Astronomy & The Sky
Moon phases, eclipses, sky geometry, stars, spectra, cosmology sketches, and comets
Light Clock & Time Dilation
Two side-by-side light clocks — one at rest, one moving at v = βc — show why a moving clock ticks slower. The photon zig-zag traces a longer Pythagorean hypotenuse cT/2 vs the rest hypotenuse cT₀/2, giving T = γT₀ with γ = 1/√(1 − β²) live. The Pythagorean diagram and the running tick ratio make the special-relativistic time-dilation derivation visual rather than algebraic.
Length Contraction (Lorentz)
A ruler of proper length L₀ in S′ flies past the lab S at v = βc and is measured to be L = L₀/γ — only in the direction of motion. Animated fly-by with on-board ruler ticks and a dotted L₀ baseline makes the contraction L = L₀ √(1 − β²) immediately readable; same factor explains why GeV cosmic-ray muons reach the ground despite their ≈ 2 μs lifetime.
Minkowski Spacetime Diagram (Lorentz Boost)
Interactive (x, ct) spacetime diagram: a Lorentz boost at v = βc rotates the (x′, ct′) axes inward by atan(β) toward the 45° light cone — relativity of simultaneity, time dilation and length contraction become pure geometry. Click events with Shift / Alt to read the invariant interval Δs² = (cΔt)² − (Δx)² and its time-/light-/space-like classification.
Relativistic Doppler Effect
Source emits at rest frequency f₀ and moves at v = βc; observer at angle θ measures f_obs = f₀ √(1 − β²) / (1 − β cos θ). Animated lab-frame wavefronts, observer at any angle, and a 380–700 nm spectrum strip showing the apparent colour shift of a 555 nm reference line — including the purely relativistic transverse Doppler (θ = 90°) red-shift f₀/γ.
Relativistic Energy–Momentum Hyperbola
Energy–momentum relation E² = (pc)² + (mc²)². The green hyperbola E = √(p² + 1) is bracketed by the Newtonian parabola E ≈ 1 + p²/2 (low-momentum limit) and the photon-like asymptote E = pc (ultra-relativistic). Pick β, p or T as the independent slider and watch all four quantities (β, γ, p, T) lock together — the operational core of accelerator and cosmic-ray physics.
Pair Production Threshold & σ(E_γ)
Pair creation channels γ + nucleus → e⁺e⁻ (Bethe–Heitler, σ ∝ Z²), the higher-threshold triplet γ + e⁻ → e⁻e⁺e⁻, and Breit–Wheeler γγ → e⁺e⁻ that limits TeV photons against the cosmic background. Live threshold marker, log-σ curve, and material presets (H, C, Al, Cu, Pb) make the 1.022 MeV / 4 m_e c² thresholds intuitive.
CMB Power Spectrum (Acoustic Peaks)
Cosmic Microwave Background temperature D_ℓ vs ℓ with Sakharov peaks: tune Ω_b h², Ω_c h², n_s, A_s, τ, h and watch the parity flip between odd / even peaks, the Silk damping tail, and the Sachs–Wolfe plateau move. Pedagogical parametric ΛCDM model.
Big Bang Nucleosynthesis (BBN)
Light-element abundance curves H, ⁴He, D, ³He, ⁷Li vs cosmic time / temperature. Weak freeze-out, neutron decay gap, deuterium bottleneck → Y_p ≈ 0.245. Slide η₁₀ and N_eff over the classic BBN curves; observed values overlaid.
EM Calorimeter Shower (Heitler / Rossi)
Toy electromagnetic cascade in a calorimeter: γ → e⁺e⁻, e⁻ → e⁻γ each X₀, with critical-energy cutoff E_c. Animate the branching tree, see N_max ≈ E₀/E_c, t_max ≈ log₂(E₀/E_c) live; presets for Pb, Cu, Si, air.
Bremsstrahlung & Synchrotron Radiation Pattern
Polar plot of dP/dΩ for an accelerating charge: a ∥ v (linear / brems) and a ⊥ v (circular / synchrotron). Pull β = v/c toward 1 — Larmor donut collapses into a forward beam of half-angle ≈ 1/γ; ω_g, ω_c shown for given B.
Venus Phases (Galileo)
Heliocentric geometry: full disk vs crescent at inferior conjunction; Earth-view inset.
Stellar Aberration
Bradley: telescope tilt v/c ~ 10⁻⁴ rad; annual ~20.5″ — not parallax.
Milankovitch Cycles
e, obliquity, precession → toy high-latitude insolation curve; ice-age pacing context.
Supernova Light Curves
Schematic Ia rise/decay vs II-P plateau; standard-candle note.
Apparent vs Absolute Magnitude
m = M + 5 log₁₀(d/10 pc); distance modulus; flux ratios.
Spin–Orbit Resonance
Moon 1:1 lock vs Mercury 3:2; schematic animations.
Pulsar Lighthouse
Rotating beam cone, pulse profile; timing / ms pulsars context.
Meteor Shower & Radiant
Earth crosses comet debris; radiant on a star field (schematic).
Cosmological Expansion (FLRW)
a(t), z, χ and c/H vs time; flat Ω_m + Λ (toy ΛCDM).
Galaxy Rotation Curve
Keplerian decline vs flat v(r); toy halo slider (dark matter motivation).
Stellar Life Cycle
Cloud → MS → giant/SN → WD / NS / BH vs initial mass (schematic).
Exoplanet Radial Velocity
K from masses & P; sinusoidal V_r(t); M sin i.
Exoplanet Transit (light curve)
Uniform disk overlap; R_p/R_*; impact b; F(t) vs period.
Sphere of Influence (Hill)
r_H ≈ a (m/3M)^(1/3): schematic secondary orbit and Hill radius vs masses and a.
Measuring c (ToF toy)
c ≈ 2D/Δt round-trip; schematic path + Fizeau/Foucault context.
GPS & Relativity
Weak-field + SR clock drift estimates vs altitude and orbital speed.
Nuclear Binding Curve
Qualitative B/A vs A with fusion/fission context.
Seasons & Axial Tilt
Obliquity ~23.4°: declination model vs day of year and noon sun altitude at latitude.
Single-Layer Climate (Toy)
S, α, ε: T_eff vs T_surface from gray-slab balance — intuition only.
Moon Phases
Sun–Earth–Moon geometry and synodic cycle; lit fraction from phase angle.
Solar Eclipse Geometry
Sun–Moon–Earth: angular sizes, umbra and penumbra cones, orbit tilt.
Lunar Eclipse Geometry
Sun–Earth–Moon: Earth’s shadow on the Moon; total, partial, and penumbral (schematic colors).
Moon: Tidal Locking
Synchronous rotation: same lunar face toward Earth as it orbits.
Mars Retrograde Loop
Earth overtakes Mars: apparent backward loop among the stars (schematic).
Sidereal vs Solar Day
Why noon returns after slightly more than 360° of rotation (~4 min shorter sidereal day).
Axial Precession
Spin axis slowly cones; ~26 kyr cycle changes the pole star (schematic).
Ecliptic & Zodiac Band
Celestial equator vs ecliptic, obliquity, Sun on the yearly path (symbols as map, not astrology).
Hertzsprung–Russell Diagram
Schematic HR regions; drag a star to see main sequence, giants, white dwarfs.
Spectral Lines & Doppler
Absorption lines on a continuum shift with radial velocity (Δλ/λ ≈ v/c).
Cosmic Distance Ladder
Log distance scale with parallax, standard candles, and Hubble-flow cartoon rungs.
Black Hole Shadow (Schematic)
Silhouette and stylized ring; Rₛ scales with mass — not full GR ray tracing.
Sunset Atmospheric Refraction
Geometric vs apparent horizon: lift of the solar disk from a layered atmosphere model.
Comet Orbit, Coma & Tails
Eccentric orbit, coma brightening near the Sun, ion and dust tails, solar wind toggle.
Aurora (Stylized)
Layered sine curtains; hue and drift — look only, not ionosphere physics.
Stellar Parallax
Earth orbit angle vs nearby star wobble on fixed background; π = 1/d(pc) arcsec, exaggerated.