Slingshot

Every body pulls the probe with Newton's inverse-square law. The game advances in fixed steps of 1/240 of a second using velocity Verlet, the same family of integrators used in real orbit simulations, so orbits stay stable instead of slowly spiraling.

Planets and stars move on fixed, precomputed paths, which keeps the dotted prediction exact: what you see before launch is what will happen. In the Lagrange level the view rotates with the planet, which is how astronomers usually draw L4 and L5.

Transfer orbit is a scale model of Earth and Mars: one year lasts 8 seconds and Mars's orbit is 1.524 times the size of Earth's, as in the NASA Mars Fact Sheet. The orbits are drawn as perfect circles in one plane (the real Mars orbit has an eccentricity of 0.09) and the planets' own pull is left out, which is how planners sketch the cruise between them. With those simplifications the cheapest path, a Hohmann transfer, takes about 259 days and needs Mars 44 degrees ahead at launch. Earth laps Mars about once every 26 months, so the line-up repeats on that cycle (NASA JPL, Mars 2020 launch press kit). Miss a window and you wait for the next one.

Equal areas shows Kepler's second law: the line from the star to the probe sweeps equal areas in equal times. Each shaded wedge covers half a second of flight. The game does not force this rule; it falls out of the inverse-square pull, because a central force cannot change the probe's angular momentum, and the integrator keeps that quantity fixed too.