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

[toam]

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).

 

[ek]

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.

 

[toam]

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...