How do we measure distance to another galaxy without using the linearity of distance with red-shift?
To other galaxies - cepheid variables and supernovae
Cepheids are a variable star where the period of the brightness change depends on the mass and so the absolute brightness. If you can measure the period (easy) and the apparent brightness you can calculate the distance since you know that for a each doubling of distance the object appears 4x fainter.
For more distant galaxies where the cepheid would be too faint you can use supernova. Certain types have very repeatable absolute brightnesses because they result from a star of a certain size goign bang - again if you measure the apparent brightness you can work out the distance.
Thanks, I understand now..
Other fairly exotic yardsticks also exist [which helps us avoid being completely reliant on a single 'candle']. Examples include:Tip of the red giant branch (TRGB), Planetary nebula luminosity function (PNLF) Globular cluster luminosity function (GCLF) Surface brightness fluctuation (SBF), Tully-Fischer relationship, and the Faber-Jackson relationship. These indicators are useful for estimating distances between Cepheid and SN1a ranges. Another candidate in the making is GRB's [gamma ray bursts], which may extend the distance ladder beyond SN1a limits.
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