Physics in This Universe — Overview

The SPACE universe is a deterministic simulation. Every state can be reproduced from just the epoch + seed + command log. Fixed timesteps, single-threaded integration, and pinned library versions eliminate floating-point non-determinism.

Coordinates · Time · Units

Scale fidelity — bodies to scale, spacecraft exaggerated

Celestial bodies (stars, planets, moons) are drawn exactly to scale by their measured radii. The relative sizes of Earth, the Moon and Mars, and the sheer emptiness of the solar system, are all true proportions. Spacecraft, the ISS, satellites and probes, however, are drawn larger than life for visibility — at true size, an object a few to a few tens of meters across would shrink below a single pixel in a planet-scale scene, leaving it impossible to find or control.

Gravity · Orbits · Gravity Assists

Restricted N-Body Gravity (One-Way Coupling)

The ship feels the combined gravity of the Sun and all the planets. The ship's mass is negligible compared to the bodies, so the bodies' orbits are computed independently (one-way coupling) and only the ship moves within that gravity field. As a result, real gravity assists (swing-by) arise naturally without any frame switching.

Kepler Orbits + Symplectic Integrator

• Everyday coasting flight is propagated analytically as a Kepler orbit, with no need to save state every tick.
• Close encounters and gravity-assist passes are refined with a velocity Verlet symplectic integrator + adaptive sub-steps. It's conservative enough that energy drift over 3 LEO orbits is 0.0000%.
• SOI (sphere of influence) tests determine the dominant body, and SOI entry/exit is reported as an event.

Single Main Engine — Thrust Always Points Forward

The Dragon capsule has its main engine in only one direction, at the nose (front). There is no retro engine. To change direction you must rotate the entire ship with attitude control (RCS) and then fire, and the rotation happens gradually within a maximum angular rate. That's why deceleration is a flip-and-burn (rotate 180°, then fire) and isn't instantaneous.

Atmospheric Reentry

When you enter a body's atmosphere, too steep an entry angle means burn-up (game over), while too shallow means a skip (bouncing off) — both are judged physically. You must enter through the proper corridor to descend safely.

Speed-of-Light Limit · Light Delay

The most fundamental rule of this universe: no information can exceed the speed of light c. Not position observations, not messages, nothing. The server simulates this constraint authoritatively.

Visible Position = Past Position (the Delay Ghost)

When ship A "sees" ship B, it is seeing B as it was in the past, by an amount equal to distance ÷ c. This is the heart of retarded time — what you see is always the past.

• When close, the delay is small and things look almost current, but the farther away, the larger the delay, so the displayed position diverges from the actual one.
• Far enough away, the current position cannot be known exactly (only past information exists) — it is shown as a blurry uncertain-position ghost.
• The position history of nearby ships is buffered for about 84 hours.

Comms Signals Spread at the Speed of Light Too

An emoji transmission is a spherical wave that spreads omnidirectionally at c from the sender's position at send time t — like radar, with no direction to aim. Nearer ships are reached sooner; the farther away, the later it arrives.

A beacon is a permanent signal source that stays in one place. A ship passing within 100km of it is recorded in its visitor register, and ships that pass each other within 100km likewise log one another. A distant party is still only visible as a ghost at its past (delayed) position, so an encounter ultimately happens only by drawing close.

Special Relativity · The Twin Paradox

Speed Limit and the Lorentz Factor γ

The speed limit for your ship is 0.9999c. The faster you move, the more time slows down, by an amount set by the Lorentz factor:

γ = 1 / √(1 − v²/c²)

Proper Time — The Onboard Clock Runs Slow

Your ship's onboard clock (proper time τ) ticks 1/γ times slower than coordinate time (t): dτ = dt / γ. Flying at 0.9999c, the onboard clock is about 70.7 times slower than the outside world. The HUD (④ PFD) shows coordinate time, onboard proper time, and γ side by side.

The Twin Paradox — Experience It Firsthand

If you sail to Proxima Centauri (4.25 light-years) at the top cruise speed of 0.99c (γ ≈ 7.09):

• Coordinate time (the outside world): about 4.3 years
• Proper time (onboard clock): 4.3 years ÷ 7.09 ≈ about 7 months (~221 days)
• On a round trip the ship ages about 1.2 years, while about 8.6 years pass in the outside world.

By comparing your accumulated proper time against another player's, you can directly confirm that the elapsed time differs between you depending on who sailed faster or through deeper gravity.

Black Holes · Gravitational Time Dilation

The Event Horizon and Strong Gravitational Fields

• Event horizon: r_s = 2GM/c² (Schwarzschild radius)
• Innermost stable circular orbit (ISCO): 6GM/c² = 3·r_s — any orbit inside this spirals inward to its doom
• Photon sphere: 1.5·r_s
• Near strong gravitational fields, the Paczyński–Wiita pseudo-Newtonian potential Φ(r) = −GM/(r − r_s) faithfully reproduces the correct ISCO, perihelion precession, and infall.

Gravitational Time Dilation

The deeper you descend into a strong gravitational field, the slower time runs:

dτ/dt = √(1 − r_s/r)

• At the photon sphere (r = 1.5 r_s), time runs at about 57.7% of the rate seen far away.
• It approaches 0 as you near the horizon — to an outside observer, time appears to stop.
• While you linger briefly near the horizon of Sagittarius A*, thousands of years pass in the outside world.
• The velocity-based γ and gravitational time dilation multiply together: γ_total = γ_velocity × √(1 − r_s/r).

Gravitational Lensing · Redshift

Light from stars and galaxies behind a black hole bends to form an Einstein ring, and the accretion disk wraps over and under the black shadow (the signature look from the film Interstellar). The single focused black hole is drawn with a real-time geodesic lens that traces each pixel's light back through the hole's gravity, so the disk's far side is genuinely light bent back into view. Signals escaping the horizon are delayed and shifted red (gravitational redshift). To an outside observer, an infalling ship slows down and reddens until it freezes at the horizon, becoming a permanently indeterminate ghost.

Fidelity note: the light bending is a Schwarzschild deflection approximation (plus a visual spin asymmetry), not the full numerical-relativity renderer (DNGR / full Kerr geodesics) that made the film — it's an honest approximation that runs in real time on the web. Low-spec devices fall back automatically to a lighter screen-space lens.

Cosmic Expansion · The Observable Universe

Press the U key to turn on the cosmological clock and read, at the largest scales, the universe's expansion and its past. The game uses standard ΛCDM cosmology (Planck 2018).

Redshift and Lookback Time

Distant objects are redshifted (z) by however much the universe has expanded since their light set out. The farther you look, the further into the past you see (lookback time):

• z ≈ 1 → about 8 billion years ago (half the age of the universe)
• z ≈ 10 → about 13 billion years ago (cosmic dawn, the first stars and galaxies)
• z ≈ 1100 → about 13.8 billion years ago (the surface of last scattering = the cosmic microwave background)

Accelerating Expansion — Receding Distances

The universe is expanding at an accelerating rate, so sufficiently distant objects recede with a recession velocity v = H × D. Several distance concepts are used together — comoving distance (the present-grid distance with expansion removed), light-travel / lookback distance (the time light traveled × c), luminosity distance for brightness correction, and angular diameter distance for angular-size correction. The coordinates themselves stay comoving (static, deterministic), while expansion is reflected in the display and render layers.

Interstellar Cruise · Wormholes

Relativistic Cruise Worldline

An interstellar cruise accelerates your ship up to 0.99c (0.9c by default) and heads toward a destination star along an analytic worldline. For a distance d, the coordinate time and the onboard proper time are:

• Coordinate time = distance ÷ (cruise speed) ≈ distance (light-years) / 0.99 years (at top cruise speed)
• Onboard proper time = coordinate time ÷ γ

Example) Proxima (4.25 light-years) at top cruise 0.99c: coordinate time ≈ 4.3 years, onboard clock ≈ about 7 months. On arrival you switch to the destination star's chart, and non-sol charts apply their own physics guards.

Causal-Island Proper-Time Fast-Forward

If you are cruising alone, outside the region where you could communicate with other ships (shared causality), the game pulls a long cruise straight to arrival — you don't have to wait years in real time. Shared causality (the range within which you could exchange signals with someone) is preserved, so physical consistency is never broken.

One-Way Wormholes

Wormholes are another way around the c barrier. Each star system has 2–3 of them at deterministic locations. You discover them with a 📡 radar scan (per ship, persistent), and reaching one instantly switches your chart to a different star system. They are one-way, so to come back you must find another wormhole opening on that side.