Geometrical distances to nearby calibrators determine the luminosities of indicators that can be observed farther away. Those indicators calibrate still more luminous indicators in turn. A ladder may connect parallax or maser distances to Cepheid variables and then to Type Ia supernovae. Each step propagates its calibration uncertainty to the final distance scale and the inferred Hubble constant.
An orbit model for a resolved maser disk combines angular positions, Doppler velocities, accelerations and sometimes proper motions to infer physical orbital dimensions and distance. For an ideal matched circular radius, and ; velocities and accelerations of unrelated maser spots cannot simply be inserted into that expression. Warps, inclination, eccentricity and feature identification enter real disk fits.[ref]
The termination of the first-ascent red giant luminosity function near helium ignition provides a calibrated population-II distance indicator. In suitable passbands the tip luminosity varies relatively weakly over a useful old, metal-poor population range. Colour/composition corrections, foreground extinction, photometric completeness and contamination by other evolved stars must be controlled; an arbitrary brightest red star is not a reliable tip measurement.
Compare the extinction-corrected apparent magnitudes of a cluster's main sequence with calibrated absolute magnitudes at matching colour or stellar parameters. The magnitude displacement estimates its distance modulus. Age, metallicity, helium abundance, reddening and unresolved binaries can move or broaden the sequence, so a colour-magnitude displacement is not uniquely a distance change.
