DZI Physics and Astronomy key terms

A conserved quantity equal to the cross product of position and linear momentum; for a rigid body it equals moment of inertia times angular velocity. It explains orbital motion, spin, and Kepler's equal-area law.

Three rules describing planetary orbits: orbits are ellipses with the Sun at one focus, equal areas are swept in equal times, and the orbital period squared is proportional to the semi-major axis cubed.

The minimum speed an object needs to leave a gravitating body permanently without further propulsion. It equals the square root of twice the gravitational parameter divided by distance from the centre.

A measure of how mass is distributed about a rotation axis, equal to the sum of each mass element times its squared distance from the axis. It determines rotational kinetic energy for a given angular speed.

Potential energy per unit mass at a point in a gravitational field, usually taken as negative and zero at infinity. Its gradient gives the local gravitational acceleration.

A state function measuring the number of microscopic arrangements consistent with a macroscopic state, or equivalently the heat reversibly exchanged divided by temperature. It never decreases in a spontaneous process in an isolated system.

A statement that spontaneous processes increase total entropy, so heat flows from hot to cold and no engine converts heat entirely into work. It defines the arrow of time and limits engine efficiency.

The maximum possible efficiency of a heat engine operating between two reservoirs, equal to one minus the ratio of cold to hot absolute temperatures. No real engine between the same reservoirs can exceed it.

A probability law stating that in thermal equilibrium the chance of occupying a state falls exponentially with that state's energy divided by the product of Boltzmann's constant and temperature. It underlies statistical mechanics.

A normalising sum over all states of the exponential of negative energy over thermal energy. From it one derives free energy, average energy, entropy, and other thermodynamic quantities of a system.

The change in observed frequency or wavelength when a source and observer move relative to each other. Approaching sources appear blue-shifted and receding ones red-shifted, which underpins radial velocity measurement.

The superposition of two or more coherent waves, producing regions of reinforced and cancelled amplitude. The pattern depends on path difference measured in wavelengths and is central to diffraction gratings and interferometers.

The spreading and bending of waves around obstacles or apertures, producing intensity patterns whose width scales with wavelength divided by aperture size. It sets the fundamental resolution limit of optical instruments.

The degree to which a wave maintains a fixed phase relationship across time or space, enabling stable interference. Lasers provide high coherence; starlight is only partially coherent over large baselines.

A rule stating two point sources are just resolved when the centre of one diffraction pattern falls on the first minimum of the other. It yields the resolution limit of about 1.22 wavelengths over aperture diameter.

A statement that the electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space. It simplifies fields of symmetric charge distributions and has a magnetic analogue forbidding monopoles.

A rule relating the circulation of the magnetic field around a closed loop to the enclosed current plus the rate of change of electric flux. It links currents and changing fields to magnetic fields.

A law stating that a changing magnetic flux through a circuit induces an electromotive force proportional to the rate of change, with a sign opposing the change. It explains generators, transformers, and induction heating.

Potential energy per unit charge at a point in an electrostatic field, measured in volts. Differences in potential drive current through conductors and define capacitance when charge is stored.

A mathematical function describing a quantum system whose squared magnitude gives the probability density of finding a particle at a location. It evolves according to the Schrodinger equation and must be normalisable.

A relation stating that certain paired quantities, such as position and momentum, cannot both be known with unlimited precision. The product of their uncertainties is bounded below by half the reduced Planck constant.

Discrete allowed energies for bound quantum systems, arising from boundary conditions on the wavefunction. Transitions between levels produce or absorb photons at characteristic frequencies.

Narrow features in a spectrum produced by absorption or emission at specific atomic or molecular transition frequencies. Their position, width, and strength reveal composition, temperature, and motion.

The set of equations relating space and time coordinates measured in two inertial frames moving at constant relative velocity. It preserves the speed of light and replaces Galilean transformation at high speeds.

The effect in which a clock moving relative to an observer ticks more slowly than the observer's own clock, by the Lorentz factor. It also occurs for clocks deeper in a gravitational potential.

A quantity combining spatial separation squared minus the square of light travel time, which all inertial observers measure identically. Its sign classifies separations as timelike, lightlike, or spacelike.

The loss of photon energy, and shift to longer wavelength, as light climbs out of a gravitational potential well. It is a key test of general relativity and affects stellar spectra.

The balance in a star between inward gravitational force and outward pressure gradient at every layer. It determines the run of pressure, density, and temperature through the stellar interior.

The band on the Hertzsprung-Russell diagram where stars fuse hydrogen to helium in their cores. A star spends most of its luminous life there, with mass setting its luminosity and surface temperature.

The production of heavier nuclei inside stars through fusion and related reactions, releasing energy that sustains the star. Successive burning stages create elements up to iron, with heavier elements made in supernovae or mergers.

The fractional increase in wavelength of light from a receding or gravitationally embedded source. Cosmological redshift measures the expansion of space between emission and observation.

The observation that a galaxy's recession speed is proportional to its distance, with the constant of proportionality being the Hubble constant. It implies an expanding universe and provides a distance indicator.

Relic radiation from the hot early universe, now cooled to a nearly uniform temperature of about 2.7 kelvin. Its tiny temperature anisotropies encode the density fluctuations that seeded galaxies.

An astronomical object whose intrinsic luminosity is known, so its observed brightness yields a distance via the inverse-square law. Type Ia supernovae are the classic example used for cosmological distances.

The ratio of a measured signal's amplitude to the random fluctuation level of the background. It determines detection confidence and, for photon counting, improves with the square root of exposure time.

The procedure for combining the uncertainties of measured quantities to find the uncertainty of a value calculated from them. For independent random errors, relative uncertainties add in quadrature for products and quotients.

A method of choosing model parameters that minimise the sum of squared residuals weighted by measurement uncertainties. The minimum value and parameter uncertainties assess goodness of fit.