On this page
How do you measure the distance to something you can never visit? For nearby stars, astronomers use parallax, but beyond a certain distance the shift becomes too small to measure. Henrietta Leavitt found a way past that limit by studying thousands of stars on glass photographs. This post explains what she found, works through the arithmetic of using it, lists the common mistakes, and ends with what a student can take from how she worked.
Who was Henrietta Leavitt?
The MacTutor biography from the University of St Andrews gives her dates as 4 July 1868, Lancaster, Massachusetts, to 12 December 1921, Cambridge, Massachusetts. She studied at Oberlin and then in the programme for women at Harvard that later became Radcliffe College. At Harvard College Observatory she worked on photographic plates of southern skies sent from the observatory's station at Arequipa in Peru, measuring the positions and brightness of stars. Carnegie Science describes her as a Harvard human "computer", the job title for the people who did this measuring.
Her career was interrupted by illness more than once. MacTutor records that she was in hospital in Boston in December 1908 and spent much of 1909 at her family's home, returning to the work when she could.
What did Leavitt discover?
Working through plates of the two Magellanic Clouds, she found an extraordinary number of variable stars. The opening of Harvard College Observatory Circular 173 (1912), which she prepared, says a catalogue of 1777 variable stars in the two Clouds had already been published. The periods of seventeen had appeared earlier, and by 1912 she had 25.
The circular states: "A remarkable relation between the brightness of these variables and the length of their periods will be noticed." When she plotted brightness against the logarithm of the period, the points fell along a straight line: "The logarithm of the period increases by about 0.48 for each increase of one magnitude in brightness."
Then comes the crucial sentence: "Since the variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light." Because all these stars sit in one distant cloud, differences in how bright they look are differences in how bright they are. The circular, dated 3 March 1912, was issued under the observatory director Edward C. Pickering's name, but its first line says the statement "has been prepared by Miss Leavitt".
How does a period become a distance?
Once the relation is calibrated with a few Cepheids of known distance, any Cepheid works as a "standard candle". Measure its period and you know its true brightness. Measure how bright it looks and the inverse-square law gives the distance. Carnegie Science explains that this is how Edwin Hubble, in October 1923, showed that a Cepheid in Andromeda was too distant to be part of the Milky Way. That story is in our post on Edwin Hubble and the expanding universe.
Worked example: using Leavitt's numbers
Magnitudes first. On the magnitude scale, a smaller number means brighter, and 5 magnitudes is a factor of 100 in brightness. So 1 magnitude is a factor of 100^(1/5), about 2.512.
1. Period to brightness difference. Two Cepheids in the Small Magellanic Cloud have periods of 3 days and 30 days. The log of the period differs by log 30 - log 3 = log 10 = 1. With Leavitt's 0.48 per magnitude, the longer-period star is 1 / 0.48 = about 2.1 magnitudes brighter. That is a brightness ratio of 10^(0.4 x 2.08) = about 6.8.
2. Brightness to distance. Two Cepheids have the same period, so the same true brightness. Star B looks 100 times fainter than star A. Light spreads out as 1/d^2, so B is the square root of 100 = 10 times farther away.
3. With the distance modulus. For a star with apparent magnitude m and absolute magnitude M, m - M = 5 log(d / 10 pc). If m - M = 15, then log(d / 10) = 3, so d = 10 x 1,000 = 10,000 parsecs.
Common mistakes
Reading the magnitude scale the wrong way round. Brighter means a smaller magnitude.
Forgetting the square root. 100 times fainter means 10 times farther, not 100.
Using natural logarithms. Leavitt's slope and the distance modulus both use base-10 logs.
If logarithms or the inverse-square law are the sticking point, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing.
How was her work recognised?
MacTutor quotes a 1917 letter in which Harlow Shapley wrote: "Her discovery of the relation of period to brightness is destined to be one of the most significant results of stellar astronomy, I believe." MacTutor also records that the Swedish mathematician Gösta Mittag-Leffler wrote to her about nominating her for the Nobel Prize in Physics for 1926, not knowing she had died in 1921.
What can a student learn from how Leavitt worked?
Patience with data finds patterns. The relation came from careful measurement of thousands of stars, not a single lucky plate.
Control what you cannot measure. She could not measure distance, so she used stars that shared one.
Say what you see, plainly. Her circular is three pages long and states its result in one sentence.
Practice routine: work out the brightness ratio for periods of 2 and 50 days, then the distance of a Cepheid with m - M = 20, and check your magnitude direction each time.
Next step: if astronomy appeals, read our guide to the astronomy olympiad (NSEA) and add one Cepheid problem to your practice this week.
