-1
y = brightness in percentage
x = apparent magnitude

What is a formula that would result in the graph below, with y representing the brightness in percentage and x the apparent magnitude (also accounting for negative values)?

enter image description here

To clarify: Each decrease by 1 in apparent magnitude will require the star to have only 100/fifth root of 100 of the illumination as it used to be

Galactic
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  • If you know the relation between apparent magnitude and brightness as in your clarification, what stops you from finding the equation? – Ross Millikan Apr 05 '20 at 00:44
  • Actually, this question is wrong. A decrease of 1 is equal to the star having a (1/fifth root of 100) decrease in brightness. – Galactic Apr 05 '20 at 00:49
  • Your data is pretty close. $100^{0.2} \approx 2.511$, not far off $2.5$ – Ross Millikan Apr 05 '20 at 02:10
  • I knew that it would not be much different from the actual value at low values of x, but a significant difference would be found at high values that I will extend the formula to. – Galactic Apr 05 '20 at 03:42

3 Answers3

0

The function

$$y = -22 + 122/x$$

works fine.

enter image description here

David G. Stork
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$$B(M)= 250(0.4)^{M} $$

obtained by fitting $y=kb^x$ using the points $(1,100)$ and $(2,40)$

WW1
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The definition of magnitude in astronomy is that an increase of $1$ in magnitude is a factor $2.5$ reduction in brightness. So if $m$ is the magnitude, we have $$y=100\cdot 2.5^{1-x}$$

Ross Millikan
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