question: How was the size of the observable universe calculated?
comment: We know the age of the Universe. We know the rate of expansion of the Universe, including the fact that the rate was faster during a short period at the beginning that we call the inflation. So we can calculate the actual distance from us an object is if the light we receive from it today is as old as the universe.
passages: Section::::Interferometry.:50 foot Stellar Interferometer.
  
  To expand on the work of the 20 foot interferometer, Pease, Michelson and George E. Hale designed a 50-foot interferometer which was installed at Mount Wilson Observatory in 1929. It successfully measured the diameter of Betelgeuse, but, other than beta Andromedae, could not measure any stars not already measured by the 20 foot interferometer.
  
  Optical interferometry reached the limit of the available technology and it took about thirty years for faster computing, electronic detectors and lasers to make larger interferometers possible again.
  
  Section::::Interferometry.:Infrared Spatial Interferometer.
   According to calculations, the current "comoving distance"—proper distance, which takes into account that the universe has expanded since the light was emitted—to particles from which the cosmic microwave background radiation (CMBR) was emitted, which represent the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years), about 2% larger. The radius of the observable universe is therefore estimated to be about 46.5 billion light-years and its diameter about 28.5 gigaparsecs (93 billion light-years, ). The total mass of ordinary matter in the universe can be calculated using the critical density and the diameter of the observable universe to be about 1.5 × 10 kg. In November 2018, astronomers reported that the extragalactic background light (EBL) amounted to 4 × 10 photons.
   Section::::Size.
  
  The comoving distance from Earth to the edge of the observable universe is about 14.26 gigaparsecs (46.5 billion light-years or ) in any direction. The observable universe is thus a sphere with a diameter of about 28.5 gigaparsecs (93 billion light-years or ). Assuming that space is roughly flat (in the sense of being a Euclidean space), this size corresponds to a comoving volume of about ( or ).
   Another class of physical distance indicator is the standard ruler. In 2008, galaxy diameters have been proposed as a possible standard ruler for cosmological parameter determination. More recently the physical scale imprinted by baryon acoustic oscillations (BAO) in the early universe has been used. 
   Another large-scale structure is the SSA22 Protocluster, a collection of galaxies and enormous gas bubbles that measures about 200 million light-years across.
  
  In 2011, a large quasar group was discovered, U1.11, measuring about 2.5 billion light-years across. On January 11, 2013, another large quasar group, the Huge-LQG, was discovered, which was measured to be four billion light-years across, the largest known structure in the universe at that time. In November 2013, astronomers discovered the Hercules–Corona Borealis Great Wall, an even bigger structure twice as large as the former. It was defined by the mapping of gamma-ray bursts.
   Section::::Matter content – number of atoms.
  
  Assuming the mass of ordinary matter is about (refer to previous section) and assuming all atoms are hydrogen atoms (which are about 74% of all atoms in our galaxy by mass, see Abundance of the chemical elements), calculating the estimated total number of atoms in the observable universe is straightforward. Divide the mass of ordinary matter by the mass of a hydrogen atom ( divided by ). The result is approximately 10 hydrogen atoms.
  
  Section::::Most distant objects.
   During the following decade, CMB anisotropies were further investigated by a large number of ground-based and balloon experiments. In 2000–2001 several experiments, most notably BOOMERanG, found the shape of the universe to be spatially almost flat by measuring the typical angular size (the size on the sky) of the anisotropies.
   The CBI was built at the California Institute of Technology, and employed sensitive radio amplifiers from the National Radio Astronomy Observatory; two similar experiments are the Very Small Array, operated on the island of Tenerife, and the Degree Angular Scale Interferometer, operated in Antarctica. Both of these experiments used radio interferometry to measure CMB fluctuations at lower resolution over larger areas of the sky. Another experiment operated from Antarctica, the Arcminute Cosmology Bolometer Array Receiver, used total power (bolometric) detection and a single antenna at higher frequency and similar angular resolution to obtain results comparable to the CBI. The confluence of these and other CMB experiments employing different measurement techniques in recent years is a great triumph of observational cosmology.
   Reported in March 2016, "Spitzer" and "Hubble" were used to discover the most distant-known galaxy, GN-z11. This object was seen as it appeared 13.4 billion years ago. (List of the most distant astronomical objects)
  
  Section::::Successors to GO instruments.
   Distance measurements in astronomy have historically been and continue to be confounded by considerable measurement uncertainty. In particular, while stellar parallax can be used to measure the distance to nearby stars, the observational limits imposed by the difficulty in measuring the minuscule parallaxes associated with objects beyond our galaxy meant that astronomers had to look for alternative ways to measure cosmic distances. To this end, a standard candle measurement for Cepheid variables was discovered by Henrietta Swan Leavitt in 1908 which would provide Edwin Hubble with the rung on the cosmic distance ladder he would need to determine the distance to spiral nebula. Hubble used the 100-inch Hooker Telescope at Mount Wilson Observatory to identify individual stars in those galaxies, and determine the distance to the galaxies by isolating individual Cepheids. This firmly established the spiral nebula as being objects well outside the Milky Way galaxy. Determining the distance to "island universes", as they were dubbed in the popular media, established the scale of the universe and settled the Shapley-Curtis debate once and for all.
   BULLET::::- MIT Cosmic X-Ray Experiment, P.I. Prof. George W. Clarke, observed cosmic X-ray sources in the range 1.5 to 9 Å. This instrument used proportional counters to observe cosmic X-ray sources in the 1 to 60 keV range, in five broad logarithmically spaced energy bands, with about 1° angular resolution.
   Many secondary sources have reported a wide variety of incorrect figures for the size of the visible universe. Some of these figures are listed below, with brief descriptions of possible reasons for misconceptions about them.
  
  BULLET::::- 13.8 billion light-years
  
  BULLET::::- 15.8 billion light-years
  
  BULLET::::- 27.6 billion light-years
  
  BULLET::::- 78 billion light-years
  
  BULLET::::- 156 billion light-years
  
  BULLET::::- 180 billion light-years
  
  Section::::Large-scale structure.
   Section::::Mission.:Galactic mapping.
  
  Interferometric measurements of stellar positions over the course of the mission would have permitted SIM to precisely measure the distances between stars throughout the Milky Way. This would have allowed astronomers to create a "roadmap" of the Galaxy, answering many questions about its shape and size.
   The organization of structure arguably begins at the stellar level, though most cosmologists rarely address astrophysics on that scale. Stars are organized into galaxies, which in turn form galaxy groups, galaxy clusters, superclusters, sheets, walls and filaments, which are separated by immense voids, creating a vast foam-like structure sometimes called the "cosmic web". Prior to 1989, it was commonly assumed that virialized galaxy clusters were the largest structures in existence, and that they were distributed more or less uniformly throughout the universe in every direction. However, since the early 1980s, more and more structures have been discovered. In 1983, Adrian Webster identified the Webster LQG, a large quasar group consisting of 5 quasars. The discovery was the first identification of a large-scale structure, and has expanded the information about the known grouping of matter in the universe. In 1987, Robert Brent Tully identified the Pisces–Cetus Supercluster Complex, the galaxy filament in which the Milky Way resides. It is about 1 billion light-years across. That same year, an unusually large region with a much lower than average distribution of galaxies was discovered, the Giant Void, which measures 1.3 billion light-years across. Based on redshift survey data, in 1989 Margaret Geller and John Huchra discovered the "Great Wall", a sheet of galaxies more than 500 million light-years long and 200 million light-years wide, but only 15 million light-years thick. The existence of this structure escaped notice for so long because it requires locating the position of galaxies in three dimensions, which involves combining location information about the galaxies with distance information from redshifts.
   The observable universe is a spherical region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There are at least 2 trillion galaxies in the observable universe. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe has a spherical volume (a ball) centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.
   CHIME is sensitive to the 21 cm radio waves emitted by clouds of neutral hydrogen in distant galaxies, and is sensitive to the red shifted waves. By measuring the distribution of the hydrogen in the Universe—a technique known as intensity mapping—CHIME will make a 3D map of the large-scale structure of the Universe between redshifts of 0.8 and 2.5, when the Universe was between about 2.5 and 7 billion years old. CHIME will thus map over 3% of the total observable volume of the Universe, substantially more than has been achieved by large-scale structure surveys to date, during an epoch when the Universe is largely unobserved.
   This unit is similar in concept to the attoparsec, combining very large and small scales. When a barn (a very small unit of area used for measuring the cross sectional area of atomic nuclei) is multiplied by a megaparsec (a very large unit of length used for measuring the distances between galaxies), the result is a human-scaled unit of volume approximately equal to of a teaspoon (about 3 ml).
  
  Section::::Volume.:Hubble-barn.
   BULLET::::- 130 Ym – redshift 1000 – 13.8 billion light years – Distance (LTD) to the source of the cosmic microwave background radiation; radius of the observable universe measured as a LTD
  
  BULLET::::- 260 Ym – 27.4 billion light years – Diameter of the observable universe (double LTD)
  
  BULLET::::- 440 Ym – 46 billion light years – Radius of the universe measured as a comoving distance
  
  BULLET::::- 590 Ym – 62 billion light years – Cosmological event horizon: the largest comoving distance from which light will ever reach us (the observer) at any time in the future
   Section::::Discovery.:Shape of the universe.
  
  Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.
  
  Section::::Discovery.:Cepheid variable stars outside of the Milky Way.
   formula_5
  
  where
  
  BULLET::::- formula_6 is the recessional velocity of the galaxy or other distant object,
  
  BULLET::::- formula_7 is the comoving distance to the object, and
  
  BULLET::::- formula_8 is Hubble's constant, measured to be km/s/Mpc by the WMAP probe.
   Because the source was nonrepeating, the astronomers had to scan large areas with the 36 telescopes of ASKAP. Once a signal was found, they used the Very Large Telescope, the Gemini Observatory in Chile, and the W. M. Keck Observatory in Hawaii to identify its host galaxy and determine its distance. Knowing the distance and source galaxy properties, enables a study of the composition of the intergalactic medium.
  
  Section::::Bursts observed.:2019.:June 2019 Report.
   The siriometer is a rarely used astronomical measure equal to one million astronomical units, i.e., one million times the average distance between the Sun and Earth. This distance is equal to about 15.8 light-years, 149.6 Pm or 4.8 parsecs, and is about twice the distance from Earth to the star Sirius.
  
  Section::::Area.
  
  Section::::Area.:Barn.
   The most distant astronomical object yet announced as of 2016 is a galaxy classified GN-z11. In 2009, a gamma ray burst, GRB 090423, was found to have a redshift of 8.2, which indicates that the collapsing star that caused it exploded when the universe was only 630 million years old. The burst happened approximately 13 billion years ago, so a distance of about 13 billion light-years was widely quoted in the media (or sometimes a more precise figure of 13.035 billion light-years), though this would be the "light travel distance" ("see" Distance measures (cosmology)) rather than the "proper distance" used in both Hubble's law and in defining the size of the observable universe (cosmologist Ned Wright argues against the common use of light travel distance in astronomical press releases on this page, and at the bottom of the page offers online calculators that can be used to calculate the current proper distance to a distant object in a flat universe based on either the redshift "z" or the light travel time). The proper distance for a redshift of 8.2 would be about 9.2 Gpc, or about 30 billion light-years. Another record-holder for most distant object is a galaxy observed through and located beyond Abell 2218, also with a light travel distance of approximately 13 billion light-years from Earth, with observations from the Hubble telescope indicating a redshift between 6.6 and 7.1, and observations from Keck telescopes indicating a redshift towards the upper end of this range, around 7. The galaxy's light now observable on Earth would have begun to emanate from its source about 750 million years after the Big Bang.
   In the model, Einstein derived simple expressions relating the density of matter, the radius of the universe and the timespan of the expansion to the Hubble constant. With the use of the contemporaneous value of 500 km·sMpc for the Hubble constant, he calculated values of 10 cm, 10 light-years and 10 years for the density of matter, the radius of the universe and the timespan of the expansion respectively. It has recently been shown that these calculations contain a slight systematic error.
  
  Section::::Einstein's blackboard.
   On February 11, 2003, NASA published the first-year's worth of WMAP data. The latest calculated age and composition of the early universe were presented. In addition, an image of the early universe, that "contains such stunning detail, that it may be one of the most important scientific results of recent years" was presented. The newly released data surpass previous CMB measurements.
  