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For a detached double-lined binary, radial velocities supply an orbital length scale times $\sin i$, while eclipse geometry supplies inclination and relative radii. Together they determine physical stellar radii. Comparing them with angular radii from a calibrated surface-brightness/colour relation gives distance. The orbital scale is geometric, but the angular-radius calibration, extinction and third light add astrophysical assumptions.^[ref]

G. Pietrzyński led a 2013 measurement of the Euclidean distance to the Large Magellanic Cloud using eight late-type eclipsing binaries. The systems contained cool giant stars, whose physical and angular sizes could be compared to infer Euclidean distance.

The study reported approximately $2.2\%$ accuracy and kept statistical and systematic uncertainties separate. Choosing these systems addressed modeling difficulties associated with hotter binaries, while improving an anchor of the cosmic distance ladder and hence the calibration of the Hubble constant.^[ref]

The Large Magellanic Cloud is a nearby galaxy interacting with the Milky Way, containing stars whose independently measurable properties help calibrate astronomical distances. Its proximity makes it possible to combine stellar observations that are much harder to separate in more distant systems.

In a late-type eclipsing binary, orbital velocities and eclipse geometry constrain linear stellar sizes; a surface-brightness calibration supplies corresponding angular sizes. Comparing the two gives a distance anchor rather than assuming one fixed luminosity for every star.^[ref] Such calibration still has systematic uncertainty and samples a galaxy with finite depth.

PASP 85, 573–578. Primary classical treatment of parallax-based luminosity calibration under a spatial-population model. Its assumptions do not justify a universal correction to every modern individual-star distance inference. Bibliographic details are also verified in the references of An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent by G. Pietrzyński and others.

annual stellar parallax uses the known Earth-orbit baseline, with $d(\mathrm{pc})=1/\varpi (\mathrm{arcsec})$. 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 $a\sin i$; eclipses give inclination $i$ and relative radii $R/a$, hence physical radii. An independently calibrated surface-brightness/colour relation gives angular radii and distance; alternatively corrected bolometric flux satisfies $F_{\mathrm{bol}}=\sigma T_{\mathrm{eff}}^4(R/d{)}^2$ 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]

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 $R=v^2/a_{\mathrm{orb}}$ and $d=R/\theta$; real fits account for disk warp and different maser locations. This geometric method calibrated an extragalactic distance independently of stellar luminosities.^[ref] These overlapping anchors cross-check the nearby-galaxy ladder; no Hubble-flow fit is needed here.