6. Projectile Motion II: Central-Force Motion

When the Feynman algorithm is applied to motion in two dimensions, the loop contains twice as many statements (one set for x, the second for y), but the algorithm itself does not change. The first example follows the trajectory of a projectile launched from the north pole at an angle of elevation of 45 degrees. The program finds the latitude at which it lands, its impact angle, and its impact velocity.

The second example is a program I have used for many years as a benchmark for testing hardware and software. It plots orbital motion in central-force fields that vary as a power of the distance from the force center. One can choose from three different powers: direct first power (the spring), inverse second power (gravity), and inverse first power. The spring and gravity orbits close, and the parameters are chosen to make the inverse first power orbit appear to close (it makes a pretty picture).