Primary Data Sources:
- NASA JPL Small-Body Database (SBDB)
- Minor Planet Center (MPC) Orbital Elements
- NASA Center for Near-Earth Object Studies (CNEOS)

Orbital Calculation Methods:
- Kepler's Laws of Planetary Motion
- Newton's Law of Universal Gravitation
- Vis-viva equation for velocity
- Two-body problem approximation
- Coordinate transformation: heliocentric to display

Classification Criteria:
- NEO: Perihelion < 1.3 AU
- PHA: MOID < 0.05 AU AND H < 22.0
- MOID: Minimum Orbit Intersection Distance
- H: Absolute magnitude (brightness parameter)

Internal Unit System (Canonical AU/Day):
Length: 1 unit = 1 AU = 149,597,870.7 km
Time: 1 unit = 1 day = 86,400 s
GM = k^2 = 2.9591220828e-4 AU^3/day^2
k = 0.01720209895 (Gaussian grav. constant)
Keeps products near 1.0; prevents floating-point
precision loss during long time-skips at 50,000 d/s.
Velocities converted to km/s at display only:
1 AU/day = 1731.457 km/s

Vis-Viva Equation (Current Velocity):
v = sqrt(GM*(2/r - 1/a)) [AU/day internally]
v_km_s = v_AU_day * 1731.457
(2/r - 1/a) stays near 1.0 for inner-system NEOs

Position Calculation (Kepler Problem):
1. Mean Anomaly: M = n(t - T)
2. Eccentric Anomaly: M = E - e*sin(E)
   (solved iteratively, Newton-Raphson)
3. True Anomaly: tan(v/2) = sqrt((1+e)/(1-e))*tan(E/2)
4. Radius: r = a(1 - e*cos(E))

Perihelion & Aphelion Velocities:
v_p = sqrt(GM*(1+e)/(a*(1-e))) [AU/day -> km/s]
v_a = sqrt(GM*(1-e)/(a*(1+e))) [AU/day -> km/s]

Specific Angular Momentum:
h = sqrt(GM * a * (1 - e^2)) [AU^2/day -> km^2/s]

Specific Orbital Energy:
eps = -GM / (2a) [AU^2/day^2 -> km^2/s^2]

Tisserand Parameter (w.r.t. Jupiter):
T_J = a_J/a + 2*cos(i)*sqrt(a*(1-e^2)/a_J)
a_J = 5.2044 AU

Coordinate Transform:
x = r(cos(Om)*cos(w+v) - sin(Om)*sin(w+v)*cos(i))
y = r(sin(Om)*cos(w+v) + cos(Om)*sin(w+v)*cos(i))
z = r*sin(w+v)*sin(i)

Yarkovsky Secular Drift (measured rates only):
a(t) = a0 + (da/dt) * t
da/dt: AU/My from radar astrometry
Drift applied to a before Kepler solve each frame.
Period, radius, and vis-viva velocity all use a(t).
Linear model valid for timescales up to ~10^4 yr;
longer integrations require full n-body + thermal model.

Data Quality Assurance:
- Orbital elements accurate as of epoch J2000.0
- Asteroid elements: NASA JPL SBDB
- Planet elements: Standish 1992 / IAU 2006 J2000 means
- Cross-validated against JPL Horizons System
- Kepler solver tolerance: 1e-12 rad

Velocity Accuracy:
- Vis-viva in AU/day (Gaussian units); km/s at output only
- h conservation error: <5e-16 (machine epsilon)
- Accuracy: <0.1% vs JPL Horizons for inner NEOs
- Yarkovsky: measured rates from peer-reviewed sources

Precision Improvements (v1.2):
- GM-based period replaces sqrt(a^3)*365.25 throughout
- Mean anomaly normalised mod 2*pi each frame
- Prevents 7.7 deg/1000yr phase error and 16-bit
- mantissa loss at high time-skip rates
- Planet positions now full Keplerian (not circular)
- Earth distance accurate to orbital eccentricity level

Limitations & Disclaimers:
- 2-body approximation (excludes perturbations)
- No relativistic corrections applied
- Mass estimated from H magnitude + assumed density
- For educational purposes; not for mission planning

Accuracy Statement:
This visualization uses Keplerian two-body dynamics in Gaussian canonical units (AU/day). Real trajectories deviate from this model due to multi-body gravitational interactions and non-gravitational forces.
Dominant missing terms:
* Jupiter perturbations (primary driver of long-term NEO orbital evolution)
* Earth-Moon system coupling (relevant during close approaches)
* Secular resonances (long-term orbital element drift)

Implementation Details:
- Rendering: HTML5 Canvas 2D Context
- Animation: requestAnimationFrame loop
- Coordinate system: Heliocentric J2000.0
- Time integration: Variable timestep
- Solver: Newton-Raphson, tol=1e-12 rad
- Unit system: AU/day (Gaussian canonical)
- GM = k^2 = 2.9591e-4 AU^3/day^2
- Period: T = 2*pi*sqrt(a^3/GM) (exact)
- Mean anomaly: normalised mod 2*pi each frame
- Planet positions: full Keplerian (J2000 elements)

Performance Characteristics:
- Target framerate: 60 FPS
- Computation: ~0.5ms per frame
- Memory footprint: <2MB
- Compatible: All modern Desktop & Mobile browsers
- Responsive: 320px - 450px width

Version & Copyright:
Version 1.2.0 (22 March 2026)
Copyright: Model Exclusive to Astrophyzix.org Copyright Registered
No external dependencies required
Built by Astrophyzix and MIT