The year is 2025. Two strange spherical particles, the Dannyon (mass $1\times 10^{-23}\,{\rm kg}$, radius $1\times10^{-6}\,{\rm m}$) and the Paulino (mass $50\times10^{-23}\,{\rm kg}$, radius $2\times10^{-6}\,{\rm m}$), have been discovered at the edge of the universe. These two particles have been observed interacting together (the Dannyon orbits the Paulino) in isolation many times, and it has been concluded that the two are bound by not only a Newtonian (gravity) force, but also something similar to a Hooke (spring) force.

The engineers hired to simulate the motion of the particles together are struggling incorporate the necessary forces, although they have available to them the necessary experimentally measured constants ($G=6.67\times10^{-11}\,{\rm N m^{2}/kg^{2}}$, $k=10\times10^{-7}\,{\rm N/m}$, $L_{0}=15\times10^{-6}\,{\rm m}$) and initial conditions ($\mbox{initial Dannyon position}=\langle20\times10^{-6},0,0\rangle\,{\rm m}$, $\mbox{initial Dannyon velocity}=\langle0,500,0\rangle\,{\rm m/s}$, $\mbox{initial Paulino position}=\langle0,0,0\rangle\,{\rm m}$, $\mbox{initial Paulino velocity}=\langle0,0,0\rangle\,{\rm m/s}$). Their work-in-progress code is attached below. Help them generate the simulation of the motion of the Dannyon around the Paulino.

• Modeling Motion with VPython
• Non-constant Force: Newtonian Gravitation
• Non-constant Force: Springs & Spring-like Interactions