A Bit of Maths - Intensity Ratio and Distance Modulus
A Bit of Maths by Lesa Moore
- The intensity ratio, IA/IB, is equal to 2.512 raised to the power of the magnitude difference, mB - mA:
IA/IB = 2.512(mB - mA)
- By taking base 10 logs of both sides and rearranging, the formula may be solved for the magnitude difference:
mA - mB = 2.5 log (IB/IA)
- Sample results from this relationship are given in the following table.
- The distance modulus relates the distance (d) to a star to the difference between its apparent magnitude (m) and its absolute magnitude (MV). The V subscript refers to "V" band, or central wavelength for visible observations (as opposed to the blue or red end of the optical spectrum).
- m-MV is called the distance modulus.
- The distance to a star (in parsecs) may be derived from the following equation.
d = 10 (m - MV + 5)/5
- Some sample distances derived from distance moduli are shown in the following table.
Author: Lesa Moore, 26th July 2017