Foundations

Measured motions constrain the gravitational mass distribution.

Disk observations and competing growth mechanisms inform planet-formation models.

CMB statistics constrain parameters within a chosen cosmological model.

Motions and lensing constrain mass beyond that accounted for by luminous material.

Gravitational evidence does not yet settle the unseen component's physical identity.

Expansion evidence motivates competing physical descriptions with unresolved origin.

Pure phases coexist at common T and p when their molar Gibbs energies are equal.

Thermal radiation in a vacuum cavity at temperature T has spectral energy density per angular frequency u_ω=ħω³/[π²c³(exp(ħω/(k_BT))−1)].

For a light source and observer receding directly from each other at relative speed v, f_obs=f_source√[(1−v/c)/(1+v/c)].

For a frame rotating at constant Ω about a common inertial origin, a_inertial=a_rot+2Ω×v_rot+Ω×(Ω×r).

For a smooth inviscid, nonconducting fixed-composition fluid, D_ts=0 and ρD_te=−P∇·v, where e and s are internal energy and entropy per mass.

An isolated Newtonian gravitational binary has relative semimajor axis a=a₁+a₂ and period T satisfying T²=4π²a³/[G(m₁+m₂)].

Independent constant decay channels have total rate λ=Σ_iλ_i and branching fractions b_i=λ_i/λ.

In a dilute nondegenerate gas of independently distributed reacting nuclei at common temperature T, reaction events per volume/time are R_ab=n_an_b⟨σv⟩/(1+δ_ab), where δ_ab=1 for the same species and 0 otherwise.

For repulsively charged nuclei with κ=Z_aZ_be²/(4πε₀)>0 and relative speed v, the Sommerfeld parameter is η=κ/(ħv) and the leading low-energy Coulomb penetration exponential is exp(−2πη)=exp[−√(E_G/E)], E_G=2μ(πκ/ħ)².

Geological history is organized into nested eons, eras, periods, epochs and ages.

Accretion, impacts, gravitational redistribution and radioactive decay contributed to early-Earth heating.

Oxygenic photosynthesis supplied oxygen while chemical reactions with reduced material consumed it.

An isotope delta compares a specified sample isotope ratio with the same ratio in a stated reference.

Gravity supplies both downslope shear and normal loading on a slope.

Coastal landforms reflect sediment supply, wave/current transport, erosion and deposition.

An ascending air parcel expands as pressure falls and can cool toward saturation.

For an isotropic source in transparent Euclidean space, bolometric flux decreases as luminosity divided by the area of a sphere.

A magnitude difference encodes a flux ratio on a logarithmic scale: brighter objects have smaller magnitudes.

Continuum shape and spectral-line patterns constrain temperature, composition and the physical conditions in a stellar atmosphere.

A CCD records photo-generated charge in pixels over an exposure.

A circular aperture has a diffraction angular scale proportional to wavelength divided by diameter.

Dust absorbs and scatters radiation along a line of sight.

A distance ladder transfers geometric calibrations to luminosity-based indicators such as Cepheids and standardized supernovae.

Along a ray, local emission adds and extinction removes specific intensity.