Benzoate said:Homework Statement
What is the combined apparent magnitude o a binary system consisting of two stars of apparent magnitudes 3.0 and 4.0
Homework Equations
m-n=2.5 log(f(m)/f(n))
The Attempt at a Solution
I know m= 3 and n=4 ,or vice versa. I'm not sure what this problem means by combined magnitude. Do they mean I should add m and n together?
dynamicsolo said:Refer to your other post on the magnitude of a variable star for the discussion on the magnitude system.
What you want to do is convert your magnitudes to intensities, since the intensities of the two stars can be added to give the total intensity (or brightness or power) of the pair. This leaves the question of what to use for a basis. You can pick any reference magnitude, say, zero, and compute the intensity of each star relative to the intensity of a zero-magnitude star. You would then add the intensities of each star and now compare the total intensity to that of the zero-mag star to find the magnitude of the pair.
Benzoate said:Is the equation for intensity, f(n)/f(m)=100^(m-n)/5
Benzoate said:can I tlet my reference magnitude be 0 and magnitude of m(1) is 3 and for the second intensity, reference magnitude n is still zero and magnitude of m(2) is 4. Once i calculated the each of the intensities for the two stars , I proceed to add the two intensities of both stars?
The formula for calculating the combined apparent magnitude of two stars is M = -2.5 log10(F1 + F2), where M is the combined apparent magnitude and F1 and F2 are the individual fluxes of the stars.
The combined apparent magnitude takes into account the total amount of light emitted by both stars, while the individual magnitudes only measure the brightness of each star on its own. The combined magnitude may be brighter or dimmer than the individual magnitudes, depending on the relative magnitudes and distances of the stars.
Yes, the combined apparent magnitude of two stars can be negative if the combined flux is very large. This would indicate that the stars are very bright and may be close together in the sky.
The flux values used in the calculation should be the apparent fluxes of the stars, meaning the amount of light that reaches Earth's atmosphere. This can be determined using a telescope and photometer to measure the stars' brightness.
No, the combined apparent magnitude is not enough information to determine the distance between the stars. Other factors such as the individual distances and relative positions of the stars must also be taken into account.