Final answer:
Stars with the same absolute magnitudes emit the same amount of light, regardless of their distance from Earth. Absolute magnitude is a measure of intrinsic brightness and is understood through an astronomical equation relating brightness and magnitude differences.
Step-by-step explanation:
Two stars will have the same absolute magnitudes if they have the same intrinsic brightness, meaning they emit the same amount of light. Absolute magnitude is a measure of a star's luminosity and does not depend on its distance from us. This can be contrasted with apparent magnitude, which is how bright a star appears from Earth and can be influenced by distance and interstellar dust, among other factors. Apparent magnitude is what ancient astronomers like Hipparchus originally categorized, but today's astronomers have tools to measure the absolute magnitude, revealing the true brightness of stars despite their distances. To express the differences in brightness between stars with different magnitudes, astronomers use an equation that establishes relations such as a 2.5 magnitude difference corresponding to a brightness factor of 10, and a 0.75 magnitude difference corresponding to twice the brightness.