Math formula for rising ascendant and internet calculator discrepancy, please help

Hi

I am a South African born at precisely 12h:13 am 28 December 1974 at exactly this location S 33.9485° - E 18.4753° In Mowbray Cape Town.

I am new to astrology and therefore naturally curious about a lot of things. One of them being the mathematics behind the programs that construct the natal charts. I am NO mathematician but I am patient and dont give up on a math problem until I solve it, no matter what I have to learn to reach that point.

My first obstacle I have come across is the Rising Ascendant sign. A quick entry of my data into one of the many ascendant calculators, calculates my ascendant as Virgo 26° 21′ . That means, as far as my understanding goes, from Aeries 0° that is 176° 21′.

However, an article on a Wikipedia site http://en.wikipedia.org/wiki/Ascendant shows this formula for calculating the ascendant.

The Ascendant, from an astronomical point of view, is the value of the ecliptical geocentric longitude (aka Celestial Longitude λ) of the point of the ecliptic which is easterly on the horizon.

Ascendant = arctan (y/x) = arctan(-cosA/(sinA×cosE + tanL × sinE))


where A is the local sidereal time in degrees, E is the inclination of Earth's equatorial plane to the ecliptic or obliquity of the ecliptic. For values referred to the standard equinox J2000.0 use 23.4392911°, for J1950.0 use 23.4457889°. L is the local latitude (Southern latitudes are negative, Northern positive). The Ascendant is then found in the correct quadrant (0 to 360 degrees) by using the 2 rules:

If (x < 0) then' Ascendant = Ascendant + 180
else if
then Ascendant = Ascendant + 360
By definition of Ascendant, we have to take the point easterly (the rising one) by using a final rule:
if (Ascendant < 180) then Ascendant = Ascendant + 180
else then
Ascendant = Ascendant - 180

My data enters into that formula as follows

My local sidereal time of birth (if worked out properly, which I am confident it is, but am more than happy to be corrected if wrong) = 19h 16m 7.0720012s

That local sidereal time of my birth converted into degrees I calculated as follows:
360° ÷ 23.9344696 hours in one sidereal day = 15.041068635
Converting my time of birth to hours and then multiplying it by 15.041068635 should equal my local sidereal time in degrees which is 19.268631111×15.041068635 = 289.82080305

So A = 289.82080305°
Therefore:
- cosA = -cos(289.82080305) = 0.339079514515

sinA = sin(289.82080305) = 0.940757717394
cosE = cos(23.4392911) = 0.917482062146
sinA × cosE = 0.940757717394×0.917482062146 = 0.863128331

tanL = tan(-33.9485) = -0.67320152444
sinE = sin(23.4392911) = 0.397777155754
tanL × sinE = -0.67320152444×0.397777155754 = −0.267784188


0.863128331+ −0.267784188 = 0.595344143

arctan(0.339079514515 ÷ 0.595344143) = 29.66376741

Then the rules apply

Rule 1
29.66376741 is greater than 0 so I add 360 = 29.66376741+360 = 389.66376741

Rule 2
389.66376741 is greater than 180 so I subtract 180 = 389.66376741−180 = 209.66376741

209.66376741° of geocentric longitude (I have a feeling this is where my error could be) taken from 0° Aeries puts me in 29.66376741° or 29° 39′ 49.562676″ in Libra. Where as the ascendant calculator on the internet put me 26° 21′ in Virgo or 26.35° Virgo. This is a 33.31376741° discrepancy.

My plea for assistance here is, if I have miscalculated something or perhaps misunderstood something, could somebody please point my error out to me and assist in calculating my correct ascendant sign without referring to a house of tables( I already know how to do that ). I would like to know how to work this out mathematically. The reason for that is I would like to confirm if what a calculator on the Internet is giving me is indeed correct.

Any assistance with regards to this would be greatly appreciated.

Kind Regards
Charlie

Goodness. You are compulsive.

I spent too many years doing that stuff....

Go to www.astro.com.
Plug in your birth data.
Bingo. An accurate chart. (I have checked many of their charts against my own calculations; they are accurate for both the angles of the chart and planetary position way back in time.) Their free service also includes the calculation of many types of chart subservient to the radix.

Here is what Kepler says about accuracy and incorrect birth times [You remember Kepler, the guy who figured out that planets follow elliptical orbits; he was also a crackerjack astrologer, Court Astrologer ("Royal Mathematician") to the Holy Roman Emperor Ruldolf]: "Astrologers recognize this [problem] and feel it strongly, but they also have methods of overcoming this uncertainty -- one better than the other... [It has been said] that if the error is only one minute it is too much, and it was calculated that many thousands of miles are overlooked here and pass by [in this time]. I have indicated that the size of the sky should not deceive us: the natural soul of the human being is no greater than a single point, and on this point the form and the character of the whole sky is potentially impressed, no matter if the sky were a hundred times greater. The error of one minute makes no greater difference than a quarter of a year. O how blessed would the astrologers consider themselves if they could predict correctly to within a quarter of a year! " Kepler predicted the assassination of Wallenstein 9 years before the fact with an accuracy of less than one month (for all you folks who say death can't be predicted.) And that was with only 7 planets -- no Chiron, no self-respecting asteroids, and no 7th, 9th, or 11th harmonic aspects [Kepler gave us the minor aspects, but rejected these (and other) minors because he found nothing in nature built upon those numbers and therefore considered that they were not used by God in creation, and that souls do not resonate with them.]

It is a very good thing that you are learning the principles and calculations. Astronomy is the backbone of astrology. But with computers, it is easier, quicker and more accurate to employ them. Another good thing to do, something that will make a better astrologer of you, is to go outside at night, sit quietly for some time and observe the sky and its motions over an extended period of time.

Consider the fact that one arc-minute is equal to 4 seconds of time at the MC...birth times are never recorded to that accuracy. Calculations refined to the degree you have carried them are pointless, except as an exercise in calculation.

Calculation is the easy part of astrology. Your talent and skill in the the interpretive/predictive art is where the rubber meets the road.

Thank you very much Greybeard for your reply to my post and although insightful as it is, it unfortunately does not address my original problem. Astro.com simply takes me back to the same ascendant calculator I have used in the past. I really, for my own peace of mind and wanting to understand fully how the calculation is made, would really be thankful to someone if they could assist with getting to the bottom of why there is a discrepancy with the math formula and internet rising ascendant calculators. Thank you once again though for your words of advice and a pleasant evening to you.
Kind Regards
Charlie

charliestars said:

Hi

I am a South African born at precisely 12h:13 am 28 December 1974 at exactly this location S 33.9485° - E 18.4753° In Mowbray Cape Town.

I am new to astrology and therefore naturally curious about a lot of things. One of them being the mathematics behind the programs that construct the natal charts. I am NO mathematician but I am patient and dont give up on a math problem until I solve it, no matter what I have to learn to reach that point.

My first obstacle I have come across is the Rising Ascendant sign. A quick entry of my data into one of the many ascendant calculators, calculates my ascendant as Virgo 26° 21′ . That means, as far as my understanding goes, from Aeries 0° that is 176° 21′.

However, an article on a Wikipedia site http://en.wikipedia.org/wiki/Ascendant shows this formula for calculating the ascendant.

The Ascendant, from an astronomical point of view, is the value of the ecliptical geocentric longitude (aka Celestial Longitude λ) of the point of the ecliptic which is easterly on the horizon.

Ascendant = arctan (y/x) = arctan(-cosA/(sinA×cosE + tanL × sinE))


where A is the local sidereal time in degrees, E is the inclination of Earth's equatorial plane to the ecliptic or obliquity of the ecliptic. For values referred to the standard equinox J2000.0 use 23.4392911°, for J1950.0 use 23.4457889°. L is the local latitude (Southern latitudes are negative, Northern positive). The Ascendant is then found in the correct quadrant (0 to 360 degrees) by using the 2 rules:

If (x < 0) then' Ascendant = Ascendant + 180
else if
then Ascendant = Ascendant + 360
By definition of Ascendant, we have to take the point easterly (the rising one) by using a final rule:
if (Ascendant < 180) then Ascendant = Ascendant + 180
else then
Ascendant = Ascendant - 180

My data enters into that formula as follows

My local sidereal time of birth (if worked out properly, which I am confident it is, but am more than happy to be corrected if wrong) = 19h 16m 7.0720012s

That local sidereal time of my birth converted into degrees I calculated as follows:
360° ÷ 23.9344696 hours in one sidereal day = 15.041068635
Converting my time of birth to hours and then multiplying it by 15.041068635 should equal my local sidereal time in degrees which is 19.268631111×15.041068635 = 289.82080305

So A = 289.82080305°
Therefore:
- cosA = -cos(289.82080305) = 0.339079514515

sinA = sin(289.82080305) = 0.940757717394
cosE = cos(23.4392911) = 0.917482062146
sinA × cosE = 0.940757717394×0.917482062146 = 0.863128331

tanL = tan(-33.9485) = -0.67320152444
sinE = sin(23.4392911) = 0.397777155754
tanL × sinE = -0.67320152444×0.397777155754 = −0.267784188


0.863128331+ −0.267784188 = 0.595344143

arctan(0.339079514515 ÷ 0.595344143) = 29.66376741

Then the rules apply

Rule 1
29.66376741 is greater than 0 so I add 360 = 29.66376741+360 = 389.66376741

Rule 2
389.66376741 is greater than 180 so I subtract 180 = 389.66376741−180 = 209.66376741

209.66376741° of geocentric longitude (I have a feeling this is where my error could be) taken from 0° Aeries puts me in 29.66376741° or 29° 39′ 49.562676″ in Libra. Where as the ascendant calculator on the internet put me 26° 21′ in Virgo or 26.35° Virgo. This is a 33.31376741° discrepancy.

My plea for assistance here is, if I have miscalculated something or perhaps misunderstood something, could somebody please point my error out to me and assist in calculating my correct ascendant sign without referring to a house of tables( I already know how to do that ). I would like to know how to work this out mathematically. The reason for that is I would like to confirm if what a calculator on the Internet is giving me is indeed correct.

Any assistance with regards to this would be greatly appreciated.

Kind Regards
Charlie

Click to expand...

CALCULATING A NATAL CHART BY HAND
EXAMPLE FROM KEN WARD'S ASTROLOGY PAGES http://www.trans4mind.com/personal_development/astrology/Calculations/calcGMT.htm

Astrology: Calculating the Chart - UT or GMT.

QUOTE

'….While few people are actually going to work out astrological charts by hand, that is, using paper, pencil,
it is important to know how to do it
because unless an astrologer spends a great deal of time doing charts by hand,
they will never fully understand astrology.
By doing charts by hand,
one begins to understand more about the movement of the planets
and how they combine to affect the lives of people on Earth.
Astrology is a sacred science
and by doing the mundane routine things,
our minds enter a meditative state
wherein we realise things we might not have been able to know or understand otherwise....'

The tools you require to make a horoscope
(in addition to writing and drawing tools)
are an atlas and an ephemeris
An ephemeris is a book or booklet containing information about the positions of planets, etc.


The information you require is the date and time and place of birth.

The place of birth is expressed in longitude and latitude.

Universal Time, or Greenwich Mean Time, is required to calculate the positions of the planets.

CALCULATING A NATAL CHART BY HAND

QUOTE

'….For some time, our NCGR Chapters have asked for an available example of how to set a natal chart.
During the Spring 2010 Board meeting, it was voted that NCGR would place such an example on its website, utilizing as a resource, Joan Negus’ out-of-print workbook, Basic Astrology: a Practical
Guide. This particular work was chosen because it offers a time-proven resource for learning to accurately set a natal chart and is an excellent way to honor Joan since she and Ken Negus
were instrumental in helping to establish the NCGR education program. Ken Negus was contacted for permission to utilize Joan’s workbook, which he graciously gave.....'

QUOTE

'….Two resources that one must have available to set a chart are:

1. Table of Houses
2. Ephemeris of the year of birth.


Many examples are found in tables of houses and some ephemerides.


Examples given herein yield acceptable results for exams. One may calculate by hand or by calculator, both methods are included.


NB

Hand and/or computer calculating
does not always yield exactly to the minute and second
the same results as from astrological software

In fact,
not all astrological software yields exactly to the minute-second the same results
as another astrological software,
thus a small amount of error is accepted by exams.....'

Hi JUPITERASC

Thank you very much for your reply. The website you referred me to is great, lots of info there. Unfortunately my original plea for help remains unanswered. It appears to me that the mathematical formula, which does not seem that complicated, does not reproduce the same value for an ascendant as the ascendant calculators on the net do. Either my math is wrong, the formula is wrong (doubtful its Jean Meeus ) or the programs on the net that calculate the ascendant signs use a different method, I don't know. For me though the discrepancy is quite large and I would really like to get to the bottom of it seeing these are my first steps with regards to this practice of astrology. The way I see it is if I am going to begin this journey I would like to do it with the correct foot forward and be confident in knowing at least that my Natal chart calculations are 100% correct.
Thank you for the links you have provided me with, they are all much appreciated.
Kind Regards
Charlie

I don't know if I even remember....

But let's take a birth for
27 December 1988
1440 EST
New York
New York is at 73*56' W
and 40*40' N.
The time zone is EST (GMT -5).

So....
we start with clock time: 1440
EST is based on 75W
So we are 4m and 16s Later in NYC than on the time zone meridian.
Our LMT is then 1444:16
And GMT is 1940 (for calculating the planets).
Those are the two times we need to cast the chart: LMT for the houses and GMT for planets.

The Sidereal Time for 27 Dec 1988 at midnight Greenwich is 06:22:47, taken from the ephemeris.
We add the LMT (distance from midnight), 1444:16
Which yields 20:66:63 or 21:07:03...our local sidereal time, or RAMC
Delta T is 55s (taken from the ephemeris)...so correct RAMC is 21:07:58
With that we get the zodiacal degree corresponding to RAMC and we have our MC
And can now calculate the Asc (or take it from tables....I like that idea).

To check our calculation....
We know Sun is in early Capricorn, about 6 degrees
An RAMC of 21 hours will give approximately the middle degrees of Aquarius on the MC.
So that would place Sun around the 9th House cusp, probably about the middle of the 8th
And that is where we ought to find the Sun at 1440 hours.
So our calculation is correct. We have not made a gross error in the time for the chart.

This method of checking (very quick in practice -- it's an eyeball thing once the Sun is put in the chart) does not catch small errors but does catch big ones. I do it even with computer generated charts, to make sure I didn't plug in a wrong time.

I think I forgot to add in the correction for 1444 hours at 10s per hour.....so the time I gave is off by that much....146s or 2m26s. So RAMC would be 21:10:24....Voila. That's the sort of mistake checking by sun's position won't catch and results in an error of around 37' of arc in the MC.

No calculator. In my head. Two bits of data from ephemeris.

Now I'll plug the data into my program and see what it gives.
15 Aquarius MC, Sun a bit lower than middle of 8th (it's winter).
Good to go.
The program I used says ST = 21:09:59, but it's using a different longitude, so the calculation I did is correct. Hehe....I haven't done that in 15 years or so.....It's like riding a bicycle and very simple -- once you understand what you are doing instead of just learning the method by rote.

It is unlikely that the given formula is wrong. It is unlikely the net calculators are wrong. Which puts the probable cause of the discrepancy squarely in your lap. Check your work. Always. And check it again.

When we old salts were learning to do these calculations there were no computers. I didn't even have a hand-held calculator. I had no one but me to rely on. If I made a mistake (and I made them all the time) I had to find it myself, and figure out what the mistake was and fix it myself. Mistakes are very easy to make, and some types of mistake are very difficult to notice. So......check your work and check it again, even if it seems to be right at first.

I don't say this to be mean....But don't ask for help. Do it yourself. Get mad, feel frustrated, feel stupid. Keep at it. All that frustration will result in mastery. Understand the principles and keep slugging it out until you get it right. Einstein worked for eleven years on his General Theory and couldn't get his math right. He found mistakes in his work even after he thought he had it right. And then he went back, checked his work, and found a formula he had discarded two years earlier and realized it was the right one. Kepler did the same thing when he was discovering the laws of planetary orbits. All the brightest and best for 2000 years before him had discounted the idea of ellipitcal orbits as too simple...but Kepler kept on working with his numbers and the ellipse popped out. Simple. Just hard frustrating work.

Guess I put this on the wrong thread. Oh well. I can hardly wait until you begin using the repetitive algorithms for Placidus houses.

You're problem is the problem of theory vs. actuality. I put in your birth info into my program and found that 26 degrees Virgo corresponds to your Tropical Ascendant! In the ancient days people found meaning in the stars by looking at the actual stars. Popular Tropical astrologers, however, erect charts where the planets and angles are not in their real positions in the stars.

If you were to switch to the Sidereal Zodiac, you will get the correct location of the planets, but you will still be off on the angles. Why? Because again astrologers nowadays turn to theoretical answers. Your ascendant will show up as 2 degrees Virgo. A lot closer, but still not exact. This is due to the fact that it is determined by using the so-called "true" east point, and not, as they claim, the actual stars rising on the eastern horizon at a particular location.

The Descendant is even more skewed because it assumes that it is always 180 degrees from the Ascendant; which is only true around the equator.

The problem is not with your calculations per se (although I did not double check your calculations for myself). The problem is that astrologers have turned away from looking at the stars themselves in leau of overly simplistic and yet very distorted version of real astrology. You may very well be a Libra rising. DO NOT trust online ascendant calculators. Kudos for taking the time to do the work yourself.

I suggest this book for the calculation of the sidereal hour.
The Only Way to Learn Astrology, Vol. 2: Math & Interpretation
Marion D. March e Joan McEvers

For a house interpolation the book by Weiss Adolfo the Astrologia Racional.

-----------------
Result calculated by the morinus program

Sidereal time 17:52:52
Obl. of ecliptic 23,2629

Rect ascesion 358,3717
asc. 28,2951
-----------------
Using windows calculator that can be learned in text.
An Easy Introduction to Primary directions
By Deborah Houlding

12h:13 am 28 December 1974
Lat 33s56'
(deg and dms are functions of the calculator)

TS 17,5252 deg ÷4*60=268,2166 dms 268,13

So A = 268,13
Therefore:
cosA = -cos(268,13)= -0,032631

sinA= -0,999467
cosE=(23,2629) =deg 23,441388 > 0,917467
sinA*cosE = - 0,916977990089 (negative)

tanL 33,56 = - 0,672816
sin=(23,2629) = 0,397810
tanL*sinE= - 0,26765293296 (negative)

Add2
(-0,916977990089)+(-0,26765293296)= -1,184630923049(negative)

cos÷add2= - 0,02754528804297495185839769553182

Arctan= - 1,577829
In grau - 1,3440

-1,3440 + 180 = 178,656 (X < 0 add 180)
178,656 + 180 = 358,656 (X < 180 add 180)

Result In graus 358,3921

Kind Regards
Ricardo G. Fliege

kdiddy said:

You're problem is the problem of theory vs. actuality. I put in your birth info into my program and found that 26 degrees Virgo corresponds to your Tropical Ascendant! In the ancient days people found meaning in the stars by looking at the actual stars. Popular Tropical astrologers, however, erect charts where the planets and angles are not in their real positions in the stars.

If you were to switch to the Sidereal Zodiac, you will get the correct location of the planets, but you will still be off on the angles. Why? Because again astrologers nowadays turn to theoretical answers. Your ascendant will show up as 2 degrees Virgo. A lot closer, but still not exact. This is due to the fact that it is determined by using the so-called "true" east point, and not, as they claim, the actual stars rising on the eastern horizon at a particular location.

The Descendant is even more skewed because it assumes that it is always 180 degrees from the Ascendant; which is only true around the equator.

The problem is not with your calculations per se (although I did not double check your calculations for myself). The problem is that astrologers have turned away from looking at the stars themselves in leau of overly simplistic and yet very distorted version of real astrology. You may very well be a Libra rising. DO NOT trust online ascendant calculators. Kudos for taking the time to do the work yourself.

Click to expand...

I Tajínk tropical astrology is based upon the seasons, not some fake and random positions in the sky. Also, I think tropical astrology is more accurate since vedic and sidereal astrology is more symbolic and thetefore general

obsidianmineral said:

I Tajínk tropical astrology is based upon the seasons,
not some fake and random positions in the sky.
Also, I think tropical astrology is more accurate
since vedic and sidereal astrology is more symbolic and thetefore general

Click to expand...

The Sidereal zodiac is a physical reality
depicting commonly acknowledged pictures made up of groups of stars
AND IS USED NOT ONLY BY ASTRONOMERS
but also by Vedic astrologers
as well as by Sidereal Western astrologers

In contrast, the Tropical zodiac
is a mathematical construct used by astrologers only

Most in the Western Hemisphere think of their astrological signs based on the Tropical zodiac
which is a math-only based system of division with the zero point starting at the Vernal Equinox
when Sun crosses ecliptic first day of Spring in Northern Hemisphere.
On the same day in the Southern Hemisphere it is the first day of AUTUMN
New babies born the day after Spring Equinox will be told that they have an Aries Sun sign.
And they will Tropically.
All Tropical astrologers mark out 12 signs, Aries to Pisces, 30 degrees each, from that point in space.
But if Tropical astrology is based on the seasons
then
different seasons in the Northern Hemisphere
and Southern Hemisphers
are designating the same sign to people born at different seasons

If you could see where the Sun actually was at Spring Equinox
you would see it in the 5th degree or thereabouts of the constellation Pisces
because Sidereal Astrologers use the physical Zodiac
which consists of 12 constellations.
So if you were born the day after Spring Equinox the Sun is physically in the Sign Pisces
not the constellation Aries

What does this mean to you?
Well, it might explain why you weren’t like all those other “Aries” born at the end of the month.
But you could have other planets in Aries that gives you the traits associate with Aries.
You need to see your birth chart to know how many planets are in each CONSTELLATION.
Check both and see for yourself
which makes more sense to you

Tropical zodiac is a mathematical construct detached from the 'Images' or constellations
and detached from precession also
often a person's tropical sun sign is different from their Sidereal sun sign.
i.e.
although some people have the same sun sign in BOTH tropical
AND sidereal
other people have two different sun signs depending on whether the astrologer
is using the tropical zodiac or the sidereal zodiac

To check your natal chart in both zodiacs go to astro.com Extended Chart Selection Page
there you can choose either the Sidereal or the Tropical option to create a chart