Okay, I’m not quite that bad. Yes, I was was a Music Major, but I really loved Music theory, which is mostly math using a different set of symbols and rules. Likewise, I loved my accounting classes, and the math-y parts of chemistry. Really, anytime Math was connected to something non-abstract, I did well with it. But when Math was all abstract numbers and fiddling with abstract numbers. . . um, not so good.
So often as students, we ask our teacher: When are we gonna use this in real life? The answers were generally so terrible I can’t even remember what they were.
I, however, have encountered a sudden need to use Trigonometry, something I haven’t even seen since, like, high school.
My problem is as follows: I’m writing a science fiction novel. Well, it might be argued that it’s more fantasy set in the future, with spaceships and such. . . like ninjas. Anyway, the elder brother (Thomas) of one of the main characters (his sister Niut) needs to get home to his sister ASAP. He is currently on the space station Birkeland 3, orbiting the star Caph (aka, Beta Casseopiae). He needs to get to the planet Fatima, orbiting the planet Hamal (aka, Alpha Arietis), where his sister Niut is. In the scene I am writing, he is meeting with the local “Station Chunin” (A chunin is literally a “middle man”, in this case, a local manager/ organizer sort of person) to plan his way home. An important part of the discussion is mention of the distance between these two stars– I have found one calculator, but I want to be sure I understand the math behind it, so I can try it myself if needed later (the site goes down, I loose the bookmark, etc.)
I get the equations from here: http://www.neoprogrammics.com/distance_between_two_stars/
I get the basic data for the stars from their respective Wikipedia entries (which is pretty decent for this sort of work).
Converting coordinate hours, minutes, seconds to decimals occurred here: http://www.robertmartinayers.org/tools/coordinates.html
Let’s see me attempt this on my own. . .
It looks like the basic idea is to take the known coordinates, translate them into X,Y,Z coordinates, and then plug those into a final equation. We need the Right Ascension (a), Declination (d), and Distance in Light years (R).
X= R * C0s(a) * Cos(d)
Y= R * Sin(a) * Cos (d)
Z= R* Sin(d)
With Star 1 labeling X1, Y1, Z1, and Star 2 labeling X2, Y2, Z2.
Caph (Star 1)
X1=54.7 * Cos(2.2945) * Cos(59.1498) =54.7 *.999198243*.51279525 = 28.0274
Y1=54.7 * Sin(2.2945) * Cos(59.1498) = 54.7 * .040035877*.51279525= 1.1230
Z1=54.7* Sin(59.1498) = 54.7 * .858510938 = 46.9605
Hamal (Star 2)
X2= 65.8 *Cos (31.7934) *Cos (23.4624)=65.8*.849953388*.917321554=51.3029
Now, we find the differences of each coordinate:
We plug these three numbers into the following equation to find for D (distance in light years):
D=SqRoot (dx*dx + dy*dy + dz*dz)
D=SqRoot (23.2755*23.2755 + 30.6780*30.6780 + -20.7625*-20.7625)
D=SqRoot (541.7489 + 941.1397 + 431.0814)
Therefore, the distance between Beta Casseopiae (Caph) and Alpha Arietis (Hamal) is 43.7489 Lightyears.
Checking against the calculator, this looks right.
Grunt (and other truly mathy sorts reading this): if you were my teacher, would you think I understood this process, based on the work shown?