# Binary star system and Apparent magnatudes

by AstroPhys
Tags: apparent, binary, magnatudes, solved, star
 P: 4 I was asked this questing in my tetbook and can't figure out how to do it. Suppose there is a binary system made up of two identical stars, each with an apparent magnitude of +4.1. However, from our 40 cm telescope they appear as one star, i.e., they are unresolved. What would be the apparent magnitude of this star?" I figure that the two stars apparent magnatudes must add together to get this magnatude somehow but I am not quite sure how, because 100 magnitude 6 stars = a magnitude 1 star. is there some simple formula to figure this out.
 Admin P: 21,915 There should be a formula for relating N stars of different magnitudes to one effective magnitude.
 P: 4 Yes, you would think so, just that i can't find any thus far.
 Admin P: 21,915 Binary star system and Apparent magnatudes If you can relate intensity to magnitude, that's a start. The two stars in a binary system are at the same distance. Do you have a formula for intensity and magnitude, or size and intensity with magnitude? If two stars have the same magnitude, then together they would have twice the intensity as either one. If you had one star that doubled in intensity, what would happen to the magnitude? Also, there should be a formula relating apparent and absolute magnitude.
 Emeritus Sci Advisor PF Gold P: 4,980 There are a couple of ways to do this (I say a couple they are the same way effectively). One could remember that a difference in magnitude of 5 is the same as a factor of 100 in brightness. So you can work from there to find what difference in magnitude gives double the brightness. Surely you have been given some sort of formula in your notes relating to apparent magnitude?