v2.0.0
2026-04-27
2026-04-27
Astro.phyzix
ORBITRAXX
N-BODY RELATIVISTIC EPHEMERIS ENGINE
CUSTOM BUILT ON MIT FRAMEWORK
ASTROPHYZIX
HPC-CLASS
ORBITRAXX
MIT FRAMEWORK
PHASE SPACE VISUALIZATION
INTEGRATING
INTEGRATION PARAMETERS
INTEGRATOR
TIME STEP (days)
LOOP PERIOD (yr)
PHYSICS FLAGS
SIMULATION SPEED
BODY REGISTRY ICRF J2000.0
| NAME | MASS(Ms) | r(AU) | v(AU/y) | TYPE |
|---|
CONSERVATION DIAGNOSTICS
OSCULATING ORBITAL ELEMENTS HELIOCENTRIC
| BODY | a(AU) | e | i(deg) | dw/dt(as/yr) |
|---|
Mercury GR prediction: 42.98 as/yr. dw/dt = perihelion precession rate.
UNCERTAINTY ELLIPSOIDS (COV. EVO.)
STM propagation [C1]. Initial 1-sigma pos: 1e-4 AU, vel: 1e-6 AU/yr. Log-scaled bars: sx(dark), sy(mid), svx(light).
SEMI-MAJOR AXIS DRIFT MONITOR
Delta-a (AU) vs time (yr) per body. Secular drift indicates integrator energy leakage.
ENERGY CONSERVATION HISTORY
log10|dE/E0| vs time (yr). Green <1e-8, amber <1e-5, red = instability.
CLOSE APPROACH LOG MIN DIST PER PAIR
Closest recorded approach per body pair (AU). Updates every 5 steps.
BODY EDITOR RUNTIME ADD/REMOVE
NEW BODY
VELOCITY
ACTIONS
EPHEMERIS EXPORT + PROVENANCE RECORD
Buffer: 0 records.
PROVENANCE + GOVERNANCE DOCUMENTATION
ALGORITHMIC PROVENANCE
[N1]RK4: Kutta (1901). Classical 4th-order Runge-Kutta. 4 derivative evaluations per step. O(dt^4) local error. Reference baseline only.
[N2]RK8: Prince-Dormand (1981) 8th-order fixed-step method. 13 stage evaluations. Coefficients from Hairer, Norsett, Wanner (1993) Table II.5.2. O(dt^8) local error.
[N3]Yoshida (1990). 6th-order symplectic integrator. Drift-kick-drift composition. Exactly preserves symplectic 2-form to machine precision; energy error bounded (does not grow secularly).
[N4]Hermite PC: Makino and Aarseth (1992). 4th-order predictor-corrector. One correction iteration. Efficient for dense N-body.
RELATIVISTIC CORRECTIONS
[R1]1PN EIH equations: Einstein-Infeld-Hoffmann. Soffel et al. (2003) IAU 2000 conventions. Damour and Deruelle (1985). Accounts for Schwarzschild + interaction terms. Mercury precession: ~42.98 as/yr.
[R2]Lense-Thirring (1918). Frame dragging from rotating body spin. S = a* G M^2 / c where a* is dimensionless Kerr parameter. Applied as spin-orbit coupling term to velocity.
[R3]Peters (1964). GW radiation back-reaction via quadrupole formula. da/dt = -(64/5)(G^3 M m (M+m))/(c^5 r^3) projected along velocity. Active only for BH-type bodies.
PERTURBATIONS
[P1]J2 oblateness: Heiskanen and Moritz (1967). Zonal harmonic. a_J2 = (3/2)(J2 GM R^2/r^5)[5(z/r)^2-1]*r_vec + z-correction. Earth J2=1.083e-3, Jupiter J2=1.47e-2.
FLOATING-POINT PRECISION
[F1]Kahan (1965) compensated summation. Reduces accumulation from O(N eps) to O(eps). Applied to energy and momentum sums. Toggle via checkbox.
[F2]Barycenter correction applied at preset load. Softening eps=1e-6 AU. IEEE 754 double: 53-bit mantissa, eps_mach ~ 2.22e-16.
COVARIANCE PROPAGATION
[C1]State transition matrix (STM). Tapley, Schutz, Born (2004). P(t)=Phi*P0*Phi^T. Jacobian via central finite differences (h=1e-7 AU). Updated every 10 steps. Block-diagonal approximation per body.
COORDINATE SYSTEM
ICRF barycentric J2000.0. Units: 1 AU, 1 M_sun, 1 Julian year. G = 4*pi^2 AU^3 yr^-2 M_sun^-1 (exact). c = 63241.08 AU/yr.
LIMITATIONS
[L1] IEEE 754 double only. No quad precision. Long arcs (>100 yr) accumulate drift.
[L2] STM linearized: valid for sigma < 1e-3 AU. Diverges in chaotic regimes.
[L3] No tidal forces, SRP, or atmospheric drag.
[L4] GW: quadrupole only, no higher multipoles.
[L5] J2 only; no J3/J4 tesseral harmonics.
[L6] Not validated to JPL Horizons production standard.
[L2] STM linearized: valid for sigma < 1e-3 AU. Diverges in chaotic regimes.
[L3] No tidal forces, SRP, or atmospheric drag.
[L4] GW: quadrupole only, no higher multipoles.
[L5] J2 only; no J3/J4 tesseral harmonics.
[L6] Not validated to JPL Horizons production standard.
GOVERNANCE
[G1]License: MIT Framework. Custom-built by Astrophyzix. Self-contained HTML. No external dependencies except Google Fonts.
[G2]No telemetry. All computation client-side. No network calls during simulation.
[G3]Reproducible: deterministic given same IC, dt, IEEE 754 env. Export via OD.exportJSON().
[G4]Validation target: dE/E0 < 1e-8 over 10 yr with RK8/Yoshida. Reduce dt if exceeded.
ICRF J2000.0IEEE 754 DBL
RK8 8TH ORDER1PN EIH
KAHAN SUMSTM COV
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