The differences in distance from Earth between the stars in any one distant galaxy are negligible compared to the vast distance to the galaxy itself. Thus, if two stars are in the same distant galaxy, any significant difference in the apparent brightness of those stars results from differences in how brightly each is actually burning. Therefore, we should be able to determine how a star's relative actual brightness correlates with other characteristics by studying stars in the same distant galaxy.
Which one of the following is an assumption the argument requires?The argument says that, for stars in the same distant galaxy, apparent brightness can be used to compare actual brightness. But the conclusion goes further: it says we can correlate actual brightness with other characteristics. For that to work, we must be able to observe at least some of those other characteristics from Earth.
That is the missing assumption.
(A) If two stars are in two different galaxies, it is not possible to determine whether or not they are approximately the same distance from Earth.
This is irrelevant. The argument is about studying stars in the same distant galaxy, not stars in different galaxies.
(B) If any two stars are in the same distant galaxy, differences in the elements each is burning will be detectable from Earth.
This is too specific. The argument does not require that differences in elements be detectable. It requires only that some
other characteristics be detectable.
(C) The stars in our own galaxy are not all approximately the same distance from Earth.
This is irrelevant. The argument concerns stars in distant galaxies, not stars in our own galaxy.
(D) There are stars in distant galaxies that have characteristics, other than brightness, discernible from Earth.
This is correct. If no other characteristics of stars in distant galaxies could be observed from Earth, then we could not determine how actual brightness correlates with those characteristics.
(E) If there are significant differences in how far away two stars are from Earth, then those stars will differ significantly in apparent brightness.
This is not required. The argument depends on the fact that stars in the same distant galaxy are approximately the same distance from Earth.
Answer: (D)