Create and explore your own exoplanetary system. Adjust the star, add planets, change orbital parameters and see how it affects temperature, habitability and orbits in real time.
Each scenario only loads a star and planets; every slider stays editable.
Each check derives a number by a different route (symplectic integration, quadrature, textbook constants) and compares it with the closed form the dashboard uses.
Kepler. Period P² = a³ / (M★ + m) in years, AU and solar masses. Position follows from Kepler's equation M = E − e sin E (Newton iteration), then x = a(cos E − e), y = a√(1−e²) sin E, rotated by inclination, node and argument of periapsis. Equal areas in equal times follow from the same solver.
Star. L = 4πR²σT⁴, in solar units L = R²(T/5778 K)⁴. Changing radius or temperature recomputes L; changing L moves the radius at fixed temperature. Main-sequence lifetime is estimated as 10 Gyr · M/L.
Equilibrium temperature. Teq = T★ √(R★/2a) (1−A)¼, orbit-averaged by (1−e²)−1/8. The surface temperature adds a grey greenhouse Ts = Teq(1 + 3τ/4)¼ with an optical depth τ per planet type (Earth: τ = 0.84 gives 288 K). Past the runaway-greenhouse flux limit τ grows sharply (a Venus-like state).
Habitable zone. Kopparapu et al. (2013) flux limits Seff(Teff) (1 Earth mass coefficients): distance d = √(L / Seff). Conservative zone: moist greenhouse to maximum greenhouse (Sun: about 0.99 to 1.69 AU); the dashed box is the optimistic zone.
Habitability Index (0 to 0.97). A heuristic, not a measurement: HI = 0.97 · forbit · fgravity · fatmosphere · fstar. forbit is a soft window on stellar flux averaged over perihelion and aphelion; fgravity peaks at 1 g; fatmosphere compares escape velocity with thermal speed; fstar penalises stars that live less than about 4 Gyr. Gas and ice giants score 0 (no solid surface). The cap exists because only one inhabited planet is known.
Spectrum. Planck's law B(λ,T) = (2hc²/λ⁵) / (ehc/λkT − 1); the peak follows Wien's law λmax = 2.898×10−³ m·K / T; the area under the curve gives σT⁴.
Planets do not perturb each other (independent Kepler orbits, planet mass only enters the period). The greenhouse is a one-layer grey model; real climates depend on composition, clouds, ocean and tides. Tidal locking, stellar flares, magnetic fields and plate tectonics are not modelled. Habitable-zone limits use 1 Earth-mass coefficients. The atmosphere text and surface state are rule-of-thumb labels. Mass-radius pairs are free: the Chen and Kipping (2017) median radius is shown as a reference, not enforced. 3D distances use a square-root display scale (the 2D orbit panel as well); sizes in the 3D system view are compressed, the Compare view and panel are to scale (panel: R0.42 drawing scale). Fraunhofer lines in the spectrum are illustrative. The asteroid belt is placed near the snow line (2.7 AU √L) and is decorative: its rocks follow circular Kepler motion but have no mass.
Planet maps, star granulation, ring strip, the sky panorama and the asteroid models (Draco GLB) were produced in Blender (Cycles baking on the GPU). This 2D companion is pure Canvas 2D (no WebGL); its physics module is the same file as the 3D page, so both give identical numbers. The sky backdrop and planet maps are the Blender-baked textures of the 3D page. Typical values quoted (Solar System planet masses, radii, distances; Kopparapu coefficients; TRAPPIST-1-like numbers rounded) should be spot-checked before use in teaching. Educational, not for research.