Chapter 12: Properties of Stars

Christian Huygens

Early distance estimates were no more than educated guesses. In the late 17th century, Dutch scientist Christian Huygens made an image of the Sun through a pinhole in a darkened room. He varied the size of the pinhole until the image seemed equal in brightness to an image of Sirius, the brightest star. Since the pinhole admitted 1/27,000 of the light of the Sun, Huygens concluded that Sirius was 27,000 times farther away than the Sun (it is actually 543,900 times farther away and substantially more luminous than the Sun). Around the same time, Issac Newton tried to use Saturn as a sort of reflecting mirror to measure the intensity of sunlight. He guessed the percentage of the Sun's light that Saturn reflects and assumed that bright stars have similar absolute brightness to the Sun. Newton concluded that the bright stars are about 18,000 times farther away than the Sun (which is simply wrong, for the same reason Huygen was wrong; neither of them knew that most bright stars in the night sky are intrinsically much brighter than the Sun).

A diagram illustrating the Inverse Square Law. S represents an ideal source of electromagnetic radiation and A represents an arbitrary segment of the surface of a sphere of radius r.

Both these men were trying to use a crude method for estimating the distance of stars; inverse square law for the propagation of light. The brightest stars have values of apparent brightness that are about 10 billion (or 10¹⁰) times fainter than the Sun. Unfortunately, the relative brightness of the Sun and other stars is impossible to measure accurately without equipment. Mistakes continued into more modern times. In 1829, English scientist William Wollaston used the inverse square law to estimate that most typical stars must be at least 100,000 (or 10⁵) times more distant than the Sun, since the inverse square law indicates that dimming 10 billion times corresponds to increasing distance 100,000 times (which is accurate for some stars).

A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object appears to have moved in front of the red square.

To understand how parallax measurements are made, hold your finger in front of your face and look past it toward a bookcase on the other side of the room. Your finger represents a nearby star — the books on the far wall represent distant stars. Your right eye represents the view on one side of the Sun. Your left eye represents the view six months later, after the Earth has traveled to a point on the opposite side of the Sun (a shift in the Earth's position by 2 A.U. as seen from the star). First wink one eye and then the other. Your finger (the nearby star) seems to shift back and forth. Hold your finger only a few centimeters from your eyes; the shift is large. Hold your finger at arm's length; the shift is smaller. Likewise, the farther away the nearby star, the smaller the parallax angle. The parallax in this experiment can be measured in degrees, but the parallaxes of actual stars are all ten thousand times smaller - less than a second of arc! Parallaxes as small as 1/100 second of arc can be reliably measured, and the distance of such a star is 100 parsecs.

The Hipparcos satellite.

The distance of a star in parsecs is simply the inverse of its parallax angle in seconds of arc. This explains the origin of the term parsec: it is the distance to a parallax of one second of arc. If a star is too distant, its parallax is too small to be measured. (Try winking your eyes to see the shift of a distant object against an even further horizon — at some distance, you will not notice a shift anymore.) Parallaxes smaller than about 1/100 second of arc are difficult to measure accurately, due to the blurring of the Earth's atmosphere. Therefore stars farther away than about 100 parsecs are beyond the distance limit for reliable parallaxes.