Foundations

An orbiting body can remain in continuous gravitational free fall.

Main-sequence stars release energy by fusing hydrogen into helium.

Expansion and relic radiation support an earlier hot, dense Universe.

Stellar structure changes as core fuel and conditions change.

Different evolutionary outcomes leave different compact remnants.

Changing observing position permits geometric distance inference.

Spectral stretching carries expansion information but is not one universal distance ruler.

Measured motions constrain the gravitational mass distribution.

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

Terrestrial planets are dominated by rock and metal; giant planets contain larger proportions of light gases and volatile-rich material.

Atmospheric mass, composition and opacity affect a planet's surface conditions.

Asteroids include bodies with differing rocky, carbon-rich and metallic material signatures; meteorites and spacecraft observations test interpretations of their histories.

The interstellar medium contains ionized, atomic and molecular gas alongside dust.

The Milky Way contains disk, bulge and halo components with differing distributions, motions and stellar populations.

Spiral galaxies commonly contain a disk, bulge and spiral patterns with gas and ongoing star formation.

A thin gravitational lens relates a source's unlensed angular position to observed image positions through a mass-dependent deflection.

In an FLRW expansion model, light emitted and observed by comoving observers is stretched by the ratio of their scale factors.

The hot expanding universe passed through changing particle and radiation conditions.

In the standard cosmological model, small density variations grow gravitationally and dark-matter structures help concentrate baryonic matter after photon coupling becomes less effective.

In an expanding FLRW model with present scale factor one, the line-of-sight comoving distance is D_C=c∫₀ᶻ dz′/H(z′), and the lookback time is t_L=∫₀ᶻ dz′/[(1+z′)H(z′)].

For transparent geometrical photon propagation in FLRW cosmology, angular diameter distance is D_A=D_M/(1+z), and luminosity distance is D_L=(1+z)D_M=(1+z)²D_A.

A spherical planet intercepts stellar power over its projected disk and emits thermal power over its surface.

At an exobase radius r_ex and temperature T_ex, λ=GMm/(r_ex k_BT_ex) compares a species' binding energy with thermal energy.

Tides arise from gravitational acceleration differences across an extended body.

In a smooth stationary axisymmetric potential, expanding about a stable circular guiding radius R_g gives small radial oscillations at epicyclic frequency κ and vertical oscillations at ν.

For a razor-thin rotating ideal fluid disk, local axisymmetric tightly wound perturbations have dispersion ω²=κ²−2πGΣ|k|+c_s²k².

In a well-mixed closed gas-plus-star system with initially zero metallicity, instantaneous recycling and constant yield p per mass locked in long-lived stars, gas metallicity follows Z=p ln(1/μ), where μ=M_gas/M_total.

For small sub-Hubble-scale perturbations of pressureless matter in a homogeneous expanding background, the Newtonian growing-density model obeys δ̈+2Hδ̇−4πGρ̄_mδ=0.

For a specified birth population, an initial mass function ξ(m) defines dN=ξ(m)dm on a stated initial-mass interval.

Active galactic nuclei can radiate strongly as matter accretes around a central supermassive black hole.