Gravity & Orbits
Orbital mechanics, solar system, tidal forces, and N-body simulations
- NewUniversity / research
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…
- NewUniversity / research
ISCO & Photon Sphere (V_eff)
Schwarzschild effective potential V_eff(r) for massive (timelike) and photon (null) test particles in geometric units. Sliding angular mo…
- NewUniversity / research
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_± =…
- NewUniversity / research
Gravitational Wave Binary Chirp (Inspiral)
Leading-order post-Newtonian inspiral of a compact binary: f(τ) ∝ τ^(−3/8), strain h(t) ∝ M_c^(5/3) f^(2/3) / D_L. Tune component masses…
- NewUniversity / research
Shapiro Time Delay (4th GR Test)
A radio signal grazing the Sun picks up an excess one-way travel time Δt ≈ (2GM/c³) ln[(r_E + r_E cos α)(r_R + r_R cos β)/b²] on top of t…
- NewUniversity / research
Three-Body Figure-Eight
Equal masses: Chenciner–Montgomery choreography in 2D (RK4, periodic orbit).
- NewUniversity / research
Restricted 3-Body (map)
CRTBP: escape vs collision vs chaos proxy; μ slider.
- NewSchool
Multistage Rocket (Tsiolkovsky)
Δv per stage; sum vs single-stage with same total propellant.
- NewSchool
Orbital Debris & Kessler (toy)
LEO shell: n = N/V, collision rate ∝ N²; optional fragment cascade.
- NewSchool
Gravity-Assist Fly-By
Planet frame |u_out|=|u_in| rotated by δ; star frame v = V + u — Δ|v| from moving planet.
- FeaturedSchool
Orbit Simulator
Fixed central mass: tune speed and launch angle for circular, elliptical, or escape trajectories.
- School
Solar System
Interactive scaled model with time controls and orbital data.
- FeaturedSchool
Gravity Sandbox
Place masses and watch N-body gravitational interactions unfold.
- School
Kepler's Laws
Elliptical orbits with equal-area sweeps visualized.
- School
Escape Velocity
Launch from different planets and see trajectory results.
- NewUniversity / research
Gravitational Lensing
Massive objects bending light. Visual distortion effects.
- NewUniversity / research
Lagrange Points L1–L5
CRTBP effective potential; L1–L5; Coriolis test particle.
- NewSchool
Earth–Moon Tides
Equilibrium tide bulges; orbit speed; ~12.4 h spacing note.
- NewSchool
Binary Star (circular)
COM orbits; r₁,r₂; Kepler T² ∝ a³/(M₁+M₂).
- NewUniversity / research
Roche Limit
Fluid d ≈ 2.456 R_p (ρ_p/ρ_s)^(1/3); vs orbit distance.
- NewSchool
Space Elevator Tether
1D tension vs height; peak near GEO (normalized model).
- NewSchool
Hohmann Transfer
Coplanar circles r₁,r₂; transfer ellipse; Δv₁, Δv₂ from vis-viva.
- NewSchool
Geostationary Orbit
ω²r = GM/r² from sidereal vs solar day; Earth-fixed view with sub-satellite longitude.
- NewSchool
Orbital Decay (Atmosphere)
Toy perigee drag: shrinking, circularizing ellipse; ISS lifetime intuition.
- NewUniversity / research
Mercury Perihelion Precession
GR Δω per orbit vs Newton; ~43″/century readout; amplified animation.
- NewSchool
Earth–Moon Barycenter Wobble
Heliocentric path of Earth’s center: barycentric ellipse plus lunar epicycle (exaggerated).
- NewUniversity / research
Oberth Effect
Same prograde Δv at peri vs apo on one ellipse; higher ε when burning deep.