Curriculum Unit 04 • General RelativitySummer Lab Mode
Space-Time Fabric & Relativistic Curvature
Albert Einstein showed that massive celestial objects do not simply pull on matter through empty space. Instead, mass physically warps the four-dimensional fabric of space-time, forcing light rays and orbital bodies along curved paths called geodesics.
Coordinate Mesh Telemetry
Real-time 2D Tensor Grid Slice • 60 FPS Geodesic Engine
LIVE PHYSICS
Well Depth:35 G•M/c²
Light Geodesic:–16.80°
Gravitational Parameters
Adjust core mass and fabric properties to observe geodesic bending in real time.
35 Solar Masses (M)
1 M (Earth-Scale)50 M (Neutron Star)100 M (Black Hole)
24 × 24 Lines
3c (Simulation Rate)
Astrophysics Telemetry Deck
Curvature Index
46.9 K-units
Schwarzschild Radius
11.20 km
Key takeaway: As mass increases, the slope of the space-time well steepens. Light travels along the shortest path (a geodesic) through this warped geometry, causing the ray to bend toward the heavy mass.
Module 04 // Planetary DynamicsYear 8 & Summer School Lab
Planetary System Lab
Experiment with gravitational attraction, orbital velocity, and multi-body resonance. Adjust masses and distance to observe stable orbits versus catastrophic stellar collisions.
GRAVITY ENGINE:NEWTONIAN 2D N-BODY
LIVE VIEWPORTGRID: WARP MESH ACTIVE
EQUILIBRIUM98%
GRAV FORCE4.82 × 10²⁴ NRadial Vector
ESCAPE VELOCITY4.12 km/sv_esc = √(2GM/r)
TRAJECTORY STATUSStable Orbite = 0.05
Multi-Body Configurations
4 PRESETSSelect a classic orbital problem to load orbital initial conditions.
Physics Parameters
Fine-tune variables to see how orbital stability balances centrifugal and gravitational forces.
Central Mass (M)1000 M_std
Low (Dwarf)High (Supergiant)
Semi-Major Axis (r)140 AU / 10
Tight Orbit (6.0 AU)Outer Boundary (24.0 AU)
Tangential Velocity (v₀)2.70 km/s
Sub-orbital InfallHyperbolic Escape
Kepler's & Newton's Law Connection
For a circular orbit, gravitational pull provides the exact centripetal force: GMm / r² = mv² / r. Increasing mass without increasing speed causes orbital decay into the host body.