The Cosmic Distance Ladder

Summary

• Astronomical distances are measured. They are not read off a model, and they are not assumed. The bottom of the scale is a triangle: a nearby star shifts against the background as the Earth moves around the sun, and the shift gives the distance. Nothing in that calculation depends on how stars work, how galaxies form, or how old anything is.
• Three independent methods skip the ladder entirely and give the same answers. Detached eclipsing binaries in the Large Magellanic Cloud give 49.59 ± 0.09 statistical ± 0.54 systematic kiloparsecs, which is one per cent.¹¹ Water masers orbiting the black hole in NGC 4258 give 7.576 ± 0.082 ± 0.076 megaparsecs.²² The light echo off the ring around SN 1987A gives 51.2 ± 3.1 kiloparsecs for the same galaxy the eclipsing binaries measure.³³ Each rests on a different kind of geometry, and they agree.
• Gaia has measured parallaxes for 1.468 billion stars.⁴ Its known systematic is a parallax offset of about −17 microarcseconds. The Gaia team found it themselves, from quasars whose true parallax is zero, published with a correction recipe, and then checked twice from outside: by red giants whose distances come from asteroseismology, and by Milky Way Cepheids.⁴⁵⁶ Both outside checks find the published correction slightly too strong, by about 15 microarcseconds, for bright stars. A bias of that size is a hundred-thousandth of an arcsecond and changes nothing about the scale of the universe.
• Every rung above parallax carries assumptions, and this article names them one by one. Cepheids assume a period-luminosity relation whose zero point shifts with chemical composition. The tip of the red giant branch assumes the helium flash happens at a nearly fixed core mass. Type Ia supernovae assume no drift in standardised brightness with redshift. These are real weaknesses and they are actively fought over.
• Gravitational waves now give distances with no astronomy in them at all. General relativity fixes the amplitude of a merger's chirp, so the distance falls straight out of the waveform. GW170817 gave 70.0 (+12.0, −8.0) km/s/Mpc for the Hubble constant "without the use of intermediate astronomical distance measurements."⁷⁷ The error bar is wide, and a 2026 refit using the radio jet's geometry moved the number down to 65.5 ± 4.4.⁸⁸ Honest reporting means saying both.
• The methods disagree at the nine per cent level, not the nine-thousand per cent level. That disagreement is the Hubble tension, and it is a fight over calibration. It is covered in full in the Hubble tension article and is not re-argued here.
• For a young universe, the distances are the hard part, and young-earth astronomers say so themselves. Danny Faulkner, who holds a PhD in astronomy, wrote in 2020 that these methods "produce distances that are millions and even billions of light-years. While all of these methods suffer from error, those errors would not reduce the distances down to just thousands of light-years."⁹⁹ He had already written in 2013 that shrinking the distances would require abandoning "even the well determined trigonometric parallax method … but this is not physically supported."¹⁰¹⁰ This article agrees with him, and the reason is arithmetic: to bring the Large Magellanic Cloud inside 6,000 light years, three unrelated geometric measurements would all have to be wrong by a factor of about 27, in the same direction, for different reasons.
• What the distances do not settle is the age question. A measured distance tells you how far away something is. Turning that into an age requires assuming that light has always travelled at today's speed along today's path, and that the clock convention used to time its arrival is the right one. Those are separate questions, argued in Young-Universe Cosmologies.

Why it is called a ladder

Nothing in astronomy measures 100 megaparsecs directly.  There is no tape measure and no radar echo.  What exists instead is a chain of methods, each one calibrated on the one below it, each one reaching further than the last.

The chain works like this.  Parallax measures nearby stars by pure trigonometry.  Some of those nearby stars are Cepheid variables, so parallax fixes how bright a Cepheid of a given period really is.  Cepheids are bright enough to be picked out in galaxies tens of megaparsecs away, and some of those galaxies have hosted Type Ia supernovae, so Cepheids fix how bright a Type Ia supernova really is.  Type Ia supernovae are visible across billions of light years.

That structure has an obvious hazard.  An error at the bottom propagates all the way up, multiplied.  If the Cepheid zero point is off by five per cent, every supernova distance is off by five per cent, and the Hubble constant is off by five per cent.  This is why the ladder is audited harder than almost anything else in astronomy, and why the audits are worth reading.

The structure also has a defence that gets less attention than it should.  The ladder is not the only way up.  Several methods reach extragalactic distances without any rungs at all:  eclipsing binaries, water masers, supernova light echoes, gravitational waves.  Those are the ones this article treats first and at greatest length, because they are the ones a skeptic cannot dismiss as circular.

Rung one: trigonometric parallax

The triangle

Hold a finger at arm's length and close one eye, then the other.  The finger jumps against the far wall.  The jump is bigger if the finger is closer.  That is the whole method.

For stars the two eyes are the Earth's position in January and in July, separated by two astronomical units.  A star nearby traces a small ellipse against the far more distant background over the year.  Half the angular width of that ellipse is the star's parallax.  A star with a parallax of one arcsecond sits at one parsec, which is 3.26 light years.  Distance in parsecs is simply one divided by the parallax in arcseconds.

There is no astrophysics in that sentence.  It does not matter what the star is made of, how it burns, how old it is, or how bright it is.  Only three things go in:  the size of the Earth's orbit, the measured angle, and plane trigonometry.  The size of the Earth's orbit was pinned by radar ranging to Venus and by tracking spacecraft around the solar system;  since 2012 the astronomical unit has been a defined constant, 149,597,870,700 metres exactly.¹¹

This is why parallax is the load-bearing rung.  Everything above it can be argued about.  This one is a triangle.

Bessel, 1838, and what he already understood

Friedrich Bessel announced the first stellar parallax in a letter to John Herschel dated 23 October 1838.  He chose 61 Cygni because its large proper motion suggested it was close, and because being a double star it could be measured more precisely.  He measured its position against two faint neighbours with a Fraunhofer heliometer, sixteen times a night.

His answer was a parallax of 0".3136, with a stated mean error of ± 0".0202.¹²¹²  Then he did the thing that matters for this article.  He converted it:

"Assuming it 0"·3136, we find the distance of the star 61 Cygni from the sun 657700 mean distances of the earth from the sun:  light employs 10·3 years to traverse this distance."¹²

The light-travel-time problem is not a modern invention and it is not a big-bang artefact.  It was stated, in print, from a triangle, in 1838, by a man measuring one nearby star.

Gaia's modern value for 61 Cygni A is 285.9949 ± 0.0599 milliarcseconds, which is 11.4 light years.¹³  Bessel was nine per cent low.  A visual measurement made with a nineteenth-century brass instrument landed within ten per cent of a satellite measurement made 180 years later.  That is the kind of track record a method has to have before its results are worth arguing about.

Hipparcos to Gaia

Parallax from the ground is hard, because the atmosphere smears star images by roughly an arcsecond.  That is larger than every stellar parallax except Proxima Centauri's.  Getting above the atmosphere changed the field twice.

ESA's Hipparcos satellite observed from 1989 to 1993, and its catalogue was released in June 1997.  It contains 118,218 entries with a median parallax precision of 0.97 milliarcseconds.  At that precision, exactly 20,853 stars had distances good to ten per cent, a sphere roughly 300 light years across.¹⁴

Gaia, launched in December 2013, moved the goalposts by a factor of about forty.  Gaia Early Data Release 3 gives "full astrometric data (positions at epoch J2016.0, parallaxes, and proper motions) for 1.468 billion sources," with "median uncertainty in parallax and annual proper motion" of "0.02-0.03 mas at magnitude G = 9 to 14, and around 0.5 mas at G = 20."⁴⁴

Run the arithmetic on that.  A parallax uncertainty of 0.025 milliarcseconds gives a ten-per-cent distance out to a parallax of 0.25 milliarcseconds, which is 4 kiloparsecs, about 13,000 light years.  That reaches the Galactic centre.  It does not reach the Large Magellanic Cloud, whose parallax is about 0.02 milliarcseconds.  That is the level of Gaia's systematic floor, not its statistical one.  Parallax alone does not measure the LMC, and no honest account should claim otherwise.  Something else has to do that job, and the next section is about what.

The remaining data release, Gaia DR4, is scheduled for 2 December 2026 and will use 66 months of data rather than 34.¹⁵  Nothing in this article depends on it.

The zero-point offset, and how it was caught

Gaia's parallaxes have a known bias.  It is worth spending a paragraph on, because it is the single best example in modern astronomy of a field finding and publishing its own systematic error.

The bias comes from the way the spacecraft's two lines of sight are combined.  Gaia measures angles between widely separated fields, and a slow drift in the angle between those fields feeds directly into the parallaxes as an additive offset.  An additive offset is invisible in the data itself:  every star's parallax is wrong by the same small amount, so nothing looks odd.

The Gaia team found it by measuring things whose parallax is known in advance to be zero.  Quasars are billions of light years away.  Their true parallax is unmeasurably small.  So whatever parallax Gaia reports for a quasar is the bias, read directly.  Lennart Lindegren and colleagues did exactly this:

"In Gaia EDR3 quasars have a median parallax of about −17 µas, and already a simple plot of the parallaxes versus the G magnitude or colour index reveals systematic variations at a level of ∼10 µas."⁴⁴

Seventeen microarcseconds is a hundred-thousandth of an arcsecond.  It matters for a star five kiloparsecs away, where it is a few per cent, and it is irrelevant for a star fifty parsecs away, where it is one part in twenty thousand.  The team mapped its dependence on brightness, colour and position, published correction formulae, and warned in the abstract that "it is not possible to derive a definitive recipe for the parallax correction."⁴

Two other groups then checked the correction against physics Gaia never saw.  Joel Zinn used more than 2,000 red giants whose distances follow from asteroseismology.  The pattern of a star's oscillation frequencies gives its radius, and radius plus brightness gives distance.  He found that Gaia's own correction goes slightly too far for bright stars:  "an over-correction sets in at G ≲ 10.8, such that Z₅-corrected EDR3 parallaxes are larger than asteroseismic parallaxes by 15±3µas."⁵⁵  Adam Riess and colleagues used 75 Milky Way Cepheids with HST photometry, letting the period-luminosity relation itself solve for the residual, and found −17 ± 6 microarcseconds in the same direction, "with no prior on the quality" of the Gaia correction.⁶⁶

Three methods, three physical principles, one answer to within a few microarcseconds.  The bias is real, small, and measured.

Zinn's paper also carries a finding that cuts against Gaia, and it should be stated:  Gaia's published error bars are too small.  He infers "an average under-estimation of EDR3 parallax uncertainties in the sample of 22 ± 6%," and puts the floor on systematic parallax uncertainty at "at least ≈ 3 − 4µas."⁵  Anyone using Gaia parallaxes at the limit of their precision has to widen the quoted errors.  That is a real defect in the catalogue, published by an outside checker, and it moves distances by parts per thousand, not by factors.

What parallax assumes

Very little, and the little it assumes has been tested independently.

• That the astronomical unit is what we think it is. Fixed by radar ranging within the solar system, and now a defined constant.
• That space is Euclidean over a baseline of two astronomical units. Any deviation from flat geometry on that scale would show up in solar-system dynamics long before it showed up in parallax.
• That the star's own motion can be separated from the parallax wobble. It can: proper motion is a steady drift, parallax is an annual ellipse locked to the Earth's orbital phase. Gaia fits both at once, along with position, from thousands of separate transits per star.
• That the instrument is calibrated. This is the real risk, and it is the one that produced the −17 microarcsecond offset. It is also the one that gets caught by quasars.

Geometry that skips the ladder

The strongest reply to "the distances are assumed" is not a better rung.  It is a method with no rungs.  Four exist, and between them they reach from the Magellanic Clouds to hundreds of megaparsecs.  Three use light and are taken here;  the fourth uses gravitational waves and gets its own section below.  They are treated at length because they are what makes the rest of the scale checkable.

Detached eclipsing binaries

Take two stars orbiting each other, far enough apart that neither distorts the other, and oriented so that each passes in front of the other as seen from Earth.  Two ordinary measurements then give the stars' physical sizes in kilometres.

• The light curve gives the radii of the two stars as fractions of their orbital separation, plus the tilt of the orbit. What is measured is how far the brightness dips during each eclipse, and for how long.
• The spectra give both stars' velocities along the line of sight through the Doppler shift. Those velocities and the orbital period together give the separation between the stars in kilometres.

Multiply the fraction by the separation and each star's radius is known in kilometres.  This is Newtonian mechanics and nothing more.

Now the distance.  If the star's angular radius on the sky were known, distance would follow at once, as physical size divided by angular size.  Angular radius cannot be measured directly for a star 160,000 light years away.  So it is inferred from the star's surface brightness, which is a function of its colour.  A hot blue star radiates more per square metre than a cool red one, in a way that can be calibrated.

That calibration is where the method stops being pure geometry, and Grzegorz Pietrzyński and colleagues attacked it directly.  They selected 41 nearby red clump giants and had the Very Large Telescope Interferometer measure their angular diameters directly to one per cent.  Red clump giants are helium-burning stars, deliberately the same kind of star as the eclipsing binaries they wanted to measure.  Combined with photometry, that yields a surface-brightness relation:

"Our new relationship allows a measurement of stellar angular diameters with a precision of 0.8% (that is, by a factor of 2.5 more precise than existing relations in the literature).  It is perfectly suited to determine very accurate distances to eclipsing binaries composed of helium-burning giant stars."¹

Applied to 20 detached eclipsing binaries in the Large Magellanic Cloud, selected out of a catalogue of 35 million stars monitored for twenty years by the OGLE survey, the result is:

"The final distane is 49.59 +/- 0.09 (statistical) +/- 0.54 (systematic) kiloparsecs."¹

That is 161,700 light years, to one per cent.

The systematic error budget is worth printing because it shows where the risk actually lives.  Pietrzyński's team list three contributions:  the surface-brightness relation itself (0.8%), photometric zero points (0.5%), and the absolute reddening scale (0.6%), combining to 1.1%.¹  They also checked the two effects a skeptic would raise first.  Gravity dependence:  the relation differs by about one per cent between giants and dwarfs, and both their calibrators and their targets are giants.  Metallicity dependence:  their calibrating stars span a full dex in metallicity, and the residuals show no trend.¹

The same team did the Small Magellanic Cloud with 15 systems and reported 62.44 ± 0.47 (stat) ± 0.81 (syst) kiloparsecs, "an accuracy of better than 2%."¹⁶¹⁶  That paper contains a detail worth noting for honesty's sake:  the SMC is not a point.  "The distance difference between the nearest and most-distant system amounts to 10 kpc with the line of sight depth reaching 7 kpc."¹⁶  A galaxy has depth, and quoting one number for it is a simplification the authors state openly.

Water masers in NGC 4258

This is the cleanest extragalactic distance measurement that exists, and it is worth understanding in detail because it involves no stars at all.

NGC 4258 has a supermassive black hole with a thin, nearly edge-on disc of gas orbiting it.  Parts of that gas amplify 22 GHz microwave radiation from water molecules.  That is a natural maser, the microwave analogue of a laser.  The maser spots are tiny and extremely bright, which means very long baseline interferometry can pin their positions to microarcseconds.

Three things are measured for each spot:

• Position on the sky, in microarcseconds, from VLBI.
• Velocity along the line of sight, in kilometres per second, from the Doppler shift of the maser line.
• Proper motion and acceleration, meaning how the spot drifts across the sky and how its Doppler velocity changes, from monitoring the same spots for years.

A physical speed measured in kilometres per second, next to an angular speed measured in microarcseconds per year, gives a distance immediately.  The 1999 measurement by James Herrnstein and colleagues states both:  orbital velocity "about 1100 km/s," average proper motion "31.5 microarcseconds per year."¹⁷¹⁷  Divide one by the other and the distance comes out near seven and a half megaparsecs, with no calibration, no candle, and no assumption about what the gas is made of.  Their published figure, from the full model including the accelerations, is 7.2 ± 0.3 megaparsecs, at the time "the most precise extragalactic distance measured to date."¹⁷

The measurement has been redone twice since, with more epochs and better modelling of the disc's warp.  Elizabeth Humphreys and colleagues in 2013 got 7.60 ± 0.17 ± 0.15 megaparsecs, a three per cent uncertainty.¹⁸¹⁸  Mark Reid, Dominic Pesce and Adam Riess in 2019 got 7.576 ± 0.082 (stat.) ± 0.076 (sys.) megaparsecs, about 1.5 per cent.²  The three values, spread over twenty years and three independent modelling efforts, agree within their errors.

What does the maser method assume?  Two things, and they are checkable.  First, that the orbits are Keplerian, meaning the gas is in free fall around a compact central mass and not being pushed by something else.  That is not a guess:  the maser velocities as a function of radius trace out the Keplerian curve, which is what Herrnstein's team mean by calling it a "thin, nearly edge-on, subparsec-scale Keplerian disk."¹⁷  Second, that the disc's warp is modelled correctly.  This is the real systematic, and it is why the 2013 and 2019 papers spend most of their length on disc geometry:  Reid's team describe their improvement as reducing "both statistical and systematic uncertainties compared to previous analyses."²

The same technique now works on other galaxies.  The Megamaser Cosmology Project has applied it to six, far enough away that their recession is dominated by cosmic expansion, giving a Hubble constant "independent of distance ladders and the cosmic microwave background."¹⁹¹⁹  That result belongs to the Hubble tension article, which treats it in full.

The SN 1987A light echo

The third geometric method is the most vivid, because the ruler is a flash of light travelling around a ring.

When SN 1987A exploded in the Large Magellanic Cloud in February 1987, the flash lit up a ring of gas the dying star had thrown off long before.  Hubble later imaged that ring.  Peter Jakobsen's team measured the image as an ellipse with major and minor axes of 1".66 ± 0".03 and 1".21 ± 0".03.³

An ellipse could be a genuinely elliptical ring, or a circular ring seen at a slant.  Panagia and colleagues showed it is the second, using two independent arguments that agree.  The agreement is the point.

• From the shape. If the ring is circular, the ratio of minor to major axis gives the tilt. Jakobsen's team got 43° ± 3°; Panagia's own final analysis gives 42.8° ± 2.6°.³³
• From the timing. Light reaching the near edge of the ring gets there first, and light reaching the far edge gets there last, and the extra path to the far edge and back toward Earth is longer still. So the ring's ultraviolet emission lines should switch on after a delay t₀ = (R/c)(1 − sin i) and peak at t_max = (R/c)(1 + sin i). Two measured times, two unknowns: the ring's physical radius R and its inclination i. The observed switch-on was under 90 days and the peak around 400 days, giving an inclination "greater than ~40°, which is virtually coincident with the value derived from the ring elliptical shape."³

Panagia's own summary of why that matters:  "since the two determinations are independent, their close agreement is clear evidence that the ring is quite circular indeed."³

The timing analysis also delivers the ring's absolute diameter, (1.27 ± 0.07) × 10¹⁸ centimetres.  That is a physical size in centimetres, obtained from a stopwatch and the speed of light.  Divide by the angular diameter Hubble measured and the distance falls out:

"d(1987A) = 51.2 ± 3.1 kpc.  Estimating the relative position of SN 1987A within the Large Magellanic Cloud on the basis of radial velocity data, the distance to the center of the LMC turns out to be 50.1 ± 3.1 kpc and its distance modulus 18.50 ± 0.13."³

Now compare that to the eclipsing binaries.  Panagia's 1991 distance modulus for the LMC is 18.50 ± 0.13.  Pietrzyński's 2019 distance modulus is 18.477 ± 0.004 (statistical) ± 0.026 (systematic).¹  The two differ by 0.023 magnitudes, which is 1.1 per cent in distance.  They were obtained 28 years apart, by different teams, using different telescopes, different physics, and different failure modes.  One timed a light echo;  the other did Newtonian orbital mechanics plus interferometry.  They land on the same number.

SN 1987A does much more than pin its own distance.  It also runs nuclear physics at laboratory rates 167,000 light years away, and shows a supernova evolving in sequence over four decades.  Those belong to a planned article of its own;  only the distance is covered here.

The three geometric distances side by side

Three assumptions, three different kinds, none shared.  For the distances to be badly wrong, all three would have to fail independently, by the same factor, in the same direction.

Standard candles

A standard candle is any object whose true brightness can be worked out from something other than its distance.  Once true brightness is known, distance follows from the inverse-square law:  an object four times further away looks sixteen times fainter.

Every candle has the same weak point.  The "something other than distance" is always a piece of astrophysics, and astrophysics can be wrong.  This section states each candle's physical basis, where its zero point comes from, and what has to hold for it to work.

Cepheid variables

Cepheids are massive young stars that pulse, brightening and dimming on a cycle of days to months.  The longer the cycle, the brighter the star.

Henrietta Leavitt found this in 1912, and the way she found it deserves attention.  She was cataloguing variable stars in the Small Magellanic Cloud.  They are all at roughly the same distance, so their apparent brightnesses could be compared directly.  Her Circular says:

"A remarkable relation between the brightness of these variables and the length of their periods will be noticed."²⁰²⁰

And, on the next page, the reasoning:

"Since the variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness."²⁰

Leavitt also named the method's own limitation, in the same three-page circular.  A relation between period and apparent brightness in one cloud gives relative distances only.  To get absolute ones, somebody has to measure a Cepheid the hard way:  "It is to be hoped, also, that the parallaxes of some variables of this type may be measured."²⁰  That is the distance ladder, described by its inventor, a century before Gaia did what she asked.

Where the zero point comes from now.  Three anchors, all geometric.  Gaia parallaxes of 75 Milky Way Cepheids, giving "a geometric calibration of Cepheid luminosities" with "1.0% precision, better than any alternative geometric anchor."⁶  The eclipsing-binary distance to the LMC.  And the maser distance to NGC 4258.  A fourth was added in 2024:  the Small Magellanic Cloud, using 88 Cepheids in its core.²¹²¹

What Cepheids assume, and what goes wrong.

• That the period-luminosity relation is universal. It is not quite. A Cepheid's brightness at fixed period depends slightly on its chemical composition. Breuval and colleagues measure that dependence as γ = −0.234 ± 0.052 magnitudes per dex of iron abundance.²¹ A metallicity error that grew with distance would fake a distance error, which is precisely why adding the metal-poor SMC mattered. It doubled the calibrated metallicity range.
• That the star can be measured cleanly. Cepheids are young, so they sit in crowded star-forming regions. Blended neighbours inflate the measured brightness and shrink the inferred distance. This was the most-feared systematic in the field until JWST tested it directly: more than 1,000 Cepheids re-observed at 2.7 times HST's angular resolution gave "no significant difference in the mean distance measurements determined from HST and JWST, with a formal difference of −0.01+/−0.03 mag."²²²²
• That reddening by dust is correctly removed. Handled by observing in several filters and using the fact that dust reddens as well as dims.

Cepheids reach far enough to do their job.  The SH0ES programme observed Cepheids "in hosts at D ≈ 40–50 Mpc, double the range of first-generation observations and a factor of 8 increase in targets."  That was enough to reach 37 galaxies which between them hosted 42 Type Ia supernovae.²³²³

The tip of the red giant branch

This is the best-understood candle in the set, because the physics behind it is a single sharp event.

A low-mass star ascending the red giant branch has a hydrogen-burning shell sitting on an inert helium core that is degenerate, held up by quantum pressure rather than by heat.  Ash from the shell rains down and the core grows.  Freedman and Madore state what happens next:

"The mass of the helium core increases with freshly formed helium from the shell burning, until the core mass reaches a threshold value of about 0.5 M⊙ independent of the initial mass of the star.  At this stage the core will have reached a temperature of about 10⁸ degrees, at which point the triple-alpha process (helium burning) can commence.  Because the core is degenerate and cannot expand, a thermonuclear runaway ensues."²⁴²⁴

The words doing the work are independent of the initial mass of the star.  Every low-mass red giant ignites helium at nearly the same core mass, hence at nearly the same luminosity.  Plot the stars in a galaxy's halo on a colour-magnitude diagram and the red giant branch stops at a sharp edge.  That edge is a standard candle, and it is one you can see as a discontinuity in a histogram rather than having to identify star by star.

Its zero point is set geometrically.  Reid's maser distance to NGC 4258 gives M_F814W = −4.01 ± 0.04 magnitudes.²  JWST extended it to a new filter:  Gagandeep Anand and colleagues measured M_TRGB^F090W = −4.362 ± 0.033 (stat) ± 0.045 (sys) in the outskirts of the same galaxy.²⁵²⁵

What it assumes.  That the tip luminosity does not drift with the age or metal content of the halo population being measured.  In the I band that sensitivity is shallow, which is why the I band is used.  Freedman's team list "only a shallow (calibrated) sensitivity to metallicity in the I-band" among the method's advantages over Cepheids, along with low halo reddening and minimal crowding.²⁶²⁶  Halo stars are also old and sparse, which removes the crowding problem that dogs Cepheids.

The honest counterweight:  the tip is a feature in a luminosity function, and different groups measure "the tip" with different edge-detection algorithms.  Riess and colleagues note "a net difference of 1.3 km s−1 Mpc−1 (or 0.04 ± 0.02 mag) between measurements by two groups of the location of the tip in NGC 4258."²³  Two teams, one galaxy, one set of images, and a four-per-cent difference in where the edge is.

JAGB stars, Miras, and surface brightness fluctuations

Three more candles, each independent of the two above.

JAGB stars are carbon-rich asymptotic giant branch stars, picked out by colour in near-infrared photometry.  Barry Madore and Wendy Freedman found that they sit at a nearly fixed absolute magnitude:  ⟨M_J⟩ = −6.20 ± 0.01 (stat) ± 0.04 (sys), calibrated separately in the LMC and SMC using those galaxies' eclipsing-binary distances.²⁷²⁷  The scatter is ±0.27 magnitudes for a single observation, falling to ±0.15 when averaged over more than a year.²⁷  They need no repeat visits to find a period, which makes them cheap.  Their weakness is that carbon-star luminosity does depend on age and metallicity, and the size of that dependence is still being measured.

Miras are old, pulsating, low-mass stars with periods of hundreds of days.  Like Cepheids they follow a period-luminosity relation.  Caroline Huang and colleagues used 115 oxygen-rich Miras in NGC 1559 to calibrate a Type Ia supernova for the first time, anchored on Miras in NGC 4258 and its maser distance, and got H₀ = 73.3 ± 4.0.²⁸²⁸  Miras matter because they are old stars, so they can be found in the early-type galaxies where Cepheids do not exist.

Surface brightness fluctuations use a fact about pixels.  A nearby galaxy's image is grainy, because each pixel catches a few hundred bright giants and the count varies from pixel to pixel.  A distant galaxy's image is smooth, because each pixel catches thousands and the fluctuations average out.  The graininess therefore scales as one over distance.  John Blakeslee and colleagues applied it to 63 mostly early-type galaxies out to 100 megaparsecs, with a median statistical uncertainty of 4 per cent per galaxy.²⁹²⁹  It assumes that the stellar population producing the graininess is similar from galaxy to galaxy, which is why it is used on early-type galaxies with old, uniform populations.

Type Ia supernovae

These are the top rung, and the only candle bright enough to be seen across billions of light years.

A Type Ia supernova is a white dwarf that detonates.  Raw, they are not standard, and the paper that established this is also the paper that fixed it.  Mark Phillips measured absolute magnitudes for nine well-observed Type Ia supernovae in 1993 and found "a significant intrinsic dispersion in the absolute magnitudes at maximum light of Type Ia supernovae, amounting to ±0.8 mag in B, ±0.6 mag in V, and ±0.5 mag in I."³⁰³⁰  In the same abstract he gave the cure:  "the absolute magnitudes appear to be tightly correlated with the initial rate of decline of the B light curve."³⁰  Brighter supernovae fade more slowly.  Measure the shape of the light curve and the colour, correct for both, and the scatter collapses.  In the current SH0ES sample the standardised supernovae in the smooth Hubble flow scatter by σ = 0.135 magnitudes, about six per cent in distance.²³

What they assume.  One thing, and it is the one that would matter most if it failed:  that a standardised Type Ia at redshift 1 has the same absolute magnitude as a standardised Type Ia next door.  Progenitor populations at high redshift are more metal-poor and younger.  If that changed the standardised brightness, every cosmological conclusion drawn from supernovae would shift.  The field tests it by looking for residual correlations with host-galaxy mass, star formation rate and metallicity, and by cross-checking supernova distances against baryon acoustic oscillations, which use completely different physics.

Phillips himself flagged the danger in 1993, and the warning has aged well:  "Considerable care must be exercised in employing Type Ia supernovae as cosmological standard candles, particularly at large redshifts where Malmquist bias could be an important effect."³⁰

There is also a nearer-term problem that is not about physics at all.  Different supernova compilations calibrate their photometry differently, and the choice moves the answer.  Taylor Hoyt and colleagues measured red giant tip distances to ten supernova hosts and found their Hubble constant "yielding 68.4 < H0 < 69.6 km/s/Mpc depending on which of four sets of SN magnitudes are used."³¹³¹  A one-and-a-half per cent spread from bookkeeping.

This list is not the whole set.  RR Lyrae variables, the planetary nebula luminosity function, the globular cluster luminosity function and the Tully-Fisher relation are all in use, and all follow the same pattern:  a piece of astrophysics fixes the true brightness, and a geometric anchor fixes the zero point.  The six above are the ones that carry the modern Hubble constant measurements, so they are the ones worth stating in detail.

What each candle costs you

Standard sirens: a distance with no astronomy in it

In August 2017 two neutron stars spiralled together about 40 megaparsecs away, and the merger was recorded three ways at once:  as a gravitational-wave chirp by LIGO and Virgo, as a gamma-ray burst two seconds later, and as an optical transient ten arcseconds from the galaxy NGC 4993.

That combination produced something astronomy had never had:  a distance that owes nothing to any telescope's calibration.  It is worth understanding why.

The physics.  As two compact objects spiral in, they radiate gravitational waves whose frequency rises.  That rise is the chirp.  General relativity fixes two things exactly.  The rate at which the frequency rises depends only on the masses.  The amplitude of the wave depends on the masses, the orientation, and the distance.  So read the masses off the frequency sweep, then read the distance off the amplitude.  Nothing else enters.  No standard candle, no calibration, no telescope zero point, no assumption about stellar populations.

The discovery paper states the consequence plainly:

"This approach does not require any form of cosmic 'distance ladder;'  the gravitational wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements.  We determine the Hubble constant to be 70.0(+12.0, −8.0) km s⁻¹ Mpc⁻¹."⁷

Now the honest part.  That error bar is huge, roughly +17% and −11%.  It is huge for one specific reason, and the reason is instructive.  Distance and orbital inclination are degenerate in the waveform.  A merger seen face-on radiates more strongly toward us than one seen edge-on, so a distant face-on merger and a nearer inclined merger produce almost the same signal.  With one event and no independent handle on the tilt, that degeneracy dominates everything.

And the number has moved.  The fix is to measure the inclination another way, using the jet the merger launched.  Radio interferometry watched that jet move across the sky and constrained the viewing angle geometrically.  Kenta Hotokezaka and colleagues did this first, in 2019, and reported "a significantly improved measurement H₀ = 68.9(+4.7, −4.6) km/s/Mpc by using these new radio observations, combined with the previous GW and EM data."³²³²  A 2026 reanalysis by Kelly Gourdji and colleagues fitted the radio data and the gravitational-wave distance jointly and obtained a viewing angle of 16.8° to 19.2°, a luminosity distance of 44.0 ± 1.6 megaparsecs, and H₀ = 65.5 ± 4.4.⁸  Their own framing:  "the peak of our H₀ posterior is within 0.5σ of the early-Universe Planck H₀ value, but 1.7σ from the late-Universe SH0ES measurement."⁸

So the siren value has wandered from 70.0 to 68.9 to 65.5 as the jet geometry was pinned down.  Anyone quoting the siren number as though it settled anything is over-claiming, in either direction.  What it settles is narrower and more important:  a luminosity distance of 44 megaparsecs was obtained from a waveform and a radio image, with no rung of the optical distance ladder involved at any point.  Forty-four megaparsecs is 143 million light years.

There is a cross-check available, and it is a good one.  Michele Cantiello and colleagues measured the distance to NGC 4993 itself using surface brightness fluctuations, and got "a linear distance d = 40.7 ± 1.4 ± 1.9 Mpc."³³³³  That is a completely different physical principle, applied to the galaxy's starlight rather than to the merger.  Against Gourdji's 44.0 ± 1.6 Mpc for the merger, that is agreement at about 1.2σ.  Gravitational waves and old red stars, measured independently, put the same object at the same place.

One more ladder-free route exists and is only named here.  When a quasar sits behind a massive galaxy, lensing produces several images, and a flare appears in each one at a different time.  The delays scale inversely with the Hubble constant and give an absolute distance with no rungs.  That method has its own long history of finding and publishing its own systematic, and the Hubble tension article tells it properly.

Sirens without an optical counterpart, called dark sirens, can be used statistically by matching the gravitational-wave sky localisation against a galaxy catalogue.  The Dark Energy Survey team's 2026 analysis of the fourth transient catalogue gives 71.7 (+22.7, −18.3), or 73.1 (+11.9, −8.5) when GW170817 is included.³⁴³⁴  Those error bars speak for themselves.  This is a method in its infancy, and the useful statement about it is that it exists and works, not that it has decided anything.

How the rungs check each other

The argument of this article does not rest on any single method.  It rests on the fact that methods with unrelated failure modes land on the same numbers.  Here is the record.

Two of those rows deserve emphasis.

The 1991-versus-2019 LMC comparison is as clean a test as this subject offers.  A light echo timed with a satellite ultraviolet spectrograph, against Newtonian orbital mechanics plus optical interferometry.  Different decade, different instruments, different physics, different people, different ways of being wrong.  Result:  one per cent apart.

The JWST crowding test was a genuine risk taken by the field.  Crowding was the most plausible way for the Cepheid ladder to be systematically wrong, and it is the objection a skeptic would raise unprompted.  When a telescope with 2.7 times the resolving power looked at the same stars, the distances could have moved.  They did not:  "no significant difference in the mean distance measurements determined from HST and JWST, with a formal difference of −0.01+/−0.03 mag."²²  The scatter in the period-luminosity relations fell by a factor of 2.5 and the distances stayed put.

Where they disagree

They do disagree, and pretending otherwise would be dishonest.  The distance ladder calibrated on Cepheids gives a Hubble constant near 73;  the microwave background and baryon acoustic oscillations, interpreted through the standard cosmological model, give near 67.4.  Two teams running distance ladders, SH0ES and the Chicago-Carnegie Hubble Program, get answers about 2.5 km/s/Mpc apart from largely the same data.

That is the Hubble tension.  It is about nine per cent, it is unresolved, and it has its own article which treats the numbers, the two teams' dispute, the ladder-free routes, and every proposed fix.  It is not re-argued here.

Two things about it belong in this article, because they are facts about distance measurement rather than about cosmology.

First, the disagreement is in the calibration, not the shape.  Licia Verde, Nils Schöneberg and Héctor Gil-Marín put it in one line in their review:  "It appears to be a matter of anchors:  the shape of the Universe expansion history agrees with the model, it is the normalizations that disagree."³⁶³⁶

Second, the two ladder teams' distances agree even when their Hubble constants do not.  SH0ES compared its HST Cepheid distances against eight independent combinations of method, sample and telescope and found mean differences of about 0.03 magnitudes, against a tension of 0.18 magnitudes.³⁵  The stars are not where the disagreement lives.  It lives in which supernovae get into the sample and how their magnitudes are calibrated.  That is why Hoyt's team could move their own answer by more than a kilometre per second per megaparsec just by swapping supernova magnitude sets.³¹

A nine-per-cent argument about calibration is what a healthy measurement field looks like at the one-per-cent level.  It is not an argument about whether galaxies are millions of light years away.

What this means for a young universe

The distances are measured.  Any young-earth account has to start there, and the two best-known young-earth astronomers say so in print.

Danny Faulkner holds a PhD in astronomy and has spent his career inside the creationist movement.  In a 2020 Answers in Genesis article on the size of the universe he ran through the methods and concluded:

"In each case, they produce distances that are millions and even billions of light-years.  While all of these methods suffer from error, those errors would not reduce the distances down to just thousands of light-years."⁹

And, naming the temptation directly:

"Many recent creationists worry about the light travel time problem and entertain possibilities of the universe being far smaller than generally thought as a way out of this dilemma.  But thinking this stumbles over something that ought to be obvious."⁹

Seven years earlier he had put the technical version of the same point:  for the shrink-the-distances solution to work, "even the well determined trigonometric parallax method must be abandoned, but this is not physically supported."¹⁰  Jason Lisle, whose anisotropic synchrony convention is the most-discussed young-earth answer to distant starlight, stipulates the same thing at the front of his 2010 paper:  "I will further stipulate that the consensus understanding of galactic distances, redshifts, and universal expansion is basically correct, having been established by good scientific procedures which are verifiable in the present."³⁷³⁷

The arithmetic behind their concession.  Take 6,000 light years as the outer limit a young universe could allow if light has always travelled at today's speed.  Then:

This is why the shrink-the-distances answer died inside the creationist movement rather than outside it.  It is not that one method would have to be wrong.  It is that four or five methods, sharing no assumptions, would all have to be wrong by the same factor in the same direction.  Worse, the factor would have to differ from object to object, growing with distance, in exactly the way that reproduces a Hubble law.

A second point matters more, and it is the one Faulkner made in 2013.  Even if every extragalactic distance collapsed, parallax does not.  Proxima Centauri's parallax is 768.0665 ± 0.0499 milliarcseconds, which is 4.25 light years.¹³  There is no room in that measurement for an error of any interesting size.  A young-earth model therefore still has to explain how Adam saw stars, and the nearest one is more than four light years away.  That problem is not solved by shrinking anything, and it is treated in Young-Universe Cosmologies.

Does the ladder assume an old universe?

No, and this is worth stating carefully because it is the natural suspicion.

Nothing in parallax requires an age.  Nothing in the eclipsing-binary method requires an age:  it uses Newtonian orbital mechanics, Doppler shifts, and interferometric angular diameters.  Nothing in the maser method requires an age.  Nothing in the SN 1987A light echo requires an age;  it requires a stopwatch and the speed of light.  Nothing in the gravitational-wave distance requires an age.

Stellar-evolution theory does enter the candles.  The red giant tip is understood in terms of a degenerate helium core growing over hundreds of millions of years.  The Cepheid instability strip is understood in terms of stellar structure.  If that theory were wrong, those candles could be wrong.

But here is the point:  the candles are not trusted on theory.  They are calibrated on geometry.  The Cepheid zero point comes from Gaia parallaxes, LMC eclipsing binaries, the SMC, and the NGC 4258 masers.  The red giant tip zero point comes from the NGC 4258 masers.  The JAGB zero point comes from the Magellanic Clouds' eclipsing binaries.  If stellar-evolution theory were badly wrong, the candles anchored to geometry would disagree with each other and with the geometry as you moved between environments.  They do not.  The disagreements are at the two-to-four per cent level.

There is one real caveat and it should be stated.  Beyond a few hundred megaparsecs, "distance" becomes partly model-dependent.  Converting a redshift into a distance at z = 1 requires the expansion history, which requires a cosmological model.  Different models give different answers at the tens-of-per-cent level.  That is a genuine dependency, and anyone quoting "13 billion light years" is quoting a model-dependent number.

It does not help a young universe.  The model dependence only becomes significant well beyond the point where the distances are already millions of times too large for a 6,000-year light travel time.  Out to about 100 megaparsecs, which is 326 million light years, distance is essentially just redshift divided by the Hubble constant, and the only thing being argued about is the nine per cent in the Hubble constant.

Objections and responses

"The whole thing is circular.  Parallax calibrates Cepheids, Cepheids calibrate supernovae, and supernovae are then used to claim the universe is big."

The chain is real, but it is not a circle.  It is a sequence, and each step is checkable against something outside it.  More to the point, several methods bypass the chain completely.  Eclipsing binaries, water masers, the SN 1987A ring, and gravitational waves all give distances without using Cepheids or supernovae at all.  The maser distance to NGC 4258 is 24.7 million light years and has no rung beneath it.  GW170817's host is 143 million light years away by a waveform.

"Gaia's parallaxes had a known bias.  How can they be trusted?"

Because the bias was found, measured, published, and confirmed three independent ways:  by quasars whose true parallax is zero, by asteroseismic red giants, and by Cepheid period-luminosity fitting.⁴⁵⁶  Its size is about 17 microarcseconds.  For a star 100 parsecs away, whose parallax is 10,000 microarcseconds, that is a 0.17 per cent error.  A field that publishes its own systematic errors at the part-per-thousand level is not a field whose distances are off by factors of thousands.

Zinn's paper also found that Gaia's quoted uncertainties are too small by 22 ± 6%.⁵  That is a real defect.  It widens the error bars.  It does not move the distances.

"The Hubble tension shows the distance measurements are unreliable."

It shows they disagree at the nine per cent level.  That is what a hard measurement problem looks like when everybody is trying to reach one per cent.  Both camps put the universe's expansion age between about 12.8 and 13.8 billion years.  Neither is anywhere near a young universe, and the tension gives no comfort to one:  the high Hubble constant implies the younger universe, and it is the high camp that comes from the distance ladder.  Reducing the age to 10,000 years would require a Hubble constant of roughly 10⁸ km/s/Mpc, taking the Hubble time 1/H₀ on its own.

"These methods all assume the laws of physics have been constant."

Parallax does not.  It assumes only that the Earth's orbit is the size we measure it to be now, and that light travels in straight lines now.  The eclipsing-binary method assumes Newtonian gravity and blackbody radiation hold in the LMC today.  Those are testable in the present, which is the standard Faulkner himself invokes when he calls the parallax method "well determined."¹⁰

Whether physics has been constant over time is a separate question, and it is the question the young-earth cosmologies are actually about.  It has no bearing on whether the LMC is 161,700 light years away right now.

"Redshift might not indicate distance at all."

That objection is about the Hubble law, not about the ladder, and it is answered in the redshift article and the expanding universe article.  Note that it does not touch anything in this article's core:  parallax, eclipsing binaries, masers, light echoes and gravitational waves all give distances without using redshift.

"If God created the light already in transit, the distances do not matter."

That is a coherent position and it is one of the eight published young-earth answers.  It concedes everything in this article.  The distances are real, the light did not have time to arrive, and the gap is bridged by a miracle.  Its problems are theological and evidential rather than astronomical, and most young-earth astronomers now reject it, Faulkner among them, because created light would carry records of events that never happened.  That argument belongs to the young-universe cosmologies article.

"Astronomers keep revising these numbers, so they clearly do not know."

Look at what the revisions have actually done.  NGC 4258:  7.2 ± 0.3 in 1999, 7.60 ± 0.17 ± 0.15 in 2013, 7.576 ± 0.082 ± 0.076 in 2019.  The LMC:  distance modulus 18.50 ± 0.13 in 1991 by light echo, 18.477 ± 0.004 ± 0.026 in 2019 by eclipsing binaries.  Every new measurement has overlapped the previous one's error bars, and the whole twenty-year drift in NGC 4258 is about five per cent.  A field whose numbers move by a few per cent over two decades, always within the stated uncertainties, is a field that knows what it is doing.

What would change this article's mind

Stating the falsification conditions is part of the honesty this project owes a skeptical reader.

• A geometric method disagreeing with another geometric method by more than its errors. If the SN 1987A light echo said 300 kiloparsecs and the eclipsing binaries said 50, the geometric foundation would be in trouble. They agree to one per cent.
• JWST finding that HST Cepheid distances were systematically compressed. It looked and found −0.01 ± 0.03 magnitudes.²²
• Gaia parallaxes disagreeing with cluster distances or asteroseismic distances at the per-cent level rather than the microarcsecond level. Zinn's check found a 15 ± 3 microarcsecond discrepancy in the correction model, not in the parallaxes themselves.⁵
• A standard siren distance disagreeing with the optical distance to the same host galaxy. Surface brightness fluctuations put NGC 4993 at 40.7 ± 1.4 ± 1.9 Mpc; the gravitational waveform plus radio jet geometry put the merger inside it at 44.0 ± 1.6 Mpc.³³⁸ That is a 1.2σ difference between a method that counts photons from old stars and a method that measures spacetime ripples.
• A demonstration that the surface brightness-colour relation, the Keplerian maser model, and the circular-ring assumption all fail in a correlated way. Nobody has proposed a mechanism that would do this, and the three share no physics.

None of these has happened.  If one did, this article would need rewriting.

Sources

Every quotation below was read from the source itself — a downloaded PDF, a publisher's own page, or an optically re-scanned journal facsimile — and not from any summarising tool.  Where a scan's optical character recognition mangles a symbol, the footnote says so.