Relativistic Energy–Momentum Hyperbola
This interactive simulator explores Relativistic Energy–Momentum Hyperbola in Астрономия и небо. 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. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Для кого: Best once you already know the basic definitions and want to build intuition. Typical context: Астрономия и небо.
Ключевые понятия
- relativistic
- energy
- momentum
- hyperbola
- relativistic energy momentum
- astronomy
Как это работает
Visualizer of the relativistic energy–momentum hyperbola E² = (pc)² + (mc²)². Pick any of β, p or T as the independent slider — the other three lock together via γ = 1/√(1−β²), p = γβ, E = γ. Newtonian (E ≈ 1 + p²/2) and ultra-relativistic (E = pc) limits are drawn for comparison.
Ещё из «Астрономия и небо»
Другие симуляторы в этой категории — или все 45.
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.
Фазы Венеры (Галилей)
Гелиоцентрическая геометрия: полный диск и серп у нижнего соединения; вставка — вид с Земли.