-5

I know what 2.5 stand for in $2.5 \log_{10}$, but what does the number 5 in $5\log_{10}$ stand for and what application does it have.

Thus, why is the number a five and not a four, or a three, or something else?

2.5 stands for the logarithmic step in apparent magnitude. There must be something similar for the 5 in 5log10. Does it stand for the logarithmic step in absolute magnitude?

Constantthin
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    Check the definition of magnitudes and the distance modulus. 5 stands for the number 5. – AtmosphericPrisonEscape Nov 09 '21 at 15:08
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    I’m voting to close this question because it belongs on Mathematics SE. – WarpPrime Nov 09 '21 at 15:12
  • 2.5 stands for the logarithmic step in apparent magnitude. There must be something similar for the 5 in 5log10. Does it stand for the logarithmic step in absolute magnitude? – Constantthin Nov 09 '21 at 15:16
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    You need to provide details about where these calculations are used. Usually, an equation is something = 5Log10(of something else). What are "something" and "something else"? As presented, 2.5 and 5 are multipliers. That is all we can say without knowing the full context. – JohnHoltz Nov 09 '21 at 15:34
  • @JohnHoltz OP is most definitely referring this answer to their previous question. – BMF Nov 09 '21 at 16:02
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    Assuming it refers to the linked posting: It's an empirical formula and 5 stands for the number 5 which happens to match whatever relation is explained in the study it comes from. – planetmaker Nov 09 '21 at 19:20
  • @Planetmaker. Usually values in a formula comes from somewhere. Is 2.5 also empirical in 2.5log10 and an accidental match with the step in apparent magnitude? Or does it actually derive from there? – Constantthin Nov 10 '21 at 03:12
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    The relation between flux and magnitude is defined (5 magnitudes is a factor of 100 in brightness) and does not follow from anything physical. – planetmaker Nov 10 '21 at 08:06
  • @fasterthanlight "because it belongs on..." is still not a close reason. If one wants to close it as off-topic here one explains why it's off-topic here. As there are already two good Astronomy answers I'm voting to keep open. – uhoh Nov 14 '21 at 10:14

2 Answers2

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A magnitude is defined as $-2.5\log_{10}$ of a flux. But flux scales as the inverse square of a distance.

$$-2.5\log_{10}\left(\frac{k}{d^2}\right) = 5\log_{10}(d) -2.5\log_{10}(k)$$

benrg
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ProfRob
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This appears to be a question directed at an answer to a previous question by the OP. https://astronomy.stackexchange.com/a/47296/26216

The 5log_10(...) appears to just be a multiplier the author of the paper cited in the aforementioned answer found to describe the visible magnitude of Neptune. Sorry, but that's probably the best answer you'll get... There may be something special about its formulation, or it could just be a curve that best fitted the data.

BMF
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