Sidereal vs Tropical Astrology

There are two main ecliptic coordinate systems used in astrology today, Sidereal and tropical. Both divide the ecliptic into 12 zodiac signs named after the zodiac constellations. Each sign is 30 degrees in longitude. The difference between the two systems is their longitudinal origins.

Tropical

In the tropical system, the origin is the vernal equinox. The vernal equinox is the intersection of the ecliptic and the celestial equator where the sun passes the equator as it is apparently moving northward. This point is also called the sun’s north node.

We know now that the sun is not orbiting around the earth. This does not change the ecliptic or the equinoxes. The vernal equinox is currently moving westward by about 50.3 arc seconds per year due to the earth’s precession.

Sidereal

The longitudinal origin in the sidereal system is defined relative to the fixed stars. Fixed is used loosely here as some stars move. This movement isn’t immediately apparent but can be realized by tracking the position of stars over thousands of years.

The difference between the sidereal and tropical origins is called ayanamsa. There is not one universally recognized ayanamsa but most of them differ by less than an arc minuet. They are also all close to the value of the earth’s axial tilt.

There is debate about which star should be referenced in the sidereal coordinate system and how it’s longitude should be calculated. For this reason, the sidereal system has many perceived origins.

Which system is correct?

There are many coordinate systems used in astronomy today. They are all correct.

Opinions and whatnot

It is important to understand that neither system correlates with the zodiac constellations and neither is meant to. A system using the constellations would have to consider the irregular shapes of the constellations. This would not make for a comprehensive coordinate system. The argument that sidereal astrology is more accurate because it follows the stars is fallacious and leads to misconceptions about astrology as a whole.

The shift of the tropical coordinates overtime means that star charts must be continuously updated. A fixed system would not require so much attention.

The sidereal system is used in Hindi astrology. Some western astrologers have adopted the coordinate system and apply it directly to tropical astrology. I do not agree with this practice. Hindi astrology has many unique elements besides the coordinate system used.

There is evidence that the Babylonians used the seasons in the development of the horoscope. It is also known that the horoscope was brought to Indian astrology by Hellenistic influence.

Looking at Hindi astrology, it is quite obviously stellar and lunar based. Western astrology is based on the seasons and the stars.

Questions for you

  • Which system do you prefer? Why?
  • Have you considered other systems such as draconic or synoptical?
  • Do you think that using an equatorial system or the international celestial reference system would be better? Why or why not?

Links

Calculating the Julian date and J2000

The Julian date is a continuous count of the solar days and fraction of the day elapsed since the beginning of the Julian period (4713 BC) at noon. It is often used in time standard conversion because the Julian calendar is simple.

J2000 is the current epoch and is the count of the Julian days since January 1st 2000 at noon UT.

How to calculate the Julian date

The Julian date of a date on the Gregorian calendar (the calendar most of us use) at a given time can be calculated using the following formula.

JD = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIME/24

TIME can be measured using any time standard but it must be converted to decimal hours.

J2000

The Julian date on January 1st 2000 at noon was 2451545.0. J2000 is calculated using,

J2000 = JD – 2451545.0

An example

The information for this example came from the Astro databank, linked below.

Marilyn Manson

Born on January 5th 1969 at 8:05pm (20:05) EST

Y =1969

M = 1

D = 5

UTC TIME = 25.083333333333333

JD = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIME/24

JD = 367*1969 – INT(7*(1969 + INT((1 + 9)/12))/4) – INT(3*(INT((1969 + (1 – 9)/7)/100) + 1)/4) + INT(275*1/9) + 5 + 1721028.5 + 25.083333333333333/24

JD= 2440227.54513888889

J2000 = JD – 2451545.0

J2000 = 2440227.54513888889 – 2451545.0

J2000 = -11317.4548611

Links

Calculating Sidereal Time

Sidereal time is the angular distance between a terrestrial meridian and the vernal equinox. The sidereal time at a given location on earth is equal to the right ascension of a star when it appears to pass over the meridian at said location. Because both right ascension and sidereal time are based on the vernal equinox, they cyclically change concurrently overtime due to changes in the earths’s axial tilt. Sidereal time is used to locate stars and other celestial objects relative to the earth because of its equivalence to right ascension.

How is sidereal time calculated?

There are many sidereal time calculators online. I only mention this because calculating sidereal time is tedious and not exactly straight forward. You can use these tools to check your work. I will leave a link to a sidereal time calculator below.

Most of the following formulas came from the Astronomical Almanac published in 2012. The methods for calculating Greenwich mean sidereal time changes as new information about the earth’s motion is discovered. As far as I know, these formulas are current as I am writing this. The formulas for determining the Julian data since the epoch J2000 came from Wolfram. Links to the Wolfram page and a scanned version of the 2012 Astronomic Almanac will be linked at the bottom of this post.

A lot of unexplained constants follow. Some of them, I can explain, but others go beyond the scope of what I am willing to learn about astrophysics. If you would like to explore time in more depth, Simon Newcomb’s “Tables of the Motion of the Earth on its Axis and Around the Sun” and “The elements of the four inner planets and the fundamental constants of astronomy“ should get you started on that journey. I should warn you though, it seems to be a pretty decently sized rabbit hole.

LST = GMST + east longitude

local sidereal time (LST) is the Greenwich mean sidereal time (GMST) corrected for the location by adding the east longitude in terms of hours. Greenwich mean sidereal time is, in essence, a close approximation of the sidereal time at Greenwich and is based on the average position of the vernal equinox.

GMST ignores the earths nutation but accounts for precession. Because precession makes up the majority of the vernal equinox’s movement and nutation is very small, GMST is sufficient for most purposes.

GMST(Du, T) = θ(Du) + GMSTp(T)

Where,

θ(Du) = 2pi(0.7790572732640 + 1.00273781191135448 * Du )

And,

GMSTp(T) = 0.014506 + 4612.156534T +  1.3915817T2 – 0.00000044T3 – 0.000029956T4 – 0.0000000368T5

Where,

Du = JDUTC – 2451545.0

And,

T = (JDTT – 2451545.0)/36525

θ(Du) is the function for the earth’s rotation angle (ERA) where Du is the number of days since the epoch J2000. GMSTp(T) is the polynomial part where T is the number of centuries since the epoch. It is separated because it is used in other calculations. I kept it separate in an attempt to keep things neat.

The ERA is the angular distance from a mostly fixed point on the equator called the celestial intermediate origin (CIO) to Greenwich. The polynomial part is the angular distance from the CIO to the vernal equinox.

θ(Du) is measured in radians while GMSTp(T) is measured in arc seconds. Before adding them together, they will need to be converted to the same unit of measurement.

To calculate JDTT, we need to convert UTC to TT like so,

TT = UTC + leap seconds added to UTC to date + 32.184

At the bottom of this post is a link to the Wiki page for leap seconds. The Wiki article has a table of all the leap seconds that have been added to UTC.

JDTT = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIMETT/24

JDUTC = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIMEUTC/24

Y is the year, M is the month, D is the day, and TIME is the time. INT means remove the decimal part. TIME is converted to decimal hours.

An example

I got the information for this example from the Astro databank.

Marilyn Manson

Born on January 5th 1969 at 20:05 EST in Canton, Ohio 40n48, 81w23

Y =1969

M = 1

D = 5

UTC TIME = 25.083333333333333

JDUTC = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIME/24

JDUTC = 367*1969 – INT(7*(1969 + INT((1 + 9)/12))/4) – INT(3*(INT((1969 + (1 – 9)/7)/100) + 1)/4) + INT(275*1/9) + 5 + 1721028.5 + 25.083333333333333/24

JDUTC = 2440227.54513888889

TT = UTC + leap seconds added to UTC to date + 32.184

TT = 25.083333333333333 + ((leap seconds added to UTC to date + 32.184)/3600)

TT = 25.0922733333

JDTT = 367Y – INT(7(Y + INT((M + 9)/12))/4) – INT(3(INT((Y + (M – 9)/7)/100) + 1)/4) + INT(275M/9) + D + 1721028.5 + TIME/24

JDTT = 367*1969 – INT(7*(1969 + INT((1 + 9)/12))/4) – INT(3*(INT((1969 + (1 – 9)/7)/100) + 1)/4) + INT(275*1/9) + 5 + 1721028.5 + 25.0922733333/24

JDTT = 2440227.54551138889

Du = JDUTC – 2451545.0

Du = 2440227.54513888889 – 2451545.0

Du = -11317.4548611

T = (JDTT – 2451545.0)/36525

T = (2440227.54551138889- 2451545.0)/36525

T = -0.30985501679

θ(Du) = 2pi(0.7790572732640 + 1.00273781191135448 * Du ) modulo 2pi

θ(Du) = 2pi(0.7790572732640 + 1.00273781191135448 * -11317.4548611) modulo 2pi

θ(Du) = -71299.4560272 modulo 2pi

θ(Du) = 2.13083867395

θ(Du) in degrees = θ(Du) * 180 / pi

θ(Du) in degrees = 2.13083867395 * 180 / pi

θ(Du) in degrees = 122.088062841

θ(Du) in hours = θ(Du) in degrees / 15

θ(Du) in hours = 122.088062841 / 15

θ(Du) in hours = 8.1392041894

GMSTp(T) = 0.014506 + 4612.156534T +  1.3915817T2 – 0.00000044T3 – 0.000029956T4 – 0.0000000368T5

GMSTp(T) = 0.014506 + 4612.156534* -0.30985501679 +  1.3915817* -0.309855016792 – 0.00000044* -0.309855016793 – 0.000029956* -0.309855016794 – 0.0000000368* -0.309855016795

GMSTp(T) = -1428.9517286

GMSTp(T) in degrees = (GMSTp(T) / 3600) Modulo 360

GMSTp(T) in degrees = (-1428.9517286 / 3600) Modulo 360

GMSTp(T) in degrees = (-0.39693103572) Modulo 360

GMSTp(T) in degrees = 359.603068964

GMSTp(T) in hours = GMSTp(T) in degrees / 15

GMSTp(T) in hours = 359.603068964 / 15

GMSTp(T) in hours = 23.9735379309

GMST(Du, T) = θ(Du) + GMSTp(T) modulo 24
GMST(Du, T) = 8.1392041894 + 23.9735379309 modulo 24

GMST(Du, T) = 32.1127421203 modulo 24

GMST(Du, T) = 8.1127421203

east longitude = 81w23 = -81.38333333333 = -5.42555555556

LST = GMST + east longitude modulo 24

LST = 8.1127421203 + -5.42555555556 modulo 24

LST = 2.68718656474 modulo 24

LST = 2.68718656474 = 2:41:13.871633064


The Astro databank, linked below, has birth dates, times, and locations for many public figures. Try calculating the sidereal time of birth for some of them. Leave your results and any questions that come up in the comments.

Links

2012 Astronomical Almanac

https://archive.org/details/astronomicalalma00naut/page/n132

Wolfram article about Julian dates

http://scienceworld.wolfram.com/astronomy/JulianDate.html

Wiki page about leap seconds

https://en.m.wikipedia.org/wiki/Leap_second

Astro databank

https://www.astro.com/astro-databank/Main_Page

Sidereal time calculator

http://neoprogrammics.com/sidereal_time_calculator/index.php

frequently changing passions

Finally finding you passion is a an exciting experience. You finally know where your time and energy is best spent. You might look for likeminded people who share your passion and make new friends. If you are lucky, your passion can be turned into a career or, at the very least, a side hustle. You are able to see your future more clearly and are sure of your path and where you fit in. You feel at peace. Passion peace.

Finding a second passion can be just as exciting. You might find ways to combine your passions to create something new. You might connect with more people through your passions and expand your network. Maybe your first passion fades. This can be disappointing. You might feel guilty for leaving your former passion behind. Maybe you feel the time you spent was wasted. You will eventually grow to understand that learning and building skills is never a waste.

Your next few passions harbor the same amount of excitement, guilt, and disappointment. Eventually, shame is added to the mix. People who care about you start to ask why you won’t just pick something and stick with it. You begin to worry that you are wasting time on your current passion. When asked what your hobbies and interests are, you respond with less confidence as you did before. You are constantly a beginner. Constantly rebranding you social media to fit your new passion. Always searching for likeminded people to share your passion with. Buying new things and trying to let go of stuff you no longer use.

Eventually you find that old passions resurface from time to time. You may feel like you’ve been a novice for years when they do. This can cause some shame. Realize that you have more tools now and can easily catch up. You may or may not realize that you are learning new things quicker and using skills from old passions to enhance the new ones. Hopefully you learn to be more minimalistic and to store things properly. Learn to Let yourself get passionate about things. Let old passions fade. Perhaps rapidly switching passions is a passion in itself.


It would be real cool if my next passion was SEO.

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