Published online 2 September 2008 | Nature | doi:10.1038/news.2008.1073


Galileo duped by diffraction

Telescope pioneer foiled by optical effect while measuring distance to the stars.

Katharine Sanderson


When Galileo Galilei used a new invention called the telescope to watch the heavens, he revolutionized astronomy. But his estimates of the distances to the stars were thousand of times too short.

A scientist has now taken a closer look at Galileo's seventeenth century results in an attempt to explain why the estimates were so far off the mark1. Christopher Graney, a physicist at Jefferson Community College in Louisville, Kentucky, argues in a paper posted to the preprint server arXiv that Galileo was tricked by a phenomenon that was only really understood two centuries later diffraction.

Graney says that Galileo was actually observing the diffraction pattern that the stars created in the telescope, instead of the stars themselves. Known as an Airy pattern, it arises when light from a point source such as a star passes through a hole. The pattern is made of concentric circles, with a bright 'Airy disk' in the middle which it seems that Galileo thought was the star.

For fainter objects, the edges of the disk are hard to see, making it look smaller, whereas brighter stars produce a larger Airy disk. Because Galileo thought that all stars were the same size and brightness as the Sun, he concluded that the smaller stars he observed through his telescope were simply further away.

So Galileo tried to infer the stars' relative distance from Earth, in terms of what we now call astronomical units (AU), by measuring their diameter. One astronomical unit is the distance from Earth to the Sun, about 150 million kilometres. He deduced that the stars were hundreds to thousands of AU away. In reality, the nearest stars are about 300,000 AU away.

Duplicitous disk

To unravel Galileo's mistake, Graney calculated the intensity of the diffraction pattern for stars of different brightnesses. He then worked out Galileo's detection threshold and calculated the size of the Airy disk that each different star would have produced in Galileo's telescope.

Drawing a graph of the stars' brightness against the apparent diameter of the Airy disk gave Graney a roughly straight line that looked very much like Galileo's own data strong evidence, says Graney, that the astronomer was indeed being fooled by the Airy disk.

Historians have long known that Galileo was looking at spurious images of the stars. But Graney's work pinpoints exactly how diffraction could have tricked Galileo, says Noel Swerdlow, a historian of science at the University of Chicago, Illinois. "Showing the linear relationship between magnitude and apparent size does explain how Galileo could believe that," he says.

Although Galileo's assumptions about all stars being identical to the Sun turned out to be wrong, they were reasonable given the state of scientific knowledge in the seventeenth century, says Graney. "He would have seen nothing to contradict that point of view."

Parallax view

Astronomers now measure the distance to stars using the parallax technique, in which the apparent location of a distant star changes slightly as Earth orbits the Sun, allowing a distance to be deduced from the angle between those locations. This technique was first used in 1838 by German astronomer Friedrich Bessel.

Graney's work shows just how good Galileo was at taking measurements, says Don Salisbury, a physicist who teaches history of science courses focusing on Galileo at Austin College, Texas. "Galileo was indeed able to measure to an accuracy in which the diffracted image would be measurable," he says.

And Galileo's estimates were far larger than the distances to any astronomical bodies known at the time. "300 AU is close compared to modern ideas about the stars, but it is more than 10 times further than Neptune, and 30 times further than Saturn, the most distant planet known in Galileo's day," says Graney. "It's a long way, and I'm sure it seemed quite far to Galileo and his contemporaries." 


1.    Graney, C. M. Preprint at (2008).



Galileo Galilei, as painted by Justus Sustermans in 1636.