Physics Lab

Projectile · Collision · Orbital — compare physics across Earth, Mars, and the Moon.

Earth Mars Moon
Launch parameters
Advanced physics
Active worlds
Earth: g=9.81 m/s², ρ₀=1.225, H=8.5 km Mars: g=3.71 m/s², ρ₀=0.020, H=11.1 km Moon: g=1.62 m/s², vacuum

Earth

g 9.81 · atm 1.225 kg/m³
Range
—
Max Height
—
Flight Time
—
Impact Speed
—
Bounces
0

Mars

g 3.71 · atm 0.020 kg/m³
Range
—
Max Height
—
Flight Time
—
Impact Speed
—
Bounces
0

Moon

g 1.62 · vacuum
Range
—
Max Height
—
Flight Time
—
Impact Speed
—
Bounces
0
Energy over time
Kinetic Potential Total

How the engine works

Integrated with classical 4th-order Runge–Kutta (RK4) at a 10 ms timestep. Equations of motion: 

F_gravity = -m · g · ŷ
F_drag    = -½ · ρ(h) · C_d · A · |v_rel| · v_rel        where v_rel = v - v_wind
F_magnus  =  ρ(h) · A · r · (ω × v_rel)                  (out-of-page spin)
a         = (F_gravity + F_drag + F_magnus) / m
ρ(h)      = ρ₀ · exp(-h / H)                              (isothermal atmosphere)

On the Moon, ρ = 0, so drag and Magnus vanish and the trajectory reduces to the ideal parabola. On Mars, the atmosphere is thin enough that heavy dense projectiles barely notice it.

Two-body collision (1D)
Collision physics is universal — v₁' and v₂' depend only on masses, velocities, and e. Post-impact sliding differs — friction force = μ·m·g, so lower g means blocks slide farther.

Earth

v₁ after
—
v₂ after
—
Slide dist (m₁)
—
Slide dist (m₂)
—

Mars

v₁ after
—
v₂ after
—
Slide dist (m₁)
—
Slide dist (m₂)
—

Moon

v₁ after
—
v₂ after
—
Slide dist (m₁)
—
Slide dist (m₂)
—

Collision + sliding friction

Momentum is always conserved: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'. Kinetic energy is conserved only when e = 1. The closed-form solution: 

v₁' = ((m₁ − e·m₂)·v₁ + (1 + e)·m₂·v₂) / (m₁ + m₂)
v₂' = ((m₂ − e·m₁)·v₂ + (1 + e)·m₁·v₁) / (m₁ + m₂)

After the collision, each body decelerates at a = μ·g. Because stopping distance is v²/(2μg), halving gravity doubles the sliding distance.

Orbital trajectory
Planet
Circular velocity vc = √(GM/r) Escape velocity ve = √(2GM/r) = vc·√2

Gravity with 1/r² falloff

Above the atmosphere, gravity weakens with distance: a = GM / r² directed toward the planet center. Integrated with RK4 at 2-second steps. A purely tangential launch at vc produces a circular orbit; between vc and ve, an ellipse; at or above ve, the projectile escapes on a hyperbolic trajectory. 

v_circ = √(GM / r)      — circular orbit speed at radius r
v_esc  = √(2GM / r)     — minimum escape speed
Earth @ 200 km:  v_c ≈ 7.78 km/s,  v_e ≈ 11.01 km/s
Mars  @ 200 km:  v_c ≈ 3.45 km/s,  v_e ≈ 4.88 km/s
Moon  @ 200 km:  v_c ≈ 1.60 km/s,  v_e ≈ 2.26 km/s
Sound propagation
Click anywhere on the canvas to emit a pulse. Each click fires a simultaneous pulse in all three lanes — watch how fast the wave propagates in each medium.
Earth 343 m/s 20°C, N₂/O₂
Mars 240 m/s −60°C, CO₂
Moon — m/s vacuum
Speed of sound c = √(γRT/M) — depends on gas composition and temperature. Amplitude ∝ 1/r × initial density — Mars pulses start quieter because the air is thin.

Sound needs a medium

Sound is a longitudinal pressure wave propagating through a gas (or liquid, or solid). Its speed is set by the compressibility and inertia of the medium: 

c = √(γ · R · T / M)
where γ = heat capacity ratio, R = gas constant, T = temperature, M = molar mass

Earth air (N₂/O₂ at 293 K) gives 343 m/s. Mars CO₂ at 213 K gives 240 m/s — slower because CO₂ is heavier and colder. On the Moon, there is essentially no atmosphere: no medium, no mechanical wave. Two astronauts standing next to each other can't hear each other directly — they have to use radios.

Amplitude also matters. A sound wave's pressure amplitude is proportional to the source intensity divided by the distance (spherical spreading). On Mars the air is ~160× thinner than Earth's, so the same source puts far less acoustic energy into the medium — it sounds muffled and faint, on top of traveling slower.

Simple pendulum
A pendulum's period depends on its length and the local gravity: T = 2π√(L/g). Same rod, three worlds — three different beats.
Earth T = —
Mars T = —
Moon T = —
T = 2π√(L/g) — period is independent of mass and (for small angles) amplitude. Earth @ 1m: ~2.0 s · Mars: ~3.3 s · Moon: ~4.9 s

Why they swing at different rates

A pendulum's restoring force is −m·g·sin(θ), and its equation of motion is 

θ''(t) = −(g/L) · sin(θ) − b · θ'

Small-angle approximation (sin θ ≈ θ):
θ(t) = θ₀ · cos(2π · t / T)    with    T = 2π · √(L/g)

Same length, three gravities, three periods. The ratio Earth : Mars : Moon is roughly 1 : 1.63 : 2.46 — exactly √(g_Earth / g_world). The mass of the bob doesn't appear anywhere: heavy or light, the period is the same.

Turn the initial angle up past ~30° and you'll see the small-angle approximation break down — the full nonlinear equation integrated here with RK4 gives a slightly longer period for larger swings.

Boiling point vs pressure
Water boils when its vapor pressure equals the surrounding atmospheric pressure. Thinner air means water boils at a lower temperature — and in a vacuum, liquid water simply cannot exist.
Earth P = 101.3 kPa, boil at —
Mars P = 610 Pa, boil at —
Moon P = 0 Pa, no liquid
Clausius–Clapeyron: ln(P/P₀) = −ΔHvap/R · (1/T − 1/T₀) ΔHvap(water) = 40.66 kJ/mol

Why boiling point depends on pressure

A liquid boils when its vapor pressure equals the ambient pressure. In a thinner atmosphere there's less "pushback," so boiling happens at a lower temperature. The Clausius–Clapeyron relation links them: 

1/T_boil = 1/T₀ − (R / ΔH_vap) · ln(P / P₀)

With water constants:
  T₀, P₀  = 373.15 K, 101.325 kPa
  ΔH_vap = 40 660 J/mol

Earth (101 325 Pa): T_boil ≈ 100 °C
Mars  (610 Pa):     T_boil ≈ −5 °C      ← below room temperature!
Moon  (0 Pa):       no liquid phase

On Mars, an astronaut's uncovered coffee would boil before it got warm enough to drink. On the Moon, water skips the liquid phase entirely — ice sublimes directly into vapor at any temperature above the triple point (0.01 °C, 611 Pa). This is why there's no standing water in any form on the lunar surface.

Live satellite tracker
Real satellites orbiting Earth right now. Positions computed live from TLE data via the SGP4 propagator — the same algorithm ground stations use.
Categories
View
Or set location manually
Click a satellite on the map to pin it — or hit Find satellites near me to see what's currently overhead.
Loading TLE data… —

How it works

Each orbit is stored as a two-line element set (TLE) — a compact 69-character format encoding orbital parameters (inclination, eccentricity, mean motion, epoch). TLEs are published publicly by CelesTrak and sourced originally from NORAD tracking. 

ISS (ZARYA)
1 25544U 98067A   26113.50000000  .00016717  00000-0  30571-3 0  9997
2 25544  51.6400  90.0000 0006000 100.0000 260.0000 15.48815308000000

The SGP4 algorithm (Simplified General Perturbations 4) propagates a satellite's state forward in time given a TLE, accounting for Earth's oblateness, atmospheric drag for low-Earth-orbit objects, and long-term secular effects. This app uses the open-source satellite.js implementation.

Positions are computed in Earth-Centered Inertial (ECI) coordinates, then converted to latitude, longitude, and altitude for the equirectangular map. The ground track is the projection of the orbit onto Earth's rotating surface — it isn't a great circle because Earth turns under the satellite as it orbits.

TLEs get stale — accuracy degrades by ~1 km/day for LEO. Click Refresh TLEs to pull the latest. For Starlink-like objects, refresh daily for sub-kilometer accuracy.

Mission Control
1 Design
2 Pad
3 Orbit
4 Launch
5 In Orbit
Spacecraft name
Form factor
Instruments (adds mass & power)
Dry mass—
Peak power load—
Solar peak—
Power balance—
T-00:00
ALT0 m
◉ FLIGHT COMMS
MISSIONAURORA-1
PHASEDESIGN
LIVE TELEMETRY · LOOP
Design your spacecraft —

How this works

Design — You spec mass, power, battery, propellant and instruments. We size power against solar input and battery storage, and track every kilogram against the launch vehicle's payload capacity. Try disabling solar panels to see what dies first — it's always the comms radio, at the top of the power pyramid.

Launch — The ascent animation uses a simplified gravity-turn profile: vertical liftoff for the first few seconds, pitch-over into a gravity turn, dynamic pressure peak around 60 s (Max-Q), first-stage cutoff at ~80 km altitude, upper-stage insertion burn at the target apogee, then a circularization kick. Event timing scales with the selected rocket's real-world cadence.

On-orbit — We propagate your orbit using classical Kepler two-body mechanics with J2 (Earth oblateness → nodal regression ≈ 5°/day for ISS-class orbits) and exponential-atmosphere drag for low-Earth-orbit decay. Position is converted to Earth-fixed lat/lon/alt each frame. Sub-solar point and Earth's shadow cone determine whether your solar panels are generating — in eclipse you're on battery.

Comms — A ground station has line-of-sight to your satellite if its elevation angle above the horizon is > 10°. While in view, you downlink at a rate set by your dish diameter and altitude (free-space path loss). Outside of view, data accumulates in the onboard buffer. 

Orbital energy:  ε = v²/2 - μ/r  = -μ/(2a)    (constant on a Kepler orbit)
Orbital period:  T = 2π·√(a³/μ)                (Kepler's third law)
Rocket eq.:      Δv = Isp·g₀·ln(m₀/m_f)        (Tsiolkovsky)
Drag accel:      a_d = ½·ρ·v²·Cd·A / m         (atmospheric entry/decay)

Built for fun, but the numbers are honest. Every constant — μ, J2, solar flux, atmospheric scale height — is real. If you design a satellite that shouldn't work, it won't.

Deep space
Everywhere humanity has reached so far, on a log-compressed map. Voyagers at ~0.002 ly · radio bubble at 125 ly · nearest SETI targets at 4–40 ly. Each concentric ring is 10× farther than the last.
V1 light was sent —
V2 light was sent —
ago — what you're seeing left the probe that long back
Voyager 1
Distance—
Speed—
Light delay—
Mission age—
Voyager 2
Distance—
Speed—
Light delay—
Mission age—
🎵 Golden Record
Etched into both probes: 27 musical tracks, greetings in 55 languages, nature sounds, 116 images — Earth's message in a bottle.
Bach · Brandenburg 2, 1st mvtBaroque Germany Chuck Berry · Johnny B. GoodeUSA, 1958 Blind Willie Johnson · Dark Was the NightUSA, 1927 Javanese gamelan · Kinds of FlowersIndonesia Beethoven · 5th, 1st mvtClassical Germany Senegalese percussionWest Africa
Full track listing (NASA) →
📊 Drake equation
N = R* · fp · ne · fl · fi · fc · L
N = — civilizations in the Milky Way
The Fermi Paradox: if N is large, where is everyone? Candidates — the Great Filter is behind us (we're alone-ish); or ahead of us (civilizations self-destruct); or they're silent on purpose.
James Webb
StationSun–Earth L₂
Distance~1.5 × 10⁶ km
Current observing schedule (STScI) →
Click a target star on the map for round-trip signal time and a "Send signal" animation.
Source: loading…
Log scale — each ring is 10× the distance of the inner one. Radio bubble: 125 ly (since Marconi, 1901). Yellow stars: inside our radio bubble (our signals could've reached them).
Voyager Cosmic Calendar
19771985199320012009201720252033

Why 1420 MHz?

The hydrogen line — 1420.405 MHz, wavelength 21 cm — is the radio emission from the spin-flip of a neutral hydrogen atom's electron. It's the most abundant photon in the universe by a wide margin. Any civilization doing radio astronomy discovers it independently. That's why SETI specifically listens around this frequency: if ET is broadcasting to be found, this is the cosmically obvious "dial setting."

The Arecibo message (1974, 2380 MHz), Voyager Golden Record, and Breakthrough Listen all acknowledge the hydrogen line explicitly. The region between 1.42 and 1.66 GHz is called the water hole — a quiet span between H and OH spectral lines, thought to be an attractive channel for any intelligent broadcast.

The whole picture

From the center outward: Earth, then the Voyager probes at ~165 and ~137 AU (around 0.002 light-years) — still transmitting 48 years after launch; then the radio bubble at ~125 light-years — the expanding sphere inside which our radio transmissions might, in principle, be detectable; finally a constellation of SETI target stars at 4–40 ly — the closest places we'd look for a reply.

The scale is log-compressed because otherwise the Voyagers would be invisible at the same zoom as the radio bubble: they're 50,000× closer. Each ring in the plot represents a factor of 10 in distance. 

Scale cheat sheet
  Voyager 1 today:    ~165 AU      ≈ 0.0026 ly
  Pluto's orbit:       ~40 AU      ≈ 0.0006 ly
  Nearest star:         —          4.24 ly (Proxima Centauri)
  Radio bubble edge:    —          125 ly
  Galactic center:      —          26,700 ly

Click any star to see the round-trip signal time — the earliest possible "hello and reply." Proxima Centauri is 4.24 ly away, so a signal sent today would reach it in 4.24 years, and any reply would come back 4.24 years after that. Send a signal now, earliest reply in 2034.