The Solar System & N-Body Gravity
All gravitational simulations use 4th-order Runge-Kutta (RK4) to integrate Newton's inverse-square law. RK4 conserves energy far better than Euler at the same time step, which matters for multi-orbit accuracy.
Two stars orbiting their common barycenter. Vary mass ratio to see
circular, elliptical and figure-8 orbits. Energy leakage over 1000
orbits is <0.01%.
RK4 N-body
Model a kinetic impactor mission (DART-style). Choose impact angle
and timing; the simulation computes whether perihelion shifts
enough to miss Earth.
RK4 · orbital mechanics
All eight planets with accurate relative semi-major axes and
periods. Verify Kepler's third law: T² is proportional to a³ for
each body.
Kepler · vis-viva
Radiation pressure from photons creates thrust. Vary sail
area-to-mass ratio; the resulting spiral trajectory can outrun a
chemical rocket over years.
RK4 · photon pressure
Orbital Maneuvers & Mission Design
These simulations implement the exact equations used by mission planners. The vis-viva relation $v = \sqrt{\mu(2/r - 1/a)}$ governs every burn.
Hohmann transfer, bi-elliptic transfer and plane changes. Minimum
Δv calculations match the textbook to four significant figures.
vis-viva · Hohmann
Powered descent from 15 km using Apollo lunar module parameters:
Isp = 311 s, g_moon = 1.62 m/s². Nail the throttle or crash on the
mare.
RK4 · Tsiolkovsky
The Tsiolkovsky rocket equation (used in lunar descent)
Δv = Isp · g₀ · ln(m₀ / m_f)
Isp = 311 s · g₀ = 9.81 m/s² · g_moon = 1.62 m/s²
Atmospheric & Re-entry Physics
Troposphere to exosphere: pressure, density and temperature vs
altitude using the International Standard Atmosphere model.
Balloon ascent simulation included.
ISA barometric formula
Buoyancy, drag and balloon expansion as ambient pressure falls.
Model a HAB payload ascent to 35 km — the stratosphere is colder
than you expect.
Archimedes · RK4
Light, Signals & Observation
Crucial for redshift cosmology. Move the source at 0.8c and watch
wavefronts compress ahead — the relativistic version is also
available.
Wave propagation
Young's experiment with adjustable slit spacing and wavelength.
The fringe pattern forms exactly as the wave equation predicts —
and collapses when you observe.
Huygens wavelets · QM collapse
Dipole and phased-array radiation patterns. Steer the main lobe by
changing element phase offsets — how radio telescopes track
distant quasars.
Superposition · phase arrays
Wien's displacement law: as stellar temperature rises, peak
emission shifts from infrared to blue-white. Colour a star by its
spectral class.
Planck radiation law
Core Algorithms in Space Simulations
Runge-Kutta 4 (RK4)
Vis-viva equation
Kepler's laws
Tsiolkovsky rocket equation
Hohmann transfer
N-body gravity
Barometric formula (ISA)
Planck / Wien radiation
Huygens wavelets
Photon radiation pressure
Recommended Learning Paths
Beginner: Kepler to Newton
- Binary Stars — Kepler orbits, barycenter
- Doppler Effect — how velocity shifts frequency
- Atmosphere Layers — pressure model
- Blackbody Radiation — stellar temperatures
Advanced: Mission Planning
- Solar Sail — radiation pressure orbits
- Orbital Maneuvers — Δv and Hohmann transfer
- Moon Landing — powered descent with fuel budget
- Asteroid Deflection — kinetic impactor design
Fun fact: The orbital simulations use the same RK4 numerical integrator as JPL's Horizons system for short-horizon propagation. The difference is time step and planet count — not the core algorithm.