The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement to an astronomical object is only possible for those objects that are "close enough" (within about a thousand parsecs) to earth. The techniques for determining distances to more distant objects are all bases on various measured correlations between methods that work at close distances with methods that work at larger distances. The ladder analogy arises because no one technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

## Direct methods of distance determination

At the base of the ladder are fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. These direct methods are:
Radar can (for practical reasons) only be used within the Solar System.

The precise measurement of stellar positions is part of the discipline of astrometry.

### Parallax based methods

The most important fundamental distance measurements come from parallax. The Earth's motion around the sun causes small shifts in stellar positions. These shifts are angles in a right triangle, with 1 AU making the short leg of the triangle and the distance to the star being the long leg. One parsec is the distance of a star whose parallax is one arc second. Astronomers usually express distances in units of parsecs; light-years are used in popular media, but almost invariably values in light-years have been converted from numbers tabulated in parsecs in the original source.

Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than the precision of the measurement. In the 1990s, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond, providing useful distances for stars out to a few hundred parsecs.

Another fundamental distance method is statistical and secular parallax. This technique combines measurements of the motions and brightnesses of members of a selected, homogeneous group of stars in a statistical way to deduce an average distance to the group. It remains an important technique for the Cepheids and the RR Lyrae variables.

Moving cluster parallax is a technique where the motions of individual stars in a nearby star cluster (only open clusters are near enough for this technique to be useful) can be used to find the distance to the cluster. In particular the distance obtained for the Hyades has been an important step in the distance ladder.

Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a supernova remnant or planetary nebula, can be observed over time, then an expansion parallax distance to that cloud can be estimated. Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means. The common characteristic to these is that a measurement of angular motion is combined with a measurement of the absolute velocity (usually obtained via the Doppler effect). The distance estimate comes from computing how far away the object must be to make its observed absolute velocity appear with the observed angular motion.

Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far away, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio interferometers which can measure very small angular motions. These combine to mean that some supernovae in other galaxies have fundamental distance estimates[1]. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.

#### Astronomical unit

The use of the parallax method usually requires precise determination of the distance between the Earth and the Sun (the radius of the Earth's orbit), called the Astronomical Unit (AU).

Other astronomical distance measures build outward from this.

Historically, observations of transits of Venus were crucial in determining the AU; in the first half of the 20th Century, observations of asteroids were also important. Presently the AU is determined with high precision using radar measurements of Venus and other nearby planets and asteroids,[2] and by tracking interplanetary spacecraft in their orbits around the Sun through the Solar System. Kepler's Laws provide precise ratios of the sizes of the orbits of objects revolving around the Sun, but not a real measure of the orbits themselves. Radar provides a value in kilometers for the difference in two orbits' sizes, and from that and the ratio of the two orbit sizes, the size of Earth's orbit comes directly.

## Distance determination based on physical assumptions

With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance.

Almost all of these physical distance indicators are standard candles. These rely upon recognizing an object as belonging to some class, which has some known absolute magnitude, measuring its apparent magnitude, and using the inverse square law to infer the distance needed to make the "candle" appear at its observed brightness. Some means of accounting for interstellar extinction, which also makes objects appear fainter, is also needed. The difference between absolute and apparent magnitudes is called the distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.

Physical distance indicators, used on progressively larger distance scales, include:
Two problems exist for any class of standard candle. The principal one is calibration, determining exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members with well-known distances that their true absolute magnitude can be determined with enough accuracy. The second lies in recognizing members of the class, and not mistakenly using the standard candle calibration upon an object which does not belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious.

(Another class of physical distance indicator is the standard ruler, but few of these are used at this time.)

A succession of distance indicators, which is the distance ladder, is needed for determining distances to other galaxies. The reason is that objects bright enough to be recognized and measured at such distances are so rare that few or none are present nearby, so there are too few examples close enough with reliable trigonometric parallax to calibrate the indicator. For example, Cepheid variables, one of the best indicators for nearby spiral galaxies, cannot be satisfactorily calibrated by parallax alone. The situation is further complicated by the fact that different stellar populations generally do not have all types of stars in them. Cepheids in particular are massive stars, with short lifetimes, so they will only be found in places where stars have very recently been formed. Consequently, because elliptical galaxies usually have long ceased to have large-scale star formation, they will not have Cepheids. Instead, distance indicators whose origins are in an older stellar population (like novae and RR Lyrae variables) must be used. However, RR Lyrae variables are less luminous than Cepheids (so they cannot be seen as far away as Cepheids can), and novae are unpredictable and an intensive monitoring program — and luck during that program — is needed to gather enough novae in the target galaxy for a good distance estimate.

Because the more distant steps of the cosmic distance ladder depend upon the nearer ones, the more distant steps include the effects of errors in the nearer steps, both systematic and statistical ones. The result of these propagating errors means that distances in astronomy are rarely known to the same level of precision as measurements in the other sciences, and that the precision necessarily is poorer for more distant types of object.

Another concern, especially for the very brightest standard candles, is their "standardness": how homogeneous the objects are in their true absolute magnitude. For some of these different standard candles, the homogeneity is based on theories about the formation and evolution of stars and galaxies, and is thus also subject to uncertainties in those aspects. For the most luminous of distance indicators, the Type Ia supernovae, this homogeneity is known to be poor; however, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there is no real alternative.

The observational result of Hubble's Law, the proportional relationship between distance and the speed with which a galaxy is moving away from us (usually referred to as redshift) is a product of the cosmic distance ladder. Hubble observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result of decades of work by many astronomers, both in amassing the measurements of galaxy redshifts and in calibrating the steps of the distance ladder. Hubble's Law is the primary means we have for estimating the distances of quasars and distant galaxies in which individual distance indicators cannot be seen.

## Notes

1. ^ Bartel, N., et al., 1994, "The shape, expansion rate and distance of supernova 1993J from VLBI measurements", Nature 368, 610-613
2. ^ Ash, M.E., Shapiro, I.I., & Smith, W.B., 1967 Astronomical Journal, 72, 338-350.
Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").
parsec (symbol pc) is a unit of length used in astronomy. The length of the parsec is based on the method of trigonometric parallax, one of the oldest methods for measuring the distances to stars.
Parallax, or more accurately motion parallax (Greek: παραλλαγή (parallagÃ©) = alteration) is the change of angular position of two stationary points relative to each other as seen by an observer, caused by the motion of an
triangulation is the process of finding coordinates and distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other known reference points, using the law of sines.
Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]), informally called trig, is a branch of mathematics that deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled
Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space position of points and the distances and angles between them. These points are usually, but not exclusively, associated with positions on the surface of the Earth, and are
speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
Radar is a system that uses electromagnetic waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain.
Astrometry is the branch of astronomy that relates to precise measurements and explanations of the positions and movements of stars and other celestial bodies. Although once thought of as an esoteric field with little useful application for the future, the information obtained by
Parallax, or more accurately motion parallax (Greek: παραλλαγή (parallagÃ©) = alteration) is the change of angular position of two stationary points relative to each other as seen by an observer, caused by the motion of an
A triangle is one of the basic shapes of geometry: a polygon with three corners or and three sides or edges which are straight line segments.

In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
1 astronomical unit =
SI units
0109 m 0106 km
Astronomical units
010-6 pc 010−6 ly
US customary / Imperial units
0109 ft 0106 mi
The
parsec (symbol pc) is a unit of length used in astronomy. The length of the parsec is based on the method of trigonometric parallax, one of the oldest methods for measuring the distances to stars.
1 light-year =
SI units
01015 m 01012 km
Astronomical units
0103 AU 0 pc
US customary / Imperial units
01015 ft 01012 mi
A light-year or lightyear (symbol:
accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeatability, the degree to which further measurements or calculations show the same or similar
Centuries: 19th century - 20th century - 21st century

1960s 1970s 1980s - 1990s - 2000s 2010s 2020s
1990 1991 1992 1993 1994
1995 1996 1997 1998 1999

- -
-
Hipparcos (for High Precision Parallax Collecting Satellite) was an astrometry mission of the European Space Agency (ESA) dedicated to the measurement of stellar parallax and the proper motions of stars.
A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. [1] Since one degree is defined as one three hundred sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle, or
RR Lyrae variables are variable stars often used as standard candles.

RR Lyrae are pulsating Horizontal branch stars, with a mass of around half the Sun's. RR Lyrae stars shed mass prior to becoming RR Lyrae and consequently, RR Lyrae were once stars with similar or slightly
open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud, and are still loosely gravitationally bound to each other. In contrast, globular clusters are very tightly bound by gravity.

Observation data: J2000.0 epoch
Constellation:
Right ascension: 04h 27m
Declination: +15° 52′
Distance: 151 ly (46 Pc)
Apparent magnitude (V) : 0.
supernova remnant (SNR) is the structure resulting from the gigantic explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and
planetary nebula is an astronomical object consisting of a glowing shell of gas and plasma formed by certain types of stars at the end of their lives. The name originates from a similarity in appearance to giant planets when viewed through a small optical telescope, and is
binary star is a stellar system consisting of two stars orbiting around their center of mass. For each star, the other is its companion star. Recent research suggests that a large percentage of stars are part of systems with at least two stars.
velocity is defined as the rate of change of position. It is a vector physical quantity, both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second (m/s). The scalar absolute value (magnitude) of velocity is speed.
Please [improve the article] or discuss this issue on the talk page. This article has been tagged since December 2006.
1 astronomical unit =
SI units
0109 m 0106 km
Astronomical units
010-6 pc 010−6 ly
US customary / Imperial units
0109 ft 0106 mi
The
1 astronomical unit =
SI units
0109 m 0106 km
Astronomical units
010-6 pc 010−6 ly
US customary / Imperial units
0109 ft 0106 mi
The