More from Gravity & Orbits
Other simulators in this category — or see all 27.
Mercury Perihelion Precession
GR Δω per orbit vs Newton; ~43″/century readout; amplified animation.
Earth–Moon Barycenter Wobble
Heliocentric path of Earth’s center: barycentric ellipse plus lunar epicycle (exaggerated).
Oberth Effect
Same prograde Δv at peri vs apo on one ellipse; higher ε when burning deep.
Schwarzschild Orbit Precession (Rosette)
Schwarzschild geodesic in the φ-form d²u/dφ² + u = 1/L² + 3u² (G = c = M = 1) integrated by RK4. The closed Newtonian ellipse is replaced by an orange precessing rosette with apsidal advance Δφ ≈ 6πM/[a(1 − e²)] per orbit — the same mechanism that produces the historic 43″/century perihelion shift of Mercury. Horizon r = 2M and ISCO r = 6M annotated.
ISCO & Photon Sphere (V_eff)
Schwarzschild effective potential V_eff(r) for massive (timelike) and photon (null) test particles in geometric units. Sliding angular momentum L collapses the stable / unstable circular pair into the innermost stable circular orbit r_ISCO = 6M (the inner edge of accretion discs); for photons the unstable photon sphere r = 3M defines the inner ring of black-hole shadow images.
Einstein Ring & Paczyński Microlensing
Point-mass thin lens (weak-field GR): lens equation β = θ − θ_E²/θ gives two images θ_± = ½(β ± √(β² + 4θ_E²)) with magnifications μ_± = ½[(u² + 2)/(u√(u² + 4)) ± 1], u = β/θ_E. Animated source transit at impact parameter u₀ over timescale t_E renders the canonical symmetric Paczyński light curve and the full Einstein ring θ_E = √(4GM·D_LS/(c² D_L D_S)) at perfect alignment.