![]() A bright star (that is, one having large apparent brightness) is a powerful emitter of radiation (high luminosity), is near Earth, or both. However, as illustrated in Figure 17.8, two nonidentical stars can also have the same apparent brightness if the more luminous one lies farther away. Thus, two identical stars can have the same apparent brightness if (and only if) they lie at the same distance from Earth. We can therefore say that the apparent brightness of a star is directly proportional to the star's luminosity and inversely proportional to the square of its distance: Doubling the luminosity doubles the energy crossing any spherical shell surrounding the star and hence doubles the apparent brightness. Of course, the star's luminosity also affects its apparent brightness. Thus, the amount of radiation received by a detector (the source's apparent brightness) varies inversely as the square of its distance from the source. Tripling the distance reduces the apparent brightness by a factor of 3 2, or 9, and so on.įigure 17.7 As it moves away from a source such as a star, radiation is steadily diluted while spreading over progressively larger surface areas (depicted here as sections of spherical shells). Doubling the distance from a star makes it appear 2 2, or 4, times dimmer. Because the area of a sphere grows as the square of the radius, the energy per unit areathe star's apparent brightnessis inversely proportional to the square of the distance from the star. Think of the energy as being spread out over an ever-larger area and therefore spread more thinly, or "diluted", as it expands into space. The amount of radiation leaving the star per unit timethe star's luminosityis constant, so the farther the light travels from the source, the less energy passes through each unit of area. Moving outward, the radiation passes through imaginary spheres of increasing radius surrounding the source. ANOTHER INVERSE-SQUARE LAWįigure 17.7 shows light leaving a star and traveling through space. In this section, we discuss in more detail how these important quantities are related to one another. Apparent brightness is a measure not of a star's luminosity but of the energy flux produced by the star, as seen from Earth it depends on our distance from the star. However, when we look at a star, we see not its luminosity but rather its apparent brightnessthe amount of energy striking a unit area of some light-sensitive surface or device (such as a CCD chip or a human eye) per unit time. It is sometimes referred to as the star's absolute brightness. Luminosity is an intrinsic property of a starit does not depend in any way on the location or motion of the observer.
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