[subego]

Well, I'm writing a program that will solve some basic astronomical equations for a planet revolving around a sun and also happens to use a bunch of math beyond my skills. Yes, this is stupid. I'm trying to teach (or relearn) what I need to get by, and I've been more or less fine up to this point.

The equation I need to solve is:

Atan(sin(λ)*cos(ε)/cos(λ))

Where λ is the ecliptic longitude of the sun as seen from the planet (i.e. an angle from 0-360º) and ε is obliquity of the planet with respect to the sun's ecliptic (an angle from 0-90º)

Okay, I can do that, but I need to figure out the correct quadrant for my solution so I can get a number between 0-360º. I could use Atan2 if I had any idea of how to properly derive x and y, but I don't. I could probably figure it out if it was just one angle, but the multiplication of angles and different trigonometric functions is just going to make my head hurt.

So I tried to brute force it for awhile by plugging in different values for λ. It appears the solution is always going to be in the same quadrant as λ, except when undefined.

Do I have this right? Can I use which quadrant λ is in to determine which quadrant my solution is in for any value of ε?

Does any of this make sense? Did I blow it by not understanding the quadrant thing from the outset?

[olePigeon]

I'm surprised I squeaked by Trig with a C cuz I haven't a clue what the f*ck you just said.

[subego]

That makes two of us.

[subego]

Worked this out with my dad, who's M.S. in math came in handy.

Since I know everyone is aching to hear the answer, here it is:

The solution is in the same quadrant as λ.

Cos(ε) is always in the 1st quadrant, so the pair of numbers that define the triangle are always both going to be positive. Multiplying something by a positive doesn't change its sign, so the pair of numbers which define the triangle for sin(λ)/cos(λ) aren't going to change their sign when multiplied by cos(ε), and therefore remain in the same quadrant.

Yay for math!

[loki74]

Cool. Although if I may, exactly what are you making this for? Any chance you could post some screens of the app and its functionality when you're done?

[subego]

Sure. It'll be awhile before I'm done. I just started.

It's going to be the first piece of a random weather generator. I want it to have proper almanac data like sunrise and sunset times, as well as have the weather it generates be influenced by such.

Of course that's the first piece of an 11th century feudal manor simulation (I want the thing to have weather, don't I?) but I wanted to start, ahem... small.

Relevant to the original topic, a few hours ago I found the answer to this question on Wiki. Not the answer in general, but the answer for this specific question (i.e. when converting ecliptic coordinates into equatorial coordinates, the quadrant for right ascension (which is what I'm solving for) is in the same quadrant as ecliptic longitude (λ))