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An astrophysical black hole is an astronomical object interpreted as a black hole through evidence about its mass, compactness and interaction with surrounding matter or gravitational waves. A black hole of stellar mass can form after stellar core collapse; a supermassive black hole can grow through black-hole accretion and mergers. The event horizon prevents light from escaping from within, but matter outside can radiate and reveal the central gravity. For Sagittarius A*, astrometry and radial velocities of nearby stars constrain a very large mass inside their small orbits. Such dynamical evidence complements observations of accretion and of binary black holes, which probe different aspects of the black-hole interpretation.^[ref]

The Galactic Center is the central region of the Milky Way, where the compact source Sagittarius A* and nearby stellar motions provide a test of a concentrated gravitational potential. It is a region, rather than another name for the entire black hole or one emitting point.

Infrared observations reduce the obscuration that limits ordinary visible-light measurements. Combining stellar astrometry with line-of-sight velocities constrains an orbit and the central mass; precise departures from a Kepler orbit can test general relativity.^[ref] A resolved apparent trajectory alone does not supply every orbital component or remove reference-frame uncertainty.

Rainer Schödel, Reinhard Genzel and collaborators combined NTT imaging with VLT adaptive-optics infrared observations. Silicon-monoxide masers registered stellar images to the radio position of Sagittarius A*. Their 2002 observations included S2's closest approach; a fitted Kepler orbit constrained a concentrated central mass. Rejecting a particular extended cluster also required its density and survival assumptions.^[ref]

Andrea Ghez and collaborators combined Keck speckle imaging and laser-guide-star adaptive optics with infrared spectra. Image fitting supplied angular positions; spectral lines supplied velocities. The 2008 analysis treated optical distortion, coordinate alignment and blended sources: a shifting photocentre can imitate motion. Joint angular and spectral fitting constrained both distance and mass, with assumptions about central radial motion affecting the result. Apparatus calibration and confusion tests are therefore part of the dynamical inference.^[ref]

mass from motion. A resolved Keplerian orbit gives $M=4{\pi }^2{a}^3/(G{P}_{\mathrm{orb}}^2)$ when the orbiting object has negligible mass. At the Galactic centre, repeated infrared astrometry and spectroscopy measure sky motion, acceleration and line-of-sight velocity of stars around Sagittarius A*. Resolving a compact enclosed mass and fitting complete orbits avoids reliance on a single projected velocity. Source confusion, reference-frame stability, distance, inclination and possible extended mass must be included in the fit.^[ref]

For an unresolved stellar-mass binary in a circular orbit, the donor's velocity semiamplitude $K_2$ and orbital period give the binary mass functionIt provides a lower mass bound; donor mass and orbital inclination are needed for an actual mass estimate. For an eccentric orbit, multiply the observational combination $P_{\mathrm{orb}}{K}_2^3/(2\pi G)$ by $(1-e^2{)}^{3/2}$ when evaluating the binary mass function. Resolved gas or maser rotation and stellar-dynamical models also measure masses, provided pressure support, noncircular motion and line-of-sight projection are modeled. Resolving the black-hole sphere of influence improves separation of central mass from the host galaxy.

For active nuclei, reverberation mapping measures a lag $\tau$ between variable continuum and broad-line response. With a line velocity scale $\Delta v$,The factor $f_{\mathrm{geom}}$ accounts for geometry and kinematics and is not known simply from the lag. Cadence, line responsivity, inclination and winds require control. Rapid variability demonstrates compactness but is not by itself a unique mass measurement.

black-hole spin from strong-field emission. Define $a_{\ast }=cJ/(G{M}^2)$. Large-radius Keplerian motion is principally a mass probe and usually insensitive to black-hole spin. In the Kerr model, the radius and binding energy of the innermost stable circular orbit vary with $a_{\ast }$ and orbital orientation, making inner-disk radiation useful.

black-hole continuum fitting infers an inner emitting radius from the disk's thermal spectrum and flux normalization, then identifies it with the innermost stable circular orbit in a relativistic thin-disk model. Independent mass, distance and inclination, together with atmospheric spectral hardening, absorption and contamination, are needed. Spectra should be selected in a disk-dominated regime where truncation and strong advection are limited. A 2011 Cygnus X-1 analysis combined such spectra with independently constrained binary parameters and reported a near-extreme black-hole spin conditional on black-hole spin–orbit alignment and its disk model.^[ref]

black-hole reflection spectroscopy instead models a relativistically broadened iron-line and reflection continuum: orbital Doppler shifts and beaming broaden the profile, while gravitational redshift contributes to the extended red wing. Its innermost emitting radius can constrain black-hole spin if reflection extends to the stable inner edge. Ionization, abundance, absorption, coronal illumination, disk thickness and possible truncation are competing parameters; a broad line is not a direct black-hole spin reading independent of these assumptions. Timing or precession models can add information but introduce their own dynamical identification.

mass is principally inferred from gravitating dynamics; black-hole spin is inferred from strong-field effects with a specified spacetime and accretion model. Agreement between independent methods is especially valuable because disk inner radius, inclination and radiation-transfer assumptions can otherwise mimic a change of black-hole spin.

The strongest pre-2014 evidence combines large gravitating mass with extreme compactness. In an X-ray binary, companion-star radial velocities determine a binary mass function; orbital inclination, donor properties and distance complete the mass inference. An unseen component above conventional neutron-star masses is a black-hole candidate. For example, a 2011 Cygnus X-1 analysis combined optical photometry, spectroscopy and distance information to infer a compact-object mass about $14.8M_{\odot }$, with model and observational uncertainties.^[ref]

Near Sagittarius A*, infrared stellar astrometry and radial velocities trace nearly Keplerian orbits around a dark compact mass. The concentration of several million solar masses in a small volume strongly challenges an extended cluster of ordinary remnants; source confusion, reference-frame errors, distance and possible extended mass must be fitted.^[ref] Gas and maser dynamics provide related compact-mass tests in other nuclei.

accretion explains luminous X-rays, rapid variability and broad relativistic disk features. These constrain size and the strong-field environment, but emission alone is not unique to an event horizon. Lack of surface-like signatures is supporting, model-dependent evidence. Mass, compactness and consistent accretion phenomenology together support the black-hole interpretation; large-radius mass measurements alone do not directly demonstrate a horizon.

Rainer Schödel led a study that traced a short-period star around Sagittarius A* at the center of the Milky Way. Ten years of high-resolution astrometry captured both the nearest and farthest parts of the star's highly eccentric orbit.

The 2002 analysis found an orbital period of about 15 years and a close approach of only about 17 light-hours. Concentrating several million solar masses inside that small region excluded plausible extended clusters as the source of the central gravitational field, strengthening the supermassive black hole interpretation.^[ref]

Reinhard Genzel investigates the central mass of the Milky Way using the motion of nearby stars. He coauthored the 2002 report led by Rainer Schödel that followed a close stellar orbit around Sagittarius A*.

An orbital path tests more than a high stellar speed: its curvature, timing and closest approach constrain how tightly the attracting mass is concentrated. The measured short-period orbit required several million solar masses in a compact central region, providing strong dynamical evidence for a supermassive black hole.^[ref]

Sagittarius A* is the compact radio source at the centre of the Milky Way. Nearby infrared stars allow its central mass concentration to be studied through their orbits.^[ref]

Stellar dynamics treats stars as gravitating bodies whose collective motions reveal and reshape their environment. In a collisionless stellar system, stars mainly follow the smooth collective gravitational potential; in a sufficiently dense star cluster, accumulated gravitational encounters produce two-body relaxation. These encounters need not involve physical contact between stars. Observers combine astrometry with radial velocities to constrain orbits and infer unseen mass. The stellar orbits at the Galactic centre provide a particularly direct example: following a short-period star around Sagittarius A* measures the compact central mass, rather than estimating it from the light emitted by its surroundings.^[ref]