Astronomy 106

Magnitude-Distance Formula

19. Magnitude-Distance Formula
    

    This formula relates the absolute magnitude of a star (how bright it really is), the apparent magnitude (how bright the star appears at Earth), and the distance to the star in parsecs. The formula reads:

    

    If one knows the distance to a star and one of the magnitudes (either apparent or absolute), one can use the formula to determine the other magnitude.
    

    Example:
    

    A star is 400 parsecs away and has an absolute magnitude = 2. How bright would this star appear to an observer on Earth? We must solve for the apparent magnitude. The formula can be rewritten to read:

    

    Your calculator should enable you to take the logarithm. Typically log is abbreviated as simply ``log.'' Thus log(400) = 2.60. Inserting this into the formula gives:

    

    Such a star would appear at = 10.

    One can also invert the formula to solve for the distance to the star given the two magnitudes. This is given in the text as:

    

    Example:
    

    A star has absolute magnitude 3 and apparent magnitude 12. How far away is this star? The argument of the distance equation (the exponent) is = (12 - 3 + 5)/5 = 14/5 = 2.8. Taking = 630 pc.