In the early years of the twentieth century, astrophysicists turned their attention to a special category of stars, known as Cepheid (造父变星) variables. A variable star is one whose apparent brightness changes from time to time. Among some variables, the change in brightness occurs so slowly as to be almost imperceptible; among others, it occurs in sudden, brief, violent bursts of energy. Cepheid variables have special characteristics that make them a useful astronomical tool. It was Henrietta Leavitt, an astronomer at the Harvard Observatory, who first examined the Cepheid variables in detail. She found that these stars vary regularly in apparent brightness over a relatively short period of time—from one to three days to a month or more. This variation in brightness could be recorded and precisely measured with the help of the camera, then still a new tool in astronomy. Leavitt also noticed that the periodicity of each cepheid variable—that is the period of time it took for the star to vary from its brightest point to its dimmest, and back to its brightest again—corresponded to the intrinsic or absolute brightness of the star. That is, the greater the star’s absolute brightness, the slower its cycle of variation. Why is this so The variation in brightness is caused by the interaction between the star’s gravity and the outward pressure exerted by the flow of light energy from the star. Gravity pulls the outer portions of the star inward, while light pressure pushes them outward. The result is a pulsating in-and-out movement that produces increasing and decreasing brightness. The stronger the light pressure, the slower this pulsation. Therefore, the periodicity of the Cepheid variable is a good indication of its absolute brightness. Furthermore, it is obvious that the more apparent brightness of any source of light decrease the further we are from the light. Physicists had long known that this relationship could be described by a mathematical formula. If we know the absolute brightness of any object—say a star—as well as our distance from that object, it is possible to use the inverse square law to determine exactly how bright that object will appear to be. This laid the background for Leavitt’s most crucial insight. As she had discovered, the absolute brightness of a Cepheid variable could be determined by measuring its periodicity. And, of course, the apparent brightness of the star when observed from the earth could be determined by measurement. Leavitt saw that with these two facts and the help of the inverse square law, it would be possible to determine the distance from earth of any Cepheid variable. If we know the absolute brightness of the star and how bright it appears from the earth, we can tell how far it must be. Thus, if a Cepheid variable can be found irt any galaxy, it is possible to measure the distance of that galaxy from earth. Thanks to Leavitt’s discovery, astronomical distances that could not previously be measured became measurable for the first time. Which of the following did Leavitt’s work provide astronomers with the means of determining