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    Resonance Width Calculator Choose Input Method Q-Factor & FrequencyResonance Lifetime Quality Factor (Q) Resonant Frequency (f₀, Hz) Resonance Lifetime (τ, seconds) Calculate Resonance Width (Γ) About the Resonance Width Calculator The Resonance Width Calculator is a precision scientific tool that instantly computes the full width at half maximum (FWHM, Γ) of any resonance […]

    Perturbation Theory Calculator Unperturbed Energy E⁽⁰⁾ (eV or a.u.) First-order matrix element ⟨ψ⁽⁰⁾|Ĥ′|ψ⁽⁰⁾⟩ Off-diagonal element ⟨ψ⁽⁰⁾|Ĥ′|ψ⁽¹⁾⟩ (for 2nd order) Unperturbed energy of excited state E₁⁽⁰⁾ Calculate Energy Corrections About the Perturbation Theory Calculator The Perturbation Theory Calculator is a precision tool that instantly computes first- and second-order energy corrections using Rayleigh-Schrödinger perturbation theory—the

    Three-Body Problem Calculator Solution Type: Figure-8 (Periodic)Lagrange Points (L4/L5)Euler CollinearChaotic InitialCustom Setup Time Step (days): Duration (years): Start Simulation Reset Toggle Trails Export Data Time: 0 years Steps: 0 Energy Error: 0% Status: Ready * Uses Euler integration with G = 4π² (AU³/yr²). Trails show 1000 steps. Valid for equal-mass systems. About the

    Orbital Stability Calculator System Type: Planet around StarMoon around PlanetBinary Star SystemThree-Body Stability Primary Mass (M☉): Secondary Mass (M⊕ or M☉): Semi-Major Axis (AU): Calculate Stability * Uses Hill radius, Roche limit, and chaos criteria from peer-reviewed literature. Valid for circular orbits. About the Orbital Stability Calculator The Orbital Stability Calculator is a

    Gravitational Binding Calculator Total Mass (M⊙): Radius (km): Density Profile: Uniform SpherePolytropic Star (n=3)Terrestrial PlanetNeutron Star Calculate Binding Energy * Uses exact formulas from astrophysics literature. G = 6.67430×10⁻¹¹ m³/kg/s². 1 M⊙ = 1.989×10³⁰ kg. About the Gravitational Binding Calculator The Gravitational Binding Calculator is a scientifically rigorous astrophysical tool that computes the

    N-Body Simulation Calculator Number of Bodies: 3 Time Step (days): Duration (years): Start Simulation Sun + Earth Earth + Moon Figure-8 Random 5 Reset Time: 0 years Steps: 0 Energy Error: 0% Status: Ready * Uses Euler integration with G = 4π² (AU³/yr²). Trails show 1000 steps. Red = unstable. About the N-Body

    Celestial Mechanics Calculator Calculation Mode: Orbital Period from DistanceSemi-Major Axis from PeriodOrbital VelocityEscape VelocityVis-Viva Equation Input 1: Input 2: Central Body: SunEarthMoonMarsJupiterCustom (enter GM) GM (km³/s²): Calculate * Based on Kepler’s 3rd Law and Newton’s gravity. Uses standard gravitational parameters from NASA JPL. Valid for circular and elliptical orbits. About the Celestial Mechanics

    Angular Diameter Calculator Actual Size (diameter): kilometers (km)meters (m)astronomical units (AU)light-years (ly)parsecs (pc)Earth diametersJupiter diameters Distance to Object: kilometers (km)meters (m)astronomical units (AU)light-years (ly)parsecs (pc) Calculate Angular Diameter * Based on small-angle approximation: δ ≈ D/d (radians). Valid for δ < 10°. Exact formula used for larger angles. About the Angular Diameter Calculator

    Cosmic Distance Calculator Distance Method: Parallax (mas)Cepheid Period-Luminosity (days, mag)Tully-Fisher (km/s, mag)Type Ia Supernova (mag, mag)Redshift (z, H₀)CMB Angular Size (θ, Ω_m, H₀) Input 1: Input 2: Calculate Distance * Based on peer-reviewed astronomical methods: Riess et al. (2022), Freedman et al. (2021), Planck Collaboration (2020). H₀ = 67.4 km/s/Mpc default. About the

    Dark Matter Calculator Dark Matter Profile: NFW (Navarro-Frenk-White)EinastoIsothermal (Cored) Circular Velocity at r₂₀₀ (km/s): Virial Radius r₂₀₀ (kpc): Concentration c = r₂₀₀/rₛ: Redshift z: Hubble Constant h: Calculate Dark Matter Halo * Based on Navarro et al. (1996), Springel et al. (2008), and Planck 2018 cosmology. About the Dark Matter Calculator The Dark