N-BODY ENGINE

NASA Horizons · 10 Bodies · Light-Delayed Gravity · Elastic Collisions

Mission Clock

Y:0000 M:00 D:00

Warp 1× → 1 week / real-sec Clock = actual sim time

Sim elapsed: 0.000 yr Week 0

NASA Horizons API

Epoch Date YYYY-MM-DD

e.g. 2026-01-01 · min 1900-01-01

Ready. Fetches all 10 bodies (Sun → Pluto) from JPL sequentially.

Time Warp1.0×

Zoom1.0

Live Telemetry

Reference Ephemeris

Horizons daily + Kepler

All planets: Kepler drift (2-body analytic vs Sun) + Horizons drift (vs JPL ephemeris) + Kepler↔Horizons gap. Requires CORS proxy for live Horizons data.

Physics Guide

Light-Delayed Gravity▸

In Newtonian gravity, force is instantaneous — the Sun would "know" Venus's position right now. This simulation instead propagates gravity at the speed of light (c = 299,792 km/s).

When computing the gravitational pull of the Sun on Venus at time t, we look up where the Sun was at the light-delay time t_ret = t − d/c, where d is the current Sun–Venus distance. The force direction points from Venus toward that past position of the Sun.

For Sun–Venus the light delay is ~360 seconds (~6 minutes). The orbital effect is tiny but physically correct — this is the same principle behind gravitational wave propagation.

Symplectic Leapfrog▸

The simulation uses Verlet/leapfrog integration, a symplectic method that conserves orbital energy over long timescales far better than Euler integration.

Each timestep: v += a·(dt/2), then x += v·dt, forces are recomputed, then v += a·(dt/2) again (kick-drift-kick). The substep size is 3,600 sim-seconds (1 hour) for accuracy despite the week-per-second tick rate.

Elastic Soft-Body Collision▸

When any two bodies' centre-to-centre distance falls below the sum of their physical radii, an elastic collision is triggered. All N(N-1)/2 pairs are checked each substep.

The impulse along the collision normal conserves both momentum and kinetic energy (coefficient of restitution = 1). Bodies are displaced apart to prevent interpenetration. There is no softening on the gravitational potential — the only floor is the physical surface collision itself.

Time Scale & Units▸

All physics runs in km · km/s · seconds — real SI-adjacent units.

Tick rate: at Warp 1×, 1 real second advances 604,800 sim-seconds (1 week). At Warp 10×, 1 real second advances 10 sim-weeks, and so on.
Mission Clock: shows the actual simulated calendar time elapsed (Y/M/D), derived directly from simTime. It speeds up and slows down with the time warp slider — there is no separate clock rate.

G = 6.674 × 10⁻²⁰ km³/(kg·s²)
c = 299,792.458 km/s

NASA Horizons Data▸

Position and velocity are fetched from JPL Horizons (ssd.jpl.nasa.gov/api/horizons.api), NASA's high-precision ephemeris service used for real mission planning.

We request state vectors — Cartesian position (km) and velocity (km/s) — for the Sun and Venus relative to the Solar System Barycenter at your chosen epoch.

Coordinate frame: Horizons defaults to ICRF (equatorial), whose x-y plane is Earth's equatorial plane — not the orbital plane. We request REF_PLANE=ECLIPTIC so the output is rotated to the J2000 mean ecliptic. In that frame, x-y is the ecliptic plane and z captures Venus's 3.39° inclination. All three axes are used — the simulation is fully 3D.

The built-in J2000 fallback stores values in ICRF (for source transparency) and applies the same ecliptic rotation via icrfToEcliptic() — a rotation by the obliquity ε = 23.439° about the x-axis — before passing data to the sim.

        ● NASA / Horizons position

        ● Kepler analytic solution

        ╌╌ Drift deviation

Source Built-in J2000

☀ Earth Delay — s

☀ Earth Dist — AU

Collision None

NASA Updated —

— AU