Hertzsprung Uses Cepheid Variables to Calculate Distances to the Stars Summary

  • Last updated on November 10, 2022

Ejnar Hertzsprung’s use of Cepheid variables as a means of measuring stellar distances led to discoveries regarding the structure of the Milky Way galaxy.

Summary of Event

Discovering the distances to heavenly objects traditionally has been a difficult undertaking for astronomers. It is possible to use parallax to determine the distance to relatively nearby stars, and this technique produced the first stellar distance measurement made by Friedrich Wilhelm Bessel in 1838. Parallax Parallax method of measuring stellar distances is a measurement of how far a star appears to move as Earth follows its orbit around the Sun. It relies on an effect similar to what one sees when one holds a finger up at arm’s length and views it first with the left eye only and then with the right eye only; the finger appears to shift position relative to background objects because of differing lines of sight. Stars are perceived to make a similar shift in position when viewed first from one end of Earth’s orbit and then again six months later, when Earth is at the opposite point in its orbit. If one can measure this shift in position, one can use trigonometry to calculate the distance of the star. This technique is of limited use, however, because for stars more distant than about 65 light-years (a light-year Light-years[Light years] is approximately 5.88 trillion miles, or 9.46 trillion kilometers), the shift is so small as to be unmeasurable. Astronomy;stars Cepheid variable stars Stellar distances Stars;Cepheids Milky Way galaxy;structure Variable stars [kw]Hertzsprung Uses Cepheid Variables to Calculate Distances to the Stars (1913) [kw]Cepheid Variables to Calculate Distances to the Stars, Hertzsprung Uses (1913) [kw]Variables to Calculate Distances to the Stars, Hertzsprung Uses Cepheid (1913) [kw]Stars, Hertzsprung Uses Cepheid Variables to Calculate Distances to the (1913) Astronomy;stars Cepheid variable stars Stellar distances Stars;Cepheids Milky Way galaxy;structure Variable stars [g]Germany;1913: Hertzsprung Uses Cepheid Variables to Calculate Distances to the Stars[03280] [c]Science and technology;1913: Hertzsprung Uses Cepheid Variables to Calculate Distances to the Stars[03280] [c]Astronomy;1913: Hertzsprung Uses Cepheid Variables to Calculate Distances to the Stars[03280] Hertzsprung, Ejnar Leavitt, Henrietta Swan Pickering, Edward Charles Shapley, Harlow

Another technique for calculating distance involves comparing a star’s apparent magnitude (its brightness as seen from Earth) and its absolute magnitude Absolute magnitude of stars Stars;absolute magnitude (its intrinsic or true brightness). The apparent magnitude, the absolute magnitude, and the distance of a star are all related: An apparently dim star can be either intrinsically dim and relatively close or intrinsically very bright and at a great distance. One can make an analogy between lightbulbs and stars: Given the appearance of a lightbulb of known wattage, an estimate can be made of its distance; given its distance and its apparent brightness, its wattage can be estimated, which represents its intrinsic or absolute brightness. Similarly, for any star, if any two of the three properties (absolute magnitude, apparent magnitude, distance) are known, the third property can be calculated.

A star’s apparent magnitude is always known; it is the distance and the absolute magnitude that are difficult to discover. Without a way to deduce a star’s absolute magnitude, one cannot begin to use this distance-calculating technique. Henrietta Swan Leavitt was able to find a key to deducing the absolute magnitudes of some stars. In 1912, Leavitt was working with Edward Charles Pickering at the Harvard College Observatory, Harvard College Observatory studying a particular type of star called a Cepheid variable. Such stars vary in brightness over time in a regular periodic cycle; they are named for the first such star known, which appears in the constellation Cepheus. A Cepheid’s light output varies as the star as a whole pulsates, periodically contracting inward and expanding outward. Leavitt discovered that there is a relationship between a Cepheid’s period (how long it takes to go from brightest to dimmest and back again) and its apparent magnitude.

Leavitt produced a plot of period versus apparent magnitude; if the period for one of the stars Leavitt studied is known, then its apparent magnitude can be inferred from this relationship. Also, one can measure simply the apparent magnitude of a star; the real importance of Leavitt’s discovery came when it was found that one could use this relationship to infer the absolute magnitude of a star and, from that, its distance. Leavitt studied stars in the Small Magellanic Cloud Small Magellanic Cloud (a small galaxy visible from Earth’s Southern Hemisphere). One can assume that all the stars in this cloud are at approximately the same distance. The absolute magnitude of a star varies according to both its distance and its apparent magnitude; as the distance is approximately constant for these stars, the absolute magnitude relates directly to the apparent magnitude and thus to the period. Leavitt and Ejnar Hertzsprung both realized this fact. Hertzsprung saw that Leavitt’s period-luminosity plot needed to be calibrated; that is, the relationship Period-luminosity relationship of stars[Period luminosity relationship] between absolute magnitude and period needed to be found. One could then use the plot to find the absolute magnitude for any Cepheid, given its period, and then, using the apparent and absolute magnitudes, to calculate its distance.

Hertzsprung’s task was to find a Cepheid variable for which he could measure the distance in some way. He could then calculate its absolute magnitude and establish the relationship between its magnitude and its period. The simplest thing would be to find a Cepheid close enough to show a measurable parallax. Unfortunately, no Cepheid variables were close enough for this to work, so Hertzsprung instead used statistical techniques to discover the distances for a group of Cepheids. First, he found Cepheids for which the proper motions were known; that is, the apparent movements of the stars across the sky had been measured. (Although the stars appear fixed to the casual eye, all are moving, and careful observation and measurement can reveal the motion of some of the ones that are closer, faster moving, or both.) From the stars’ proper motions, Hertzsprung was able to deduce the component of the proper motion that, on the average, was caused by parallax. Once he had the parallax for a star, he could calculate its distance and its absolute magnitude. He then constructed a plot of absolute magnitude versus period for these Cepheids, which showed the relationship between the two quantities.

This was the tool astronomers needed: For any Cepheid, given the period, one could read from the plot the absolute brightness, and then one could calculate the distance. A relatively simple measurement of the time it took a star to vary in its brightness thus enabled an astronomer to deduce its distance. Hertzsprung first used this tool on the Cepheids studied by Leavitt and calculated the distance to the Small Magellanic Cloud, where these Cepheid variables were located. He arrived at the figure of about 33,000 light-years. This was greater than any previously determined distance, and this surprising and vital result had implications for the later debate on the size of the Milky Way and of the universe as a whole.

Later distance-measuring techniques have given a higher distance measurement for the Small Magellanic Cloud, about five times what Hertzsprung found. There are varying reasons for the discrepancy, chief among them the fact that starlight is absorbed and dimmed as it passes through the Milky Way. This dimming must be taken into account in the equation involving apparent magnitude, absolute magnitude, and distance; however, in 1913 no one was aware of this fact. Harlow Shapley, in his early work with the period-luminosity scale, recalibrated the period-luminosity plot using techniques similar to those used by Hertzsprung. He arrived at similar results.

Later discoveries regarding interstellar absorption of light led to a more accurate calibration, as did the discovery that there are actually two different types of Cepheids, with two different period-luminosity relationships. The work of Leavitt and Hertzsprung opened a host of new possibilities to astronomers by giving them a powerful new tool for answering one of astronomy’s most difficult questions: How far away are the stars? This led to other answers regarding the nature of the Milky Way and of the universe.


The Cepheid variable technique of measuring stellar distances proved to be extremely powerful and yielded some vital results that changed astronomers’ basic beliefs about the structure of the universe. It enabled Shapley to determine the shape and size of the Milky Way galaxy, and it enabled Edwin Powell Hubble Hubble, Edwin Powell to determine that the Milky Way is not the whole universe, but that there are other galaxies that are huge, independent stellar systems. Shapley studied the Cepheid variables he observed in globular clusters of stars, so named for their appearance as tightly packed balls of stars. These clusters are not distributed at random in the sky; rather, they appear to be concentrated around a certain section of the sky in the direction of the constellation Sagittarius. Shapley found this pattern important and guessed that perhaps the clusters were gathered around the center of the galaxy. He made measurements of their distances, used these measurements to make a map of the locations of the clusters, and arrived at a distance scale for the Milky Way galaxy. His results, presented in 1918, gave a first estimate of the size of the Milky Way and also revealed some of the structure of the galaxy.

Hubble was the first to realize that there are Cepheid variables in spiral nebulas, Spiral nebulas Nebulas;spiral which are now recognized to be spiral galaxies similar to the Milky Way. At the time, no one knew for certain the nature of these spiral nebulas; it was not known if they were parts of our galaxy that were relatively close and small. Astronomers also were not certain if they were huge, separate, independent systems, appearing small only because of their great distance. At the beginning of the twentieth century, this was a subject of intense astronomical debate.

Shapley’s results for the size of the Milky Way indicated that if these objects were indeed similar to our galaxy, they must be very distant to appear as small as they do. This great distance would extend vastly the scale of the known universe and also would shift our galaxy’s place in it: If there are other galaxies similar to Earth’s, then the Milky Way is not in any special or privileged location in the universe. Hubble was able to settle the debate on this important cosmological question by studying photographic plates taken with the new 100-inch (254-centimeter) telescope at the Mount Wilson Observatory Mount Wilson Observatory in Southern California. Hooker telescope He studied plates of the Andromeda nebula and discovered Cepheid variables in the nebula. By using the period-luminosity scale to deduce the distance of these stars, and assuming the stars were indeed physically part of the nebula, Hubble arrived at a great distance for the nebula, which indicated that it was a separate galaxy. This result settled the debate and gave astronomers important information about the size of the universe and Earth’s place in it.

Corrections and modifications have been made to the period-luminosity relationship over the years, notably the correction for the fact that there are really two types of Cepheid variables. In addition, astronomers have discovered other stars with similar period-luminosity relationships and have been able to use that knowledge to advance their understanding of the structure of the universe. Astronomy;stars Cepheid variable stars Stellar distances Stars;Cepheids Milky Way galaxy;structure Variable stars

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Asimov, Isaac. The Universe: From Flat Earth to Quasar. Rev. ed. New York: Walker, 1971. A chapter on the Milky Way tells, in Asimov’s usual lucid and engaging style, the story of the development of the Cepheid period-luminosity scale and its use in the discovery of the size and structure of the Milky Way and the nature and distance of external galaxies. Includes some drawings and photographs; brief bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Chaisson, Eric, and Steve McMillan. Astronomy Today. 4th ed. Upper Saddle River, N.J.: Prentice Hall, 2001. Chapter 17, titled “Measuring the Stars,” includes discussion of Hertzsprung’s work.
  • citation-type="booksimple"

    xlink:type="simple">Kaufmann, William J. Discovering the Universe. New York: W. H. Freeman, 1987. Chapters such as “Our Galaxy” and “Galaxies” include the story of the discovery of the size and structure of our galaxy and the nature and distance of external galaxies. An earlier chapter explains also the physical properties of Cepheids that result in their variability. Intended as a text for an introductory astronomy class. Includes study aids such as chapter summaries, review questions, and glossary, as well as photographs and drawings.
  • citation-type="booksimple"

    xlink:type="simple">Mitton, Simon, ed. The Cambridge Encyclopædia of Astronomy. New York: Crown, 1977. The chapter titled “Cosmology, the Nature of the Universe” includes the story of the first realization of the size of our galaxy and the distance to other galaxies. “Variable Stars” discusses the period-luminosity relationship. Contains many lovely photographs as well as helpful diagrams and drawings. Also includes a brief outline of principles of physics relevant to astronomy.
  • citation-type="booksimple"

    xlink:type="simple">Struve, Otto, and Velta Zebergs. Astronomy of the Twentieth Century. New York: Macmillan, 1962. Cowritten by an astronomer who observed firsthand some of the events the book covers, this account emphasizes the contributions of Shapley more than those of Hertzsprung and explains Shapley’s method of recalibrating the period-luminosity scale. Includes discussion of Hubble’s and Shapley’s work concerning the Milky Way and Andromeda galaxies. Drawings, photographs, glossary, and bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Vaucouleurs, Gérard Henri de. Discovery of the Universe: An Outline of the History of Astronomy from the Origins to 1956. New York: Macmillan, 1957. Includes discussion of Hertzsprung’s and Leavitt’s work on the discovery of the period-luminosity relationship and its use in distance determination. Discusses the work done by Shapley and Hubble in using Cepheid variables as a tool to study the Milky Way and other galaxies. Some drawings and photographs; short bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Zeilik, Michael, and Stephen A. Gregory. Introductory Astronomy and Astrophysics. 4th ed. Monterey, Calif.: Brooks/Cole, 1997. This introductory text provides a useful overview of general astronomy, including basic spectral issues.

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Categories: History