Calculating the Right Ascension and Declination of the Sun

Question

I've been following this guide, porting it to javascript: http://www.saao.ac.za/public-info/sun-moon-stars/sun-index/how-to-calculate-altaz/

Everything was going swimmingly up until 9.(right ascension) and 10.(declination). I can't recreate the answers they give for these.

(9) find alpha the right ascension of the sun: (a) for cape town:

lambda = 326.186
epsilon = 23.4396
alpha = arctan (tan(lambda) x cos(epsilon)) // in same quadrant as lambda

// THEIR RESULT
alpha = 328.428

// MY RESULT
var DEGREES = function (val) {
    return val / (Math.PI / 180);
};
var alpha = Math.atan(Math.tan(lambda) * Math.sin(epsilon));
alpha = 0.495;
alpha = DEGREES(0.495) = 28.39;

I also tried:

var alpha = Math.atan2(Math.tan(lambda) * Math.sin(epsilon), lambda);
alpha = DEGREES(result) = 1.321;

Not even close!

And 10(a), the declination

delta = arcsin (sin(lambda) x sin(epsilon))

// THEIR RESULT
(a) delta = -12.789

// MY RESULT
var result =  Math.asin(Math.sin(eclipticLong) * Math.sin(obliq));
result =  DEGREES(result);
result = -10.966;

As you can see I'm clutching at straws as I don't really have a clue about this. Any help would be much appreciated.

Answer 1

Well, the biggest issue I see is here:

alpha = arctan (tan(lambda) x cos(epsilon)) // in same quadrant as lambda
...
var alpha = Math.atan(Math.tan(lambda) * Math.sin(epsilon));

You went from using cosine to sine in the second expression.

Now, this on the face of it doesn't lead to the same result, so lets dig in a bit deeper. For clarity, I'm going to use these functions and constants:

var lambda = 326.186;
var epsilon = 23.4396;
function rad (v) { return v * Math.PI / 180 }
function deg (v) { return v * 180 / Math.PI }

Javascript math functions take a radial coordinate, so lets give this a try:

var result = deg(Math.atan(Math.tan(rad(lambda)) * Math.cos(rad(epsilon)))); 
console.log(result); // -.31.5717

Thanks to the magic of how degrees work, this is the same answer as 360 + -31.5717 = 328.428.