Cosmic distance ladder

standard candlestandard candlesdistanceextragalactic distance scaledistance indicatorastronomical distance scalestandard sirendistance ladderother distances in astronomygalactic and extragalactic distances
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Parallax

solar parallaxmotion parallaxtrigonometric parallax
The most important fundamental distance measurements come from trigonometric parallax.
These distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.

RR Lyrae variable

RR Lyr variableRR LyraeRR Lyrae stars
This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars, including Cepheids and the RR Lyrae variables.
They are used as standard candles to measure (extra)galactic distances, as a part of the cosmic distance ladder.

Cepheid variable

Cepheidperiod-luminosity relationshipCepheids
This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars, including Cepheids and the RR Lyrae variables.
A strong direct relationship between a Cepheid variable's luminosity and pulsation period established Cepheids as important indicators of cosmic benchmarks for scaling galactic and extragalactic distances.

Astronomical unit

AUastronomical unitsAUs
Direct distance measurements are based upon the astronomical unit (AU), which is the distance between the Earth and the Sun.
The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance of an asteroid, whereas other units are used for other distances in astronomy.

Baryon acoustic oscillations

baryon acoustic oscillationBAOacoustic peaks
More recently the physical scale imprinted by baryon acoustic oscillations (BAO) in the early universe has been used.
In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology.

Tip of the red-giant branch

tip of the red giant branchTRGB
Tip of the red-giant branch (TRGB) distance indicator.
Tip of the red-giant branch (TRGB) is a primary distance indicator used in astronomy.

Planetary nebula luminosity function

PNLF
Planetary nebula luminosity function (PNLF)
Planetary nebula luminosity function (PNLF) is a secondary distance indicator used in astronomy.

Gaia (spacecraft)

GaiaGaia spacecraftGaia'' spacecraft
In 2018, Data Release 2 from the Gaia space mission provides similarly accurate distances to most stars brighter than 15th magnitude.
To determine the intrinsic luminosity of a star requires knowledge of its distance. One of the few ways to achieve this without physical assumptions is through the star's parallax. Ground-based observations would not measure such parallaxes with sufficient precision due to the effects of the atmosphere and instrumental biases. For instance, Cepheid variables are used as standard candles to measure distances to galaxies, but the accuracy in their own distance measurement is poor. Thus, quantities depending on them, such as the speed of expansion of the universe, remain inaccurate. Measuring their distances accurately has a great impact on the understanding of the other galaxies and thus the whole cosmos (see cosmic distance ladder).

Surface brightness fluctuation

Surface brightness fluctuation (SBF)
Surface brightness fluctuation (SBF) is a secondary distance indicator used to estimate distances to galaxies.

Astronomy

astronomicalastronomerastronomers
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects.
The measurement of stellar parallax of nearby stars provides a fundamental baseline in the cosmic distance ladder that is used to measure the scale of the Universe.

Parsec

Mpcpckpc
A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand parsecs) to Earth.
The parallax method is the fundamental calibration step for distance determination in astrophysics; however, the accuracy of ground-based telescope measurements of parallax angle is limited to about 0.01 arcseconds, and thus to stars no more than 100 pc distant.

Binary star

spectroscopic binaryeclipsing binarybinary
Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means, and don't suffer from the above geometric uncertainty. Eclipsing binaries — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), Andromeda Galaxy and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology to a distance of around 3 Mpc (3 million parsecs).
This makes it feasible to use them to directly measure the distances to external galaxies, a process that is more accurate than using standard candles.

Hyades (star cluster)

HyadesHyades clusterHyades star cluster
In particular the distance obtained for the Hyades has historically been an important step in the distance ladder.
The fact that three independent measurements agree makes the Hyades an important rung on the cosmic distance ladder method for estimated the distances of extragalactic objects.

Milky Way

galaxyMilky Way Galaxyour galaxy
As a result, the population II stars were actually much brighter than believed, and when corrected, this had the effect of doubling the distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way.
This value is estimated using geometric-based methods or by measuring selected astronomical objects that serve as standard candles, with different techniques yielding various values within this approximate range.

Type Ia supernova

Type Iatype Ia supernovaetype 1a supernova
For example, all observations seem to indicate that Type Ia supernovae that are of known distance have the same brightness (corrected by the shape of the light curve).
The stability of this value allows these explosions to be used as standard candles to measure the distance to their host galaxies because the visual magnitude of the supernovae depends primarily on the distance.

Edwin Hubble

HubbleEdwin P. HubbleHubble, Edwin Powell
Edwin Hubble observed that fainter galaxies are more redshifted.
He used the strong direct relationship between a classical Cepheid variable's luminosity and pulsation period (discovered in 1908 by Henrietta Swan Leavitt ) for scaling galactic and extragalactic distances.

Astrometry

astrometricastrometricalastrometrist
The precise measurement of stellar positions is part of the discipline of astrometry.
Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way.

Hubble's law

Hubble constantcosmological redshiftHubble parameter
Redshifts and Hubble's law
(See cosmic distance ladder for details.)

Supernova

supernovaesupernovastype II supernova
There are several different methods for which supernovae can be used to measure extragalactic distances.
During the 1960s, astronomers found that the maximum intensities of supernovae could be used as standard candles, hence indicators of astronomical distances.

Large Magellanic Cloud

LargeLMCGreater Magellanic Cloud
Eclipsing binaries — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), Andromeda Galaxy and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology to a distance of around 3 Mpc (3 million parsecs).
The distance to the LMC has been calculated using a variety of standard candles, with Cepheid variables being one of the most popular.

Stellar parallax

parallax shiftparallaxparallax method
This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars, including Cepheids and the RR Lyrae variables.
Stellar parallax remains the standard for calibrating other measurement methods (see Cosmic distance ladder).

Standard ruler

Another class of physical distance indicator is the standard ruler.
Distances can also be measured using standard candles; many different types of standard candles and rulers are needed to construct the cosmic distance ladder.

Distance

proximitydistancesdepth
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects.
Cosmic distance ladder

Small Magellanic Cloud

SMCSmall292
Eclipsing binaries — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), Andromeda Galaxy and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology to a distance of around 3 Mpc (3 million parsecs).
Hence, once the distance to the SMC was known with greater accuracy, Cepheid variables could be used as a standard candle for measuring the distances to other galaxies.

Tully–Fisher relation

Tully–FisherTully-Fisher RelationTF relation
The Tully–Fisher relation
Thus the TFR constitutes a rung of the cosmic distance ladder, where it is calibrated using more direct distance measurement techniques and used in turn to calibrate methods extending to larger distance.