A certain mystery of mine.

Discussion in 'Astronomy, Exobiology, & Cosmology' started by HDE226868, Jun 20, 2003.

  1. HDE226868 Registered Member

    Messages:
    3
    This being my first post I thought I'd just say a little about myself first for the benefit of all. I'm 24 and I've studied astronomy as a hobby for something like 20 years. Over the past two years I've taught myself a bit of math and physics and I would say my main focus in Astronomy is on Stars, their composition, evolution and lifetimes.

    Anyway there is a fact which has puzzled me for sometime, and no one has yet explained it in a way I've been able to grasp. I discovered this rule whilst doing some work on determining the Visual Comfort Zone (VCZ) of various stars. I say visual because it is finding the area at which a star, of any type, would appear to be magnitude -26.72 in the sky (as it is on Earth). Anyway, here is what happened.

    I've found that one can find the distance, in parsecs (which one must convert to AU) from a star at which it will appear at a given magnitude with the equation: 10^((Mv-m-5)/-5)=D. In this case Mv is the absolute magnitude and m is the apparent magnitude. The equation seems to work fairly well, however, there is another, simpler way to come up with a similar result.

    By using the equation 2.5^(4.85-m) where m is the absolute magnitude of a star, one can find the stars brightness relative to the sun. The significance here is, if one takes the Brightness value given above, and finds the square root, the result is the distance from the star, in AU, where it would roughly appear to be magnitude -26.72. The error in the root(B) formula increases as the absoulte magnitude of the star increases.

    Example Data: Star, mag: 4.16

    10^(4.16+26.72-5)/-5)=.00000666807 Parsecs.
    .00000666807*204264.81=1.3620516 AU.

    2.5^(4.85-4.16)=1.88182228 Sol
    root(1.88182228)=1.371795276 AU.

    So as you can see the results are quite similar, with a difference of only .009743696 AU. That translates to being off by about 1,457,636.185 Km. Not much in a cosmic sense.

    Now I've heard it is some sort of inverse square law at play here, but as I've said no one has actually said WHY it should be so, can any of you lend a hand in this endeavour? Thanks!
     
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  3. eburacum45 Valued Senior Member

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    I suspect this difference is due to the radius of the sun- most of these formulae work best for point sources, which the sun certainly is not.
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  5. cjmowery Registered Senior Member

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    37
    Star size

    Thats a good point, considering there are stars out there that are 1000 of times for volumous than our own. That can definately throw your numbers off. Since the visible light is from the surface, not a point sorce.
     
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