charliestars
Active member
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
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
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