pentagram


A big milestone awaits for Venus on November 1, 2013, as this planet reaches its greatest eastern (evening) elongation from the Sun. This monumental event happens 5 times every 8 Earth years or 13 Venusian years. Some people may not know what "greatest eastern elongation" means, so let me pause a bit to explain.


Venus' Greatest Eastern (Evening) Elongation


Because Venus orbits the Sun inside of Earth's orbit, Venus appears rather closely tethered to the Sun, as seen from our planet. For instance, Venus can never be opposite (180o from) the Sun in our sky (like the Full Moon), or even be as far as 90o from the Sun (like the half-lit Quarter Moon).


At the end of its tether - at the outer edge of its orbit as seen from Earth - Venus, at most, goes a little over 47o from the Sun. If Venus shines east of the Sun, we see it in the west after sunset; if this world shines west of the Sun, we see it in the east before sunrise. On November 1, 2013, Venus swings 47o 04' east of the sun, exhibiting its greatest elongation in the evening sky.


The Golden Triangle & Venus' Cycles


It is quite uncanny, really. Once you become conversant with the Golden Triangle, you automatically possess the "Rosetta Stone" to Venus and her golden cycles. You can almost do without an astronomical almanac, at least as far as Venus is concerned.


Simply remember that the Golden Triangle is an isosceles triangle with two of its angles = 72o and the third angle = 36o. These two numbers, 72 and 36, give you the means to master Venusian cycles beyond your wildest dreams.


Look at the illustration below to see Venus' orbit inside of Earth's orbit. We're viewing the north side of the solar system plane, whereby the planets revolve counter-clockwise around the Sun. Venus is at its greatest eastern (evening) elongation at left and its greatest western (morning) elongation at right.


Amazingly enough, about 72 days after reaching its greatest eastern elongation in the evening sky, Venus passes in between the Sun and Earth at what's called inferior conjunction. Then 72 days after reaching inferior conjunction, Venus swings out to its greatest western elongation in the morning sky. Yes, remember the Golden Triangle and the number 72!


Diagram of Venus' and Earth's Orbits



Once Again, Remember the Number 72!


Look through the telescope, and you'll see that Venus' disk always displays a half-lit (50% illuminated) quarter phase at the vicinity of its greatest elongation, either in the evening or morning sky. It's a waning quarter Venus in the evening sky and a waxing quarter Venus in the morning sky.


At its greatest elongation, Venus makes a right (90o) angle with the Earth and Sun. The innovative astronomer Copernicus used a greatest elongation and trigonometry to figure out that Venus's distance from the Sun equals 0.72 the Earth's distance from the Sun. Uncanny how that number 72 keeps cropping up!


Don't forget the Number 36!


This may come as a major shock to you, but Venus shines at greatest brilliancy in the evening sky when its disk is approximately one-quarter (25%) illuminated by sunshine. Midway between a greatest evening elongation and an inferior conjunction, Venus is said to be at its "greatest illuminated extent," because this is when the illuminated portion of Venus covers the greatest square area of sky.


It just so happens that Venus reaches its greatest illuminated extent in the evening sky some 36 days after its greatest evening elongation, or 36 days before inferior conjunction. The converse is also true: Venus reaches its greatest illuminated extent in the morning sky about 36 days after inferior conjunction, or 36 days before greatest morning elongation.


Yes, remember the Golden Triangle and the number 36!


Venus & the Pentagram


Venus is oftentimes represented by the Pentagram, which is composed of 5 Golden Triangles. The Pentagram well symbolizes Venus because these Venus' milestones (greatest evening elongation, greatest illuminated extent in the evening sky, inferior conjunction, greatest illuminated extent in the morning sky, greatest morning elongation & superior conjunction) recur 5 times in 8 Earth-years or 13 Venus-years. Some of you may recognize the 5:8:13 Fibonacci sequence, a tribute to the beauty of Venus and the Golden Ratio!


Venus returns to its greatest eastern (evening) elongation 5 times in 8 years (8 x 365 days = 2920 days). So we can expect the following greatest evening elongation to recur some 584 days (2920/5 = 584) later. The 584-day period is equal to about 8/5 (1.6) years, or 1 year and 7.2 months.


By the way, one year on Venus equals about 224.6 Earth-days (2920/13 = >224.6).


Yes, remember the star-shaped Pentagram! Relative to the Sun, Venus rotates on its axis 5 times in 584 days. Thereby, one day on Venus lasts for about 116.8 Earth-days (584/5 = 116.8).


Make friends with the Golden Triangle and the Pentagram. Then Venus, the goddess of love and beauty, is destined to become your friend for life!


Constructing the Golden Triangle


copyright 2013 by Bruce McClure


September 2013 Feature * November 2013 Feature