An Astronomical Statement in The DaVinci Code

Introduction

This page is an analysis of an astronomical statement in The DaVinci Code by Dan Brown. In chapter 6, a police investigator asks the main character, Robert Langdon, to explain the meaning of the pentacle symbol:

"Langdon decided not to share the pentacle's most astonishing property—the graphic nature of its ties to Venus. As a young astronomy student, Langdon had been stunned to learn the planet Venus traced a perfect pentacle across the ecliptic sky every eight years." [Italics in the original. Early editions of the book have the incorrect phrase "every four years".]

[Two forms of the pentacle or pentagram.]
Figure 1. Two forms of the pentacle or pentagram.

The DaVinci Code is a very popular novel. In it, the characters make statements about the history and symbology of art and religion. I'm not qualified to comment on any of those issues. If you're looking for an opinion about the accuracy of the character's comments, you won't find it here. This page is narrowly devoted to an analysis of the statement quoted above. What does the statement mean, and is it accurate?

Observing Venus

Skywatchers have been observing Venus since prehistoric times. According to the Wikipedia article on Venus, one of the earliest surviving astronomical documents, from around 1600 BC, is a 21-year record of the appearances of Venus.

Venus is the brightest object in the sky after the Sun and the Moon. Of these three objects, it has the most complex motions, appearing in the morning sky for a time, then becoming lost in solar glare, then appearing in the evening sky, then again becoming lost in solar glare, and then finally reappearing again in the morning sky. This full cycle, Venus' synodic period, takes about 584 days (actually 583.92 days). A sky object's synodic period is the time between repeated appearances of that object, as seen from the Earth, in the same position with respect to the Sun. For a complete description of each aspect of Venus' synodic period, see my tutorial: The Synodic Period of Venus.

The orbit of Venus lies nearly in the same plane as the orbit of the Earth. This means that we always see Venus near the ecliptic, which is the projection of the Earth's orbital plane into the sky, and therefore in one of the twelve traditional constellations of the zodiac.

[The orbits of the Earth and Venus
at two consecutive re-appearances of Venus in the morning sky, separated
by about 584 days.]
Figure 2. The orbits of the Earth and Venus at two consecutive re-appearances of Venus in the morning sky, separated by about 584 days.

(Please note that Figure 2 above and Figure 3 below show the ecliptic, or zodiacal, constellations as though all of their stars were at the same distance from the Sun. Of course, that's not true, but that's the way it seems when we see the stars in the night sky. Any sky object like the Moon or the planets also seems to be at the same distance, even though they are much closer than any of the stars, and thus we see them among the stars. For more information about the ecliptic (zodiacal) constellations, see my tutorial: Learn the Zodiac (Ecliptic Constellations)!.)

Since Venus' synodic period is about 584 days, consecutive appearances of Venus in the same position with respect to the Sun would occur so that the Earth has moved through one complete orbit (= one year or about 365 days) and three-fifths of the next orbit (= about 219 days). In that same time, Venus would have moved through two of its own orbits and three-fifths of the next. Therefore, Venus would re-appear in a new constellation that is three-fifths of the way around the zodiac, as is depicted in Figure 2 above.

In the same way, the next four consecutive appearances of Venus would each occur a further three-fifths of the way around the zodiac. Then if we connect the points on the zodiac at which six consecutive appearances of Venus occur, we get the symbol of the pentacle:

[The apparent positions of Venus in
its orbit at six consecutive re-appearances of Venus in the morning
sky, connected to form a pentacle, representing about eight years of
observation.]
Figure 3. The apparent positions of Venus in its orbit at six consecutive re-appearances of Venus in the morning sky, connected to form a pentacle, representing about eight years of observation.

Five synodic periods of Venus is about 2920 days (actually, 2919.6 days), and eight years is 2922 days. So the full cycle would take about two days less than eight years.

Ancient observers of Venus would not have made a diagram like the one shown above. They did not understand that Venus and the Earth both orbit the Sun, and so they would not have thought of making such a drawing. However, they could observe Venus' consecutive re-appearances as the morning star, and they could have recorded which constellation Venus was in, but they would have used a different representation of the "ecliptic sky":

[The ecliptic sky, showing the zodiacal
constellation band.]
Figure 4. The ecliptic sky, showing the zodiacal constellation band.

The band of symbols around the perimeter of the circle represent the traditional constellations of the zodiac:

Table 1. Constellation symbols and names.

Symbol	Latin name	English name
	Pisces	Fishes
	Aries	Ram
	Taurus	Bull
	Gemini	Twins
	Cancer	Crab
	Leo	Lion

Symbol	Latin name	English name
	Virgo	Virgin
	Libra	Scales
	Scorpius	Scorpion
	Sagittarius	Archer
	Capricornus	Sea Goat
	Aquarius	Water Carrier

Then, over a period of eight years, they would have recorded consecutive re-appearances of Venus as the morning star, and connected the positions to reveal the pentacle:

[The ecliptic sky, showing the
zodiacal band and marked at five consecutive re-appearances of Venus in
the morning sky, connected to form a pentacle, representing about eight
years of observation.]
Figure 5. The ecliptic sky, showing the zodiacal band and marked at six consecutive re-appearances of Venus in the morning sky, connected to form a pentacle, representing about eight years of observation.

And then, if we remove just the constellation band or the entire circumscribed circle, we get:

[Two forms of the pentacle or pentagram.]
Figure 6. Two forms of the pentacle or pentagram.

The quote at the top of the page says that "... Venus traced a perfect pentacle across the ecliptic sky every eigth years." But as I mentioned above, five of Venus' synodic period is about 2920 days, which is two days less than eight years. Thus, the pentacle is not perfect, and successive pentacles would be slightly offset:

[The ecliptic sky,
showing the zodiacal band and marked at ten consecutive re-appearances
of Venus in the morning sky, connected to form two slightly offset
pentacles, representing about sixteen years of observation.]
Figure 7. The ecliptic sky, showing the zodiacal band and marked at eleven consecutive re-appearances of Venus in the morning sky, connected to form two slightly offset pentacles, representing about sixteen years of observation.

From this we can conclude that the statement quoted above is for the most part correct. Venus does trace a pentacle across the ecliptic sky every eight years, even though it's not quite perfect.

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Last modified: Saturday, 09-May-2020 16:14:15 EDT