this is a math problem on my homework

A star is basically a ball of very hot gas in constant motion. From a distance it is a point of light, with the exception of the sun, our nearest star. The sun has a generally uniform appearance so its rotational symmetry could be considered of infinite order. But if its granular appearance is considered then there would be no symmetry since there is so much randomness.

Its magnitude (brightness) is -27, while the full moon's magnitude is -13. The brighter an object the more negative is its magnitude. So faint stars have positive magnitude. A step of 5 in the magnitude between two stars is a change in brightness by a factor of 100, so a step of 1 is 100^(1/5). A piano keyboard can be used as an analogous system. The lower notes correspond to brighter stars while the higher notes correspond to dimmer stars. A piano keyboard is logarithmic as is the magnitude system. To use the magnitude system we need to define a reference magnitude. Middle C on a piano could represent magnitude 0. The note below would be a star with magnitude -1, or roughly 2.5 times brighter than a star with magnitude 0. The note above would be about 2.5 times dimmer. A star with magnitude -5 is a hundred times brighter than a magnitude 0 star, magnitude 5 100 times dimmer. The magnitude is not restricted to integers.

The formula apparent magnitude, M=M0-2.5log(I[m]/I[m0]) applies, where I denotes measurable intensity, M0 is the reference magnitude (star with magnitude 0). Absolute magnitude requires knowledge of a star's distance. To determine the apparent magnitude of a star you would need to measure the brightness of a reference object (e.g., the moon) using, for example, power per unit area, then use the same units to measure the star's brightness. Knowing the magnitude of the moon's brightness, M0=-13, plug the values into the equation to find M.

by Top Rated User (813k points)