Deriving Distance Modulus: m - M = 5log(d/10)

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In summary, the conversation discusses the derivation of the distance modulus, which is represented by the equation m - M = 5log(d/10). This is related to the equation for absolute magnitude, m = m(sun) - 2.5log((L/L(sun)).(r(sun)/r)^2), and the subtraction of the two cancels out unknowns and sun values. The distance modulus is derived from the formula for radiant flux and the definition of five magnitudes being a difference of 100x. The solar versions of the equations are specific to the sun and not fundamental to the derivation. The conversation concludes with the reminder that absolute magnitude is the apparent magnitude at a distance of 10 parsecs.
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toam
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Distance modulus derivation

(I hope this is the correct subforum)


I was wondering if anyone can help me, I am hoping to show a derivation of the distance modulus

m - M = 5log(d/10)



It looks very similar to the m = m(sun) - 2.5log((L/L(sun)).(r(sun)/r)^2) so I'm assuming that they are somehow related but I'm not sure how exactly (ie: I can't find anything that says how - I'm guessing that the equation for absolute magnitude is similar and then the subtraction cancels out all the unknowns and sun values).
 
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The distance modulus is derived from the formula for radiant flux as a function of stellar luminosity and distance, as well as the definition of five magnitudes being a difference in observed brightness of 100x.

The solar versions of the formulae are just that, forumlae formulated with the sun in mind. They are not fundamental and will not serve any purpose in the derivation.
 
  • #3
Ahh yeah I worked it out now...


m1 - m2 = 2.5log(F1/F2)


Just needed to be reminded that absolute magnitude is what the apparent magnitude would be at a distance of 10 parsecs...
 

1. What is the purpose of calculating the distance modulus?

The distance modulus formula is used to determine the distance to an astronomical object, such as a star or galaxy, by measuring its apparent magnitude (m) and absolute magnitude (M). This allows scientists to study the size, structure, and evolution of these objects.

2. How is the distance modulus formula derived?

The distance modulus formula is derived from the inverse square law, which states that the apparent brightness of an object decreases with the square of its distance. By rearranging the equation for the inverse square law, we can solve for the distance to an object in terms of its apparent and absolute magnitudes.

3. Why is the logarithm used in the distance modulus formula?

The logarithm is used in the distance modulus formula because it allows for easier calculations and comparisons of very large numbers. In astronomy, distances can range from thousands to billions of light-years, and using logarithms helps to condense these numbers into a more manageable range.

4. Can the distance modulus be negative?

No, the distance modulus cannot be negative. The absolute magnitude (M) is always larger than or equal to the apparent magnitude (m), so the difference between them (m-M) will always be a positive value. Additionally, the logarithm of a negative number is undefined, so the distance modulus formula would not be valid if it resulted in a negative value.

5. Is the distance modulus formula accurate for all objects in the universe?

No, the distance modulus formula is only accurate for objects within the observable universe, which is limited by the speed of light. Objects that are beyond our observable horizon will have a different distance modulus due to the expansion of the universe. Additionally, the formula assumes that objects are not affected by factors such as dust or gas, which can alter their apparent magnitude.

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