Posted: Mon Nov 27, 2006 5:52 am
Hello,
First we need the obliquity of the ecliptic, obl
obl = 23.45229444 - [0.4684 x (year-1900)/3600]
(This is an empirical formula to calculate obliquity of the ecliptic w/o having to refer to astronomical table)
example in year 1616
obl = 23.45229444 - (0.4684 x (1616-1900)/3600)
obl=23.489246
obl = 23 deg 29 min 21.3 sec
Comparison with solar fire, obl = 23deg 29 min 21 sec
Another example (Year 2006)
Using the above formula, obl = 23.43849677 = 23 deg 26 min 18.6 sec
Comparison with solar fire, obl = 23deg 26 min 18 sec
Calculation of Right Ascension (RA):-
tan RA = tan (long) x cos (obl)
long = longitude, obl = obliquity of the ecliptic
Let us calculate the right ascension, RA of midheaven, MC in Lilly's English Merchant example,
the year was 1616,
obl (calculated above) = 23.489246 deg
longitude of the MC (given) = 14 deg 39 min Scorpio
From Aries, longitude of MC then equals to 224 deg and 39 min = 224.65 deg.
tan RA = tan (224.65) x cos (23.489246)
tan RA = 0.905997877
RA = 42.17651082 deg***
but this is in the 3rd sector (longitude is between 180 to 270 deg), hence
RA = 42.17651082 + 180 = 222.1765108 deg = 222 deg 10 min 35 sec (***see below).
Using the site that you gave the RA for longitude 224 deg 40 min (round off from 224 deg 39 min) is 222 deg 12 min.
*** if RA is greater than 0 and longitude is less than 180, leave RA as is
if RA is greater than 0 and longitude is greater than 180, add 180 to RA
if RA is less than 0 and longitude is less than 180, add 180 to RA
if RA is less than 0 and longitude is greater than 180, add 360 to RA
if longitude is 0 deg, RA = 0 deg
if longitude is 90 deg, RA = 90 deg
if longitude is 180 deg, RA = 180
Observe that place is not required to calculate RA, only year (for obliquity) and of course the corresponding degree (in this case the MC).
Next, the calculation of oblique ascension, OA
To Calculate right ascension, RA and oblique ascension, OA:-Tony, I see that we have slight difference is the directed arc. I have 28? 44?, while you have 27? 49?. Where do you get your oblique ascensions from? I?m trusting that web site I cited but who know how they calculate it.
First we need the obliquity of the ecliptic, obl
obl = 23.45229444 - [0.4684 x (year-1900)/3600]
(This is an empirical formula to calculate obliquity of the ecliptic w/o having to refer to astronomical table)
example in year 1616
obl = 23.45229444 - (0.4684 x (1616-1900)/3600)
obl=23.489246
obl = 23 deg 29 min 21.3 sec
Comparison with solar fire, obl = 23deg 29 min 21 sec
Another example (Year 2006)
Using the above formula, obl = 23.43849677 = 23 deg 26 min 18.6 sec
Comparison with solar fire, obl = 23deg 26 min 18 sec
Calculation of Right Ascension (RA):-
tan RA = tan (long) x cos (obl)
long = longitude, obl = obliquity of the ecliptic
Let us calculate the right ascension, RA of midheaven, MC in Lilly's English Merchant example,
the year was 1616,
obl (calculated above) = 23.489246 deg
longitude of the MC (given) = 14 deg 39 min Scorpio
From Aries, longitude of MC then equals to 224 deg and 39 min = 224.65 deg.
tan RA = tan (224.65) x cos (23.489246)
tan RA = 0.905997877
RA = 42.17651082 deg***
but this is in the 3rd sector (longitude is between 180 to 270 deg), hence
RA = 42.17651082 + 180 = 222.1765108 deg = 222 deg 10 min 35 sec (***see below).
Using the site that you gave the RA for longitude 224 deg 40 min (round off from 224 deg 39 min) is 222 deg 12 min.
*** if RA is greater than 0 and longitude is less than 180, leave RA as is
if RA is greater than 0 and longitude is greater than 180, add 180 to RA
if RA is less than 0 and longitude is less than 180, add 180 to RA
if RA is less than 0 and longitude is greater than 180, add 360 to RA
if longitude is 0 deg, RA = 0 deg
if longitude is 90 deg, RA = 90 deg
if longitude is 180 deg, RA = 180
Observe that place is not required to calculate RA, only year (for obliquity) and of course the corresponding degree (in this case the MC).
Next, the calculation of oblique ascension, OA