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Distance Modulus
This page requires working with logarithms.

Now we need to find out how to calculate distance from absolute magnitude (M) and apparent magnitude (m). We assume that we will have a way to find the absolute magnitude of stars. We will come back to that later.

Absolute magnitude is defined as the apparent magnitude at a distance of 10 pc. So the flux ratio between the flux (FD) we receive at our distance D and the flux at the standard distance of 10 pc (F10) is

form2

(this derives from Pogson’s ratio, or the definition that 5 units in magnitude correspond with a factor of 100 in flux).

Each flux can be expressed in Luminosity (L) from the Inverse Square Law as (units for distance are parsec)

form3

form4

Substitution into the first formula gives

form5

Taking the logarithm and re-arranging gives

form6

with D in pc.

This is the Distance Modulus , the relationship between apparent and absolute magnitude and distance.

Apparent magnitude m is what we observe. Provided that we have a way to find absolute magnitude, we can calculate the distance from the Distance Modulus.

 

Calculate an example

Question:
A star has an absolute magnitude of -1.0 and an apparent magnitude of +14.0. What is the distance to that star?

Answer:

form7

Or

form8

Take power of 10 on both sides

form9

Or

form10

Hence the star is at a distance of 10,000 parsec.

 

 

 



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