Astronomy
Tilt a reflecting sail. Resolve photon pressure into radial and tangential thrust and find the angle that gives the strongest sideways push.
Perfectly reflecting flat sail at 1 AU. Force vectors and a short constant-acceleration displacement are calculated; no full orbit, wrinkling or thermal limits.
Equations a = 2S cos²α/(c σ); a_r = a cos α; a_t = a sin α
Astronomy
Thousands of asteroids integrated under an eccentric Jupiter: the resonances pump their eccentricities until the orbits cross Mars or Jupiter, and the gaps open by themselves. Make Jupiter heavier to watch it happen within the run.
Astronomy
Swarms integrated about the triangular points in the rotating frame: tadpoles at small amplitude, horseshoes past the critical one, dispersal once the planet exceeds Routh’s limit.
Astronomy
Tilt an Earth orbit. Watch its orbital plane precess and compare the node drift with the special polar case.