This 2D companion runs the identical Kepler-orbit propagation as the 3D scene — the Sun at one focus, position found by solving Kepler's equation for the eccentric anomaly E from the mean anomaly M = 2π·t/T (Newton–Raphson), then rotated by inclination and longitude of ascending node — but draws it as a bird's-eye map instead of a free 3D camera.
M(t) = M0 + 2π t / T T = a^1.5 (years, a in AU, solar mass)
E - e·sinE = M (solved numerically each frame)
px = a(cosE - e) pz0 = a·sqrt(1-e²)·sinE
py = pz0·sin(i) (height, not drawn) pz1 = pz0·cos(i) (foreshortened in-plane)
x = px·cosΩ - pz1·sinΩ z = px·sinΩ + pz1·cosΩ
q = a(1-e) perihelion Q = a(1+e) aphelion
Looking straight down on an inclined ellipse compresses it along the direction perpendicular to the line of nodes by a factor of cos(i) — that foreshortening is genuine geometry, not a stylised effect, so the map still tells you the true shape of each orbit even though the vertical (out-of-plane) coordinate itself is never drawn.
The detachment puzzle: Neptune (a ≈ 30 AU) can gravitationally scatter any object whose perihelion dips within roughly its own orbit — that's the "scattered disk," objects with q near 30–40 AU that get kicked around every close pass. Sedna (q ≈ 76 AU, a ≈ 506 AU) and 2012 VP113 (q ≈ 80 AU) are different: their perihelia sit far *outside* Neptune's reach, so nothing in the known Solar System can have put them there or can currently perturb them. They are dynamically detached.
- a, e sliders — set your test object's semi-major axis and eccentricity; q and Q update live, and the badge flips between "coupled" and "detached" at the q ≈ 40 AU threshold used in the literature.
- Inclination slider — tilts the orbital plane; watch the test object's orbit visibly flatten toward its line of nodes as you raise it, exactly the foreshortening real detached objects show in sky surveys.
- Time scale — because periods range from ~250 years (classical Kuiper belt) to over 11,000 years (Sedna), this compresses simulated time so orbits are watchable.
- Drag to pan, scroll/pinch to zoom — the map is not fixed to one scale; zoom in near the Sun to compare Neptune and the classical KBO, or out to see Sedna's full 500+ AU aphelion.
Leading explanations for detached orbits: a passing star during the Sun's birth cluster tugging perihelia outward, an undiscovered distant "Planet Nine," or a stellar flyby raising perihelion after formation in the scattered disk. No single mechanism is confirmed — it remains an open question in Solar System dynamics.