{"section":"methods","label":"Evidence & Methods","count":16,"generatedAt":"2026-03-20","items":[{"slug":"parallax","path":"/methods/parallax/","title":"Trigonometric Parallax in Astrometry","description":"How astronomers measure stellar distances directly from Earth's 2 AU orbital baseline using microarcsecond space astrometry from Hipparcos and Gaia.","questionOrTopic":"How does trigonometric parallax measure direct geometric distances to stars?","epistemicStatus":"strong-observational-evidence","formula":"d (pc) = 1 / p (arcsec)  ;  σ_d / d ≈ σ_p / p","keyMetricsCount":4,"sources":["src:gaia-dr3","src:hipparcos-new","src:simbad-cds"]},{"slug":"astronomical-spectroscopy","path":"/methods/astronomical-spectroscopy/","title":"Astronomical Spectroscopy & Spectral Analysis","description":"How diffraction gratings and echelle spectrographs disperse starlight to measure radial velocity, temperature, surface gravity, and elemental abundances.","questionOrTopic":"How does astronomical spectroscopy extract velocity, composition, and physical state from light?","epistemicStatus":"strong-observational-evidence","formula":"R = λ / Δλ = c / Δv","keyMetricsCount":4,"sources":["src:gaia-dr3","src:jwst-archive","src:simbad-cds"]},{"slug":"multi-band-photometry","path":"/methods/multi-band-photometry/","title":"Multi-Band Photometry & Magnitude Systems","description":"How calibrated broadband filters (UBVRI, ugriz, Gaia G/BP/RP) measure stellar fluxes, color indices, interstellar reddening, and photometric redshifts.","questionOrTopic":"How does multi-band photometry measure brightness, color temperature, and galaxy redshifts?","epistemicStatus":"strong-observational-evidence","formula":"m₁ − m₂ = −2.5 log₁₀(F₁ / F₂)  ;  m − M = 5 log₁₀(d / 10 pc) + A_λ","keyMetricsCount":4,"sources":["src:gaia-dr3","src:simbad-cds","src:gcvs-v5"]},{"slug":"cosmological-and-doppler-redshift","path":"/methods/cosmological-and-doppler-redshift/","title":"Measuring Cosmological & Doppler Redshift","description":"How astronomers distinguish kinematic Doppler shifts, gravitational redshift, and cosmological metric expansion from observed spectral wavelengths.","questionOrTopic":"How is redshift measured and how do astronomers separate Doppler motion from cosmic expansion?","epistemicStatus":"strong-observational-evidence","formula":"1 + z_obs = (1 + z_cosmo)(1 + z_pec)(1 + z_grav)","keyMetricsCount":4,"sources":["src:planck-2018","src:jwst-archive","src:simbad-cds"]},{"slug":"standard-candles-cepheids-and-type-ia","path":"/methods/standard-candles-cepheids-and-type-ia/","title":"Standard Candles: Cepheids & Type Ia Supernovae","description":"How Cepheid period-luminosity relations, Tip of the Red Giant Branch stars, and Phillips-standardized Type Ia supernovae measure extragalactic distances.","questionOrTopic":"How do Cepheid variables and Type Ia supernovae act as standardizable candles across cosmic distances?","epistemicStatus":"strong-observational-evidence","formula":"M_W = a · [log₁₀(P / 10 d)] + b + γ · [Fe/H]  ;  d = 10^((m − M + 5) / 5) pc","keyMetricsCount":4,"sources":["src:shoes-2022","src:gaia-dr3","src:gcvs-v5","src:jwst-archive"]},{"slug":"transit-detection","path":"/methods/transit-detection/","title":"Exoplanet Transit Photometry & Spectroscopy","description":"How periodic stellar flux dips measure exoplanet radii, orbital inclinations, mean densities, and atmospheric transmission spectra.","questionOrTopic":"How does transit photometry detect exoplanets and measure their sizes and atmospheres?","epistemicStatus":"strong-observational-evidence","formula":"ΔF / F ≈ (R_p / R_★)²  ;  P_transit = (R_★ + R_p) / a ≈ 0.00465 (R_★/R_☉)(1 AU / a)","keyMetricsCount":4,"sources":["src:nasa-exoplanet-archive","src:jwst-archive"]},{"slug":"radial-velocity-doppler-wobble","path":"/methods/radial-velocity-doppler-wobble/","title":"Radial Velocity & Stellar Doppler Wobble","description":"How ultra-stable echelle spectrographs measure sub-meter-per-second stellar reflex motion to determine exoplanet minimum masses and orbital eccentricities.","questionOrTopic":"How does the radial velocity method detect exoplanets and measure their masses?","epistemicStatus":"strong-observational-evidence","formula":"K_★ = (28.43 m/s) · (M_p sin i / M_Jup) · (P / 1 yr)^(−1/3) · (M_★ / M_☉)^(−2/3) / √(1 − e²)","keyMetricsCount":4,"sources":["src:nasa-exoplanet-archive","src:simbad-cds"]},{"slug":"direct-exoplanet-imaging-and-coronagraphy","path":"/methods/direct-exoplanet-imaging-and-coronagraphy/","title":"Direct Exoplanet Imaging & Coronagraphy","description":"How extreme adaptive optics, vortex coronagraphs, and angular differential imaging suppress starlight by 10⁶–10¹⁰ to image wide-orbit exoplanets directly.","questionOrTopic":"How do coronagraphs and extreme adaptive optics directly image exoplanets next to bright stars?","epistemicStatus":"strong-observational-evidence","formula":"θ (arcsec) = a (AU) / d (pc)  ;  C_reflected = A_g · Φ(α) · (R_p / a)²","keyMetricsCount":4,"sources":["src:nasa-exoplanet-archive","src:jwst-archive","src:gaia-dr3"]},{"slug":"gravitational-lensing-and-microlensing","path":"/methods/gravitational-lensing-and-microlensing/","title":"Gravitational Lensing & Microlensing","description":"How spacetime deflection produces strong Einstein rings, weak cosmic shear maps of dark matter, and microlensing detections of cold wide-orbit exoplanets.","questionOrTopic":"How do astronomers use strong, weak, and microlensing to map dark matter and find exoplanets?","epistemicStatus":"strong-observational-evidence","formula":"θ_E = √[ (4GM / c²) · (D_LS / (D_L D_S)) ]","keyMetricsCount":4,"sources":["src:nasa-exoplanet-archive","src:jwst-archive","src:gaia-dr3"]},{"slug":"very-long-baseline-interferometry","path":"/methods/very-long-baseline-interferometry/","title":"Very Long Baseline Interferometry (VLBI)","description":"How atomic-clock-synchronized radio telescopes across continents synthesize an Earth-sized aperture with 20-microarcsecond angular resolution.","questionOrTopic":"How does Very Long Baseline Interferometry achieve microarcsecond resolution across the globe?","epistemicStatus":"strong-observational-evidence","formula":"θ_res ≈ λ / B_max  ;  V(u, v) = ∬ I(l, m) e^(−2πi(ul + vm)) dl dm","keyMetricsCount":4,"sources":["src:eht-m87-sgra","src:simbad-cds"]},{"slug":"x-ray-and-high-energy-astronomy","path":"/methods/x-ray-and-high-energy-astronomy/","title":"X-Ray & High-Energy Gamma-Ray Astronomy","description":"How Wolter grazing-incidence mirrors, microcalorimeters, pair-conversion trackers, and Cherenkov arrays observe extreme relativistic astrophysics.","questionOrTopic":"How do astronomers focus X-rays and detect gamma rays from black holes, neutron stars, and clusters?","epistemicStatus":"strong-observational-evidence","formula":"θ_c ≈ √(2δ) ∝ √Z · ρ^(1/2) / E_γ","keyMetricsCount":4,"sources":["src:simbad-cds","src:gwtc-3"]},{"slug":"infrared-and-submillimeter-astronomy","path":"/methods/infrared-and-submillimeter-astronomy/","title":"Infrared & Submillimeter Astronomy","description":"How cryogenic space telescopes (JWST) and high-altitude submillimeter interferometers (ALMA) pierce interstellar dust to observe cold gas and early galaxies.","questionOrTopic":"Why do astronomers use cryogenic infrared telescopes and submillimeter arrays to study dust-obscured regions and the early universe?","epistemicStatus":"strong-observational-evidence","formula":"A_K / A_V ≈ 0.11  ;  λ_obs = λ_rest · (1 + z)","keyMetricsCount":4,"sources":["src:jwst-archive","src:simbad-cds"]},{"slug":"gravitational-wave-interferometry","path":"/methods/gravitational-wave-interferometry/","title":"Gravitational-Wave Laser Interferometry","description":"How 4-km Fabry-Pérot Michelson interferometers (LIGO, Virgo, KAGRA) measure 10⁻²² spacetime strain from compact binary mergers.","questionOrTopic":"How do laser interferometers measure gravitational-wave strains smaller than a thousandth of a proton diameter?","epistemicStatus":"strong-observational-evidence","formula":"h = 2 ΔL / L  ;  h(t) ∝ (G 𝓜_c / c²)^(5/3) · (π f / c)^(2/3) / d_L","keyMetricsCount":4,"sources":["src:gwtc-3"]},{"slug":"cosmic-distance-ladder","path":"/methods/cosmic-distance-ladder/","title":"The Cosmic Distance Ladder Explained","description":"How astronomers link radar ranging, Gaia parallaxes, Cepheid variables, TRGB stars, and Type Ia supernovae into a continuous extragalactic distance scale.","questionOrTopic":"How are the rungs of the cosmic distance ladder calibrated from the Solar System to the Hubble flow?","epistemicStatus":"strong-observational-evidence","formula":"5 log₁₀ H₀ = M_B^0 + 5 a_B + 25","keyMetricsCount":4,"sources":["src:shoes-2022","src:gaia-dr3","src:jwst-archive"]},{"slug":"isochrone-fitting-and-cluster-ages","path":"/methods/isochrone-fitting-and-cluster-ages/","title":"Isochrone Fitting & Star Cluster Ages","description":"How astronomers determine the ages of open and globular clusters by fitting theoretical stellar evolution tracks to the main-sequence turnoff.","questionOrTopic":"How does isochrone fitting measure the ages of star clusters from their color-magnitude diagrams?","epistemicStatus":"strong-observational-evidence","formula":"τ_cluster ≈ 10 Gyr · (M_MSTO / M_☉)^(−2.5) · f([Fe/H], [α/Fe])","keyMetricsCount":4,"sources":["src:harris-globulars","src:gaia-dr3"]},{"slug":"measurement-error-systematics-and-bayesian-inference","path":"/methods/measurement-error-systematics-and-bayesian-inference/","title":"Measurement Error, Systematics & Bayes","description":"How modern astrophysics separates statistical photon noise from calibration systematics and uses Bayesian inference and MCMC to constrain physical models.","questionOrTopic":"How do astronomers distinguish statistical from systematic uncertainty and infer parameters from noisy data?","epistemicStatus":"strong-observational-evidence","formula":"P(θ | D) = [ P(D | θ) · P(θ) ] / P(D)  ;  −2 ln ℒ = (d − m(θ))ᵀ C⁻¹ (d − m(θ))","keyMetricsCount":4,"sources":["src:gaia-dr3","src:planck-2018","src:shoes-2022","src:gwtc-3"]}]}