EARTH & MOON · ORBIT LAB

Interactive orbital physics laboratory

Real Earth–Moon constants · 384,400 km baselinevelocity Verlet · 60 s step · ≤4000 substeps/frame

In orbit · t = 0.0 hours

Actual path
Predicted orbit
V velocity
G gravity

EARTH & MOON

ORBIT LAB

Loading 3D laboratory…

Orbit status

Circular1.00× circular speed

Distance: 384,400km
Speed: 1.018km/s
Eccentricity: 0.000e
Orbit type: Circular

Speed vs circular1.018 of 1.440 km/s escape

Below 1.44× circular the orbit stays bound. Past escape speed the total energy turns positive and gravity can never bring the Moon back.

Scenarios

Sideways speed exactly balances the fall. Distance holds steady and eccentricity stays near 0.000.

Controls

Moon velocity1.018 km/s= 1.00× circular

0.05×2.00×

Earth gravity1.00× Earthμ = 3.99×10^14 m³/s²

0.10×3.00×

Simulation speed1.0 days / secondplayback rate only

0.1 days/s8 days/s

Camera

Orbit the laboratory with drag and pinch.

Show physicsVelocity, gravity, orbital plane and radius

Energy

bound

Kinetic0.518 MJ/kg½v²

Potential-1.037 MJ/kg−μ/r

Total-0.518 MJ/kgε = ½v² − μ/r

kinetic 33%potential 67%

Kinetic + gravitational potential = total orbital energy, per kilogram of Moon. On a stable orbit the total stays constant: the Moon trades speed for height and back again. It turns positive only when the Moon is fast enough to escape for good.

Orbit information

t = 0.0 hours

Circular velocity1.018 km/s√(μ/r) here and now

Escape speed1.440 km/s√2 × circular

Period27.45 daysT = 2π√(a³/μ)

Semi-major axis384,400 km

Periapsis384,400 km

Apoapsis384,400 km

Angular momentum3.91×10^11 m²/sh = |r × v|

Collision radius8,108 kmEarth + Moon, physical radii

Experiments

0 saved

Stores the current gravity, velocity, distance, speed, eccentricity, orbit type and elapsed time. Tick two runs to compare.

No runs saved yet. Set up an orbit, then capture it.

Why doesn't the Moon fall into Earth?

Gravity constantly pulls the Moon toward Earth.

But the Moon also has sideways velocity — at its real distance, 1.018 km/s.

So while the Moon is falling toward Earth, Earth’s surface curves away beneath it. It keeps falling, and keeps missing.

The result is an orbit: a continuous fall with enough sideways speed that the ground never arrives.

Advanced physics (show)

F = G·M·m / r²

a = μ / r² μ = G·M_earth

v_circular = √(μ/r)

v_escape = √(2μ/r) = √2 · v_circular

ε = ½v² − μ/r

e = |((v² − μ/r)·r⃗ − (r⃗·v⃗)·v⃗) / μ|

T = 2π√(a³/μ)

Reference distance: 384,400 km
Circular velocity there: 1.018 km/s
Escape speed there: 1.440 km/s
Resulting period: 27.45 days
Physics timestep: 60 s (velocity Verlet)

This laboratory holds Earth fixed, so μ = G·M_earth and the period works out at 27.45 days. The Moon’s real 27.32-day sidereal period comes from the two-body mass G(M_earth + M_moon) — a 1.2% difference, and the reason the figure here is slightly longer.

A single experiment of a larger design: the physics engine keeps Earth–Moon separate from the renderer, so Sun, Lagrange points, spacecraft and n-body gravity can be added later without rewriting this interface.