calculating the transfer/included angle between two coplanar position vectors

[cdeaglejr]

This post is a short HP Prime program that demonstrates how to calculate the transfer or “included” angle between two position vectors. The software assumes both position vectors are coplanar and relative to the same celestial body. Coplanar implies the two position vectors are locations on the same Keplerian orbit.

The user can define the components of the initial and final position vectors in kilometers starting at line 53 in the HP PPL source code.

// first position vector (kilometers)

r1(1) := 0.139058874109e9;
r1(2) := 0.540740344397e8;
r1(3) := -0.141100894780e4;

// second position vector (kilometers)

r2(1) := -0.156874862616e9;
r2(2) := -0.172068693183e9;
r2(3) := 0.246522313449e6;

Can you describe the orbital mechanics defined by the mathematics?