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    Hi, i was just running through the proof for the relationship between apparently magnitude and absolute magnitude and im a bit confused....

    in my book it said


    m = -2.5lgI + constant

    and then goes to

    Ia/Ib = 100^[(mb-ma)/5]

    Ia = intensity of star a
    Ib= intensity of star b

    ma= apparent magnitude of star a
    mb = apparent magnitude of star b


    Now i can get from the first line to the second line but only if i ignor the constant?? cant anyone explain why this is... im confused as to what happens to the constant

    cheers

    Soph
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    (Original post by kingmonkeywoman)
    m = -2.5lgI + constant

    and then goes to

    Ia/Ib = 100^[(mb-ma)/5]
    I am guessing that the first line is in fact
    m = -2.5logI + k
    hence
    m - k = -2.5logI
    10^(m-k) = I^(-2.5)

    10^(mb - k)/10^(ma - k) = (Ia /Ib )^(-2.5)
    10^(mb - k - ma + k) = (Ia /Ib )^(-2.5)
    10^(mb - ma) ^(-2/5) = Ia /Ib
    100^(mb - ma) ^(-1/5) = Ia /Ib
    100^([mb - ma]/5) = Ia /Ib
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    Hey, thanks for you reply, yeah i understand all the logs bit and stuff, i just dont know what the constant is ?? im guessin from what u wrote there that the constant must be the same for all stars?? i just presumed it would change with distance?

    Soph
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    (Original post by kingmonkeywoman)
    Hey, thanks for you reply, yeah i understand all the logs bit and stuff, i just dont know what the constant is ?? im guessin from what u wrote there that the constant must be the same for all stars?? i just presumed it would change with distance?

    Soph
    Funny thing about constants. They are constant.
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    Personaly id say its not funny, but u know, i obviously dont share ur sense of humour on that one... i was just wondering because in physics they usualy specify constants and i thought theire might be a reason why they hadnt. Obviously they just decided to write constant instead of givin a name or number this time though.
    U got any idea how they got to the -2.5lgI + c bit in the first place cos they dont seem to tell us that bit either?
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    TBH the words apparent magnitude and absolute intensity make absolutely no sense what so ever to me. In fact the equation isn't even dimensionally possible. If you are taking ALevel Physics, then I don't think you need to know anything about this malarky. You just need to learn to play with equations to give the right answer.

    The reason for the difference may lie in the fact that your eye detects light in a logrithmic scale (you need 10 times more light or something for it to seem twice as bright), like sound. The constant may just be factoring background effects (ie light that got scattered in the atmosphere and appears to come from the star). The other constant[-2.5] is invariably a constant found by "experiment".
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    ok cheers, yeah it is a bit of a weird equation i agree. I think its somin to do with a difference of one magnitude means a ratio of 2.5 in intensity... but when i rearange it i get I ^-2.5 = 10^m which doesnt really make sense because ud expect it to be (2.5^ something) if its a ratio... if that makes sense
    never mind, cheers for ur help

    Soph
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    (Original post by Mehh)
    TBH the words apparent magnitude and absolute intensity make absolutely no sense what so ever to me. In fact the equation isn't even dimensionally possible. If you are taking ALevel Physics, then I don't think you need to know anything about this malarky. You just need to learn to play with equations to give the right answer.

    The reason for the difference may lie in the fact that your eye detects light in a logrithmic scale (you need 10 times more light or something for it to seem twice as bright), like sound. The constant may just be factoring background effects (ie light that got scattered in the atmosphere and appears to come from the star). The other constant[-2.5] is invariably a constant found by "experiment".
    Yes. The original magnitude scale developed by the Greeks went from 1-6 with 1 being brightest. However, now we use the same scale, but there is a ratio of ~2.5 in light intensity for each one step of the magnitude scale, because magnitude 1 stars are 100x brighter than magnitude 6 stars.

    We have to know this for OCR Physics Cosmology, ie. the derivation for apparent magnitude given absolute magnitude. Apparent magnitude enables proper comparisson of stars by removing the effect of distance on intensity of radiation received.
 
 
 
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