Schwarzschild Orbit Precession (Rosette)
This interactive simulator explores Schwarzschild Orbit Precession (Rosette) in Gravity & Orbits. 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. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Gravity & Orbits.
Key terms
- schwarzschild
- orbit
- precession
- rosette
- schwarzschild orbit precession
- gravity
- orbits
How it works
Schwarzschild orbit equation d²u/dφ² + u = 1/L² + 3u² integrated by RK4 (G = c = M = 1). The orange GR geodesic precesses by Δφ ≈ 6πM/[a(1−e²)] per orbit — the same mechanism that produces the famous 43″/century perihelion advance of Mercury. A gray Newtonian ellipse is overplotted to isolate the GR correction; ISCO (r = 6M) and horizon (r = 2M) are marked.
More from Gravity & Orbits
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Einstein Ring & Paczyński Microlensing
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Gravitational Wave Binary Chirp (Inspiral)
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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 the Newtonian light-time. Cassini, Mariner and Viking presets, with the round-trip delay readout in microseconds and an animated bent-photon path against a straight Newtonian baseline. The Cassini 2003 conjunction constrains |γ_PPN − 1| < 2 × 10⁻⁵ — the strongest weak-field GR test to date.
Three-Body Figure-Eight
Equal masses: Chenciner–Montgomery choreography in 2D (RK4, periodic orbit).
Restricted 3-Body (map)
CRTBP: escape vs collision vs chaos proxy; μ slider.