Astronomical Algorithms
[WIP]
People who write their own computer programs often wonder why the machine gives inaccurate planet positions, an unreal eclipse track, or a faulty Moon phase. Sometimes they insist, bewildered, “and I used double precision, too.” Even commercial software is sometimes afflicted with gremlins, which comes as quite a shock to anyone caught up in the mystique and presumed infallibility of computers. Good techniques can help us avoid erroneous results from a flawed program or a simplistic procedure–and that’s what this book is all about.
1. Hints and Tips
RA \(\alpha\)(Right Ascension) to degrees conversion: 1h = 15 degrees
Avoid powers in calculations using Horner’s method. Suppose that one wants to calculate the value of the polynomial
\[y = A + Bx + Cx^2 + Dx^3 + Ex^4\]
It is better to write it as
\[y = A + x(B + x(C + x(D + E)))\]
so that all power functions have disappeared and we only perform additions and multiplications. This is especially well suited for automatic calculation because powers are avoided.
Interesting way to exchange two variables X and Y (equivalent to X, Y = Y, X in Python):
X = X + Y
Y = X - Y
X = X - Y