To calculate the distance modulus (m-M):
\[ m-M = 5 \cdot \log_{10}\left(\frac{r}{10}\right) \]
Where:
A distance modulus is defined as the total distance to an object with respect to its apparent magnitude and absolute magnitude. Distance modulus is used to understand the distance of extragalactic objects that are extremely far away in relative terms.
Let's assume the following value:
Using the formula:
\[ m-M = 5 \cdot \log_{10}\left(\frac{100}{10}\right) = 5 \cdot \log_{10}(10) = 5 \cdot 1 = 5 \]
The distance modulus is 5.
Let's assume the following value:
Using the formula:
\[ m-M = 5 \cdot \log_{10}\left(\frac{1000}{10}\right) = 5 \cdot \log_{10}(100) = 5 \cdot 2 = 10 \]
The distance modulus is 10.
