annual stellar parallax uses the known Earth-orbit baseline, with . Repeated positions separate parallax from proper motion; calibration offsets, binarity and noisy-parallax selection require checks. Nearby stars calibrate absolute luminosities. Extinction-corrected distance modulus then givesmain-sequence fitting compares a cluster sequence with nearby calibrated stars; age, metallicity, reddening and unresolved binaries limit the match. Cepheid variables extend the range to nearby galaxies: measure periods and mean multiband magnitudes, calibrate the Cepheid period-luminosity relation, and correct for extinction, metallicity, crowding and pulsation mode. RR Lyrae stars and the tip of the red giant branch provide complementary population-II routes with their own composition and calibration dependence.
Some anchors bypass intermediate rungs. An eclipsing-binary distance starts from a double-lined eclipsing binary: velocities give ; eclipses give inclination and relative radii , hence physical radii. An independently calibrated surface-brightness/colour relation gives angular radii and distance; alternatively corrected bolometric flux satisfies for a component. temperature, extinction, third light and surface-brightness calibration remain systematic errors. Eight late-type binaries gave a 2.2%-accuracy LMC anchor in 2013.[ref]
An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent by G. Pietrzyński and others. abstract, Nature 495, 76–79; photometric and orbital information
A maser-disk geometric distance uses water masers orbiting in the nearly edge-on nuclear disk of NGC 4258. very-long-baseline interferometry, Doppler velocities, proper motions and accelerations constrain its orbit scale and distance. In an ideal circular, matched-radius example and ; real fits account for disk warp and different maser locations. This geometric method calibrated an extragalactic distance independently of stellar luminosities.[ref]
A 4% Geometric Distance to the Galaxy NGC4258 from Orbital Motions in a Nuclear Gas Disk by J. R. Herrnstein and others. abstract; orbital proper motions and accelerations, 1999
These overlapping anchors cross-check the nearby-galaxy ladder; no Hubble-flow fit is needed here. Very Long Baseline Array 2026-10-20
The Very Long Baseline Array is a radio-telescope array used for very-long-baseline interferometry. In a solar-deflection experiment, differential astrometry of nearby compact sources compares their apparent directions as their angular separation from the Sun changes. Measurements at several frequencies can distinguish dispersive refraction in the solar corona from achromatic gravitational deflection.[ref]
Very-long-baseline interferometry Created 2026-10-20 Updated 2026-10-20
very-long-baseline interferometry correlates accurately time-referenced radio signals recorded at widely separated collectors, giving angular resolution of order wavelength divided by projected baseline. Geometric delays, frequency standards, atmospheric propagation and source structure enter the calibration. Compact maser positions and motions are one application.