{"section":"physics","label":"Astrophysics","count":12,"generatedAt":"2026-03-20","items":[{"slug":"gravity-and-orbital-mechanics","path":"/physics/gravity-and-orbital-mechanics/","title":"Gravity, Kepler's Laws & Virial Theorem","description":"How Newtonian gravitation, Kepler's third law, the vis-viva equation, and the virial theorem allow astronomers to weigh stars, exoplanets, and galaxies.","questionOrTopic":"How do astronomers use orbital mechanics and the virial theorem to measure masses across the cosmos?","epistemicStatus":"strong-observational-evidence","formula":"P² = (4π² a³) / [G (M_1 + M_2)];   v² = G (M_1 + M_2) (2/r − 1/a);   M_vir ≈ (5 R_e σ_v²) / G","keyMetricsCount":4,"sources":["src:jpl-horizons","src:hipparcos-new","src:eht-m87-sgra"]},{"slug":"electromagnetic-spectrum-in-astronomy","path":"/physics/electromagnetic-spectrum-in-astronomy/","title":"The Electromagnetic Spectrum in Astronomy","description":"How radio, submillimeter, infrared, optical, UV, X-ray, and gamma-ray bands probe cosmic temperatures, non-thermal plasmas, and atmospheric windows.","questionOrTopic":"Why must astronomers observe across the entire electromagnetic spectrum from radio to gamma rays?","epistemicStatus":"strong-observational-evidence","formula":"E = h ν = h c / λ;   E (eV) ≈ 1239.84 / λ (nm);   T_char = E / k_B ≈ 11,604.5 K/eV","keyMetricsCount":4,"sources":["src:jwst-archive","src:ngc-ic-steinicke","src:planck-2018"]},{"slug":"atomic-spectra-and-absorption-lines","path":"/physics/atomic-spectra-and-absorption-lines/","title":"Atomic Spectra, Saha-Boltzmann & Spectral Types","description":"How quantized electronic transitions, Kirchhoff's laws, and the Boltzmann-Saha equations explain the OBAFGKM stellar spectral sequence.","questionOrTopic":"Why do stars of the same chemical composition show completely different absorption lines at different temperatures?","epistemicStatus":"strong-observational-evidence","formula":"N_b / N_a = (g_b / g_a) exp(−ΔE / (k_B T));   (N_{i+1} n_e) / N_i = (2 Z_{i+1} / Z_i) (2π m_e k_B T / h²)^{3/2} exp(−χ_i / (k_B T))","keyMetricsCount":4,"sources":["src:gaia-dr3","src:simbad-cds","src:hipparcos-new"]},{"slug":"nuclear-fusion-in-stars","path":"/physics/nuclear-fusion-in-stars/","title":"Nuclear Fusion in Stars: pp-Chain & CNO Cycle","description":"How quantum tunneling through the Coulomb barrier enables the proton-proton chain, CNO cycle, and triple-alpha fusion at stellar core temperatures.","questionOrTopic":"How do stars fuse hydrogen at 15 million kelvin when the classical Coulomb barrier requires 10 billion kelvin?","epistemicStatus":"strong-observational-evidence","formula":"4 ¹H → ⁴He + 2 e⁺ + 2 ν_e + 26.731 MeV (Δm / m = 0.0071);   ε_pp ∝ ρ X² T^4;   ε_CNO ∝ ρ X Z_CNO T^{16–18}","keyMetricsCount":4,"sources":["src:gaia-dr3","src:simbad-cds","src:hipparcos-new"]},{"slug":"electron-and-neutron-degeneracy-pressure","path":"/physics/electron-and-neutron-degeneracy-pressure/","title":"Electron & Neutron Degeneracy Pressure","description":"How Pauli exclusion and Fermi-Dirac statistics generate temperature-independent degeneracy pressure in brown dwarfs, white dwarfs, and neutron stars.","questionOrTopic":"How does quantum degeneracy pressure hold up compact stellar remnants without thermal heat?","epistemicStatus":"strong-observational-evidence","formula":"P_NR = (ℏ² / (5 m_f)) (3π²)^{2/3} n_f^{5/3} ∝ ρ^{5/3} / m_f;   P_UR = (ℏ c / 4) (3π²)^{1/3} n_f^{4/3} ∝ ρ^{4/3}","keyMetricsCount":4,"sources":["src:gaia-dr3","src:gwtc-3","src:simbad-cds"]},{"slug":"astrophysical-plasmas-and-magnetic-fields","path":"/physics/astrophysical-plasmas-and-magnetic-fields/","title":"Astrophysical Plasmas, MHD & Synchrotron Light","description":"Why >99% of visible baryonic matter in the cosmos is ionized plasma governed by magnetohydrodynamics, flux freezing, dynamos, and synchrotron emission.","questionOrTopic":"How do magnetic fields interact with ionized plasma across stars, accretion disks, and nebulae?","epistemicStatus":"strong-observational-evidence","formula":"v_A = B / √(4π ρ);   Φ_B = B · R² ≈ const;   ν_sync ≈ (3 e B sin α / (4π m_e c)) γ² ≈ 4.2 MHz × (B / 1 G) γ²","keyMetricsCount":4,"sources":["src:planck-2018","src:simbad-cds","src:ngc-ic-steinicke"]},{"slug":"general-relativity-and-spacetime-curvature","path":"/physics/general-relativity-and-spacetime-curvature/","title":"General Relativity & Spacetime Curvature","description":"How Einstein's field equations link stress-energy to spacetime curvature, predicting gravitational lensing, time dilation, and gravitational waves.","questionOrTopic":"How does general relativity replace Newtonian gravity in strong fields and cosmology?","epistemicStatus":"strong-observational-evidence","formula":"G_{μν} + Λ g_{μν} = (8π G / c⁴) T_{μν};   α_deflect = (4 G M) / (c² b);   1 + z_grav = (1 − 2GM / (r c²))^{−1/2}","keyMetricsCount":4,"sources":["src:eht-m87-sgra","src:gwtc-3","src:gaia-dr3"]},{"slug":"blackbody-radiation-and-stellar-temperatures","path":"/physics/blackbody-radiation-and-stellar-temperatures/","title":"Blackbody Radiation, Planck's Law & Wien's Law","description":"How Planck's quantum blackbody distribution, Wien's displacement law, and the Stefan-Boltzmann law link stellar color, temperature, luminosity, and radius.","questionOrTopic":"How do a star's color and total luminosity reveal its surface temperature and physical radius?","epistemicStatus":"strong-observational-evidence","formula":"B_λ(T) = (2hc²/λ⁵) / [exp(hc/(λk_BT)) − 1];   λ_max T = 2.89777 × 10^6 nm·K;   R / R_☉ = (L / L_☉)^{1/2} (T_☉ / T_eff)²","keyMetricsCount":4,"sources":["src:gaia-dr3","src:hipparcos-new","src:planck-2018"]},{"slug":"hydrostatic-equilibrium","path":"/physics/hydrostatic-equilibrium/","title":"Hydrostatic Equilibrium & the Jeans Mass","description":"How the radial pressure gradient dP/dr = −Gm(r)ρ(r)/r² stabilizes stars, planets, and cluster atmospheres, and when Jeans instability triggers collapse.","questionOrTopic":"What keeps a star from collapsing under its own gravity or exploding from its internal heat?","epistemicStatus":"strong-observational-evidence","formula":"dP / dr = −(G m(r) ρ(r)) / r²;   t_ff = √(3π / (32 G ρ));   M_J ≈ (π / 6) ρ λ_J³ ∝ (T / μ)^{3/2} ρ^{−1/2}","keyMetricsCount":4,"sources":["src:gaia-dr3","src:gcvs-v5","src:simbad-cds"]},{"slug":"doppler-shift-and-relativistic-beaming","path":"/physics/doppler-shift-and-relativistic-beaming/","title":"Doppler Shift & Relativistic Beaming","description":"How classical and relativistic Doppler shifts measure radial velocities from 10 cm/s exoplanet wobbles to relativistic AGN jets and superluminal motion.","questionOrTopic":"How does relative motion shift photon wavelengths and amplify jet brightness in special relativity?","epistemicStatus":"strong-observational-evidence","formula":"1 + z_SR = γ (1 + β cos θ_rec);   δ = [γ (1 − β cos θ)]^{−1};   β_app = (β sin θ) / (1 − β cos θ) ≤ γ β","keyMetricsCount":4,"sources":["src:nasa-exoplanet-archive","src:eht-m87-sgra","src:gaia-dr3"]},{"slug":"opacity-and-radiative-transfer","path":"/physics/opacity-and-radiative-transfer/","title":"Opacity, Optical Depth & Radiative Transfer","description":"How radiative transfer dI_ν/dτ_ν = −I_ν + S_ν, photon random walks, H− photospheric opacity, and Kramers opacity govern stellar interiors and atmospheres.","questionOrTopic":"Why does a photon take 100,000 years to escape the Sun and what makes the Sun's visible surface sharp?","epistemicStatus":"strong-observational-evidence","formula":"dI_ν / dτ_ν = −I_ν + S_ν;   T(τ)⁴ = (3/4) T_eff⁴ (τ + 2/3);   t_diff ≈ (R_☉ / ℓ_mfp)² (ℓ_mfp / c) ≈ 3 R_☉² κ ρ̄ / c","keyMetricsCount":4,"sources":["src:gaia-dr3","src:simbad-cds","src:jwst-archive"]},{"slug":"tidal-forces-and-roche-limit","path":"/physics/tidal-forces-and-roche-limit/","title":"Tidal Forces, Roche Limit & Tidal Disruption","description":"Why differential gravity scales as 1/r³, how the Roche limit shreds moons and comets into rings, and how black holes trigger tidal disruption events.","questionOrTopic":"How do differential gravitational tides deform orbits, create planetary rings, and shred stars near black holes?","epistemicStatus":"strong-observational-evidence","formula":"a_tidal = (2 G M R) / r³;   d_Roche (fluid) = 2.44 R_primary (ρ_primary / ρ_satellite)^{1/3}","keyMetricsCount":4,"sources":["src:jpl-horizons","src:nasa-exoplanet-archive","src:harris-globulars"]}]}