[VA] SRC #012f - Then and Now: Angle

[Valentin Albillo]

  
Hi, all,

Welcome to the 6^th and last part of my SRC #012 - Then and Now, where I'm showing that advanced vintage HP calcs which were great problem-solvers back THEN in the 80's are NOW still perfectly capable of solving recent non-trivial problems intended to be tackled using modern PCs, never mind ancient handheld calcs.

Now, try and solve the last problem using your vintage HP calcs while abiding by this one rule, s'il vous plait:

Use any VINTAGE HP CALC (physical/virtual,) coding in either RPN/Mcode, RPL/SysRPL or HP-71B BASIC/FORTH/Assembler. NO CODE PANELS.

Problem 6:  Angle

Once P1 (Probability), P2 (Root), P3 (Sum), P4 (Area) and P5 (Roots) are over, now's the turn for P6 (Angle), the last and allegedly the hardest of the lot, which deals with optimization, namely:

Six stars of unit mass are fixed at points (2, -1), (2, 0), (2, 1), (3, -1), (3, 0) and (3, 1). A planet of unit mass starts at (0, 0) with unit velocity in direction Angle (in radians, counterclockwise from the X axis,) and travels according to Newton's gravitational law, i.e. under a force of magnitude (d_i )^-2 from each of the six stars, where d_i is the distance to each star.




Write a program to compute the value of Angle which makes the planet reach the point (4, 1) in the shortest time (a fake path is depicted above) and output the Angle and corresponding minimum time. Assume the gravitational constant G is 1.

Your program should take no inputs and must produce at least 4-5 correct digits (give or take a few ulp), the faster the better.

In a week I'll post my original solution (a straightforward 12-line HP-71B program that does the job) plus comments on my solving strategy and possible enhancements, but first let's see your very own clever solutions. It's your last chance !

V.
Edit: corrected two typos.