# What are the RAs of the boundaries between traditional zodiacal signs?

I'm trying to figure out at what right ascension (RA) — not celestial longitude — the sun enters the various traditional (Western) astrological signs of the Zodiac; but I can't figure out how to calculate this.

What are the right ascensions of the boundaries between traditional zodiacal signs along the ecliptic?

• I'm voting to close this question as off-topic because appears to be asking about the astrological division of the sky. – James K Aug 27 '18 at 22:36
• @JamesK it’s asking how to calculate RA from a given list of longitudes. Also note the history tag: I’m not casting horoscopes, I’m making a chart for a discussion of the history of astronomy. – orome Aug 27 '18 at 22:37
• The Western Zodiac has used equal 30 degree divisions of ecliptic longitude since Babylonian times, and these divisions have been aligned with the equinoxes & solstices since Ptolomy (0 degrees Aries, aka the first point of Aries, being the northern spring equinox point). See en.wikipedia.org/wiki/Zodiac Conversion of coordinates in ecliptic latitude & longitude to RA & declination is simple spherical trigonometry. – PM 2Ring Aug 27 '18 at 23:45
• @JamesK A quick check of What questions are off topic here? would confirm that it's not off-topic to ask how current astronomical coordinates correlate with historic celestial divisions. – Chappo Hasn't Forgotten Monica Aug 28 '18 at 0:00
• @PM2Ring Thanks, yes: what this boils down to is (a) confirming that and (b) doing that calculation (beyond my skills). Thx – orome Aug 28 '18 at 0:12

TL;DR: Calculating the right ascension (i.e. converting from ecliptic to equatorial coordinates) requires some spherical trigonometry, but fortunately there are internet tools that will do this, such as here. The resulting RA coordinates are: Aries 0h 0m 0s; Taurus 1h 51m 39s; Gemini 3h 51m 16s; Cancer 6h 0m 0s; Leo 8h 8m 44s; Virgo 10h 8m 21s; Libra 12h 0m 0s; Scorpio 13h 51m 39s; Sagittarius 15h 51m 16s; Capricorn 18h 0m 0s; Aquarius 20h 8m 44s; Pisces 22h 8m 21s.

Explanation and background

Since traditional (Western) astrology uses the same tropical year as astronomical celestial coordinates, the tropical zodiac commences with Aries at 0˚ longitude on the ecliptic, and each subsequent zodiac sign (NB not the constellation, which is different) commences exactly 30˚ further along the ecliptic. So, the zodiac division of Taurus is from 30.00˚ to 59.99˚, Gemini from 60.00˚ to 89.99˚, and so on. It's then just a matter of converting ecliptic longitude to celestial coordinates (right ascension).

Further useful information on the relationship between the ecliptic and right ascension can be found in Mike G's answer to "Effect of the obliquity of the ecliptic / tilt of the Earth on the equation of time".

Both the traditional tropical zodiac and modern astronomical coordinates are based on the northern hemisphere vernal equinox. This starting point, also known as the First Point of Aries, is one of the two points at which the celestial equator crosses the ecliptic.

When Hipparchus defined the First Point of Aries in 130 BCE, it actually aligned with the border between the constellations of Pisces and Aries. However, due to the precession of the equinoxes, the tropical zodiac's starting point has a retrograde movement along the ecliptic at the rate of one degree every 71.5 years. As a result, the First Point of Aries is currently deep in Pisces! Using the current official IAU constellation boundaries, the point of 0h RA will cross into Aquarius in the year 2597, so we have quite some time to wait for the "Age of Aquarius".

Note that not all astrological traditions are based on the tropical year. Hindu astrology, for instance, is based on the sidereal zodiac - i.e. it aligns permanently with the visible stars, regardless of the Earth's axial precession. Some modern Western astrologers also use a sidereal zodiac, in which sidereal Aries currently begins on 15 April.

• Due to ecliptic obliquity, 30 deg longitude spans as much as 2h10m RA at the solstices or as little as 1h50m RA at the equinoxes, see this answer. – Mike G Aug 28 '18 at 2:49
• Thanks for the comment @MikeG, I've given myself a crash course in coordinate systems and corrected my half-baked post. A good opportunity for me to advance my learning while also providing the OP (and the site) with - hopefully - a worthwhile answer :-) – Chappo Hasn't Forgotten Monica Aug 28 '18 at 5:35
• As noted in astronomy.stackexchange.com/questions/35663/… this (which is a great answer) applies only to the Sun or other celestial body on the ecliptic. Bodies that have non-0 ecliptic latitude will have different RA boundaries. Also, as I'm sure you knew, it's unlikely Mayan astronomers were using IAU boundaries <G> – user21 Apr 1 '20 at 15:38

It is going to depend on where you draw the lines, but they're not equally spaced... and it also depends on whether or not you include Ophiuchus. Since they're not evenly spaced, it's not like you can start with a point on the ecliptic and calculate an even spacing for them.

• That's all given n the question: traditional (Western) astrological signs; and no presumption of even spacing. Even if they were evenly spaced along the celestial equator, the question is how that translates to the ecliptic. – orome Aug 27 '18 at 21:54
• This answer is incorrect: the zodiac divisions are exactly equally spaced. I suspect what you're referring to is the division between constellations, which is a different matter entirely. – Chappo Hasn't Forgotten Monica Aug 28 '18 at 0:04
• A sign is not the same as a constellation, see this answer. – Mike G Aug 28 '18 at 2:54
• @J.M.Haynes Astronomy has astrological roots, and this is about the history of astronomy (as tagged). – orome Aug 29 '18 at 13:43
• @PM2Ring My response was about why this answer (just a remark, really, that adds nothing that's not already implicitness in the question) didn't really have anything to do with the question. – orome Aug 29 '18 at 23:15