**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 (

*). We assume that we will have a way to find the absolute magnitude of stars. We will come back to that later.*

**m**Absolute magnitude is defined as the apparent magnitude at a distance of 10 pc. So the flux ratio between the flux (* F_{D}*) we receive at our distance

*and the flux at the standard distance of 10 pc (*

**D***) is*

**F**_{10}(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)

Substitution into the first formula gives

Taking the logarithm and re-arranging gives

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**:

Or

Take power of 10 on both sides

Or

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