A Bit of Maths - Intensity Ratio and Distance Modulus

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A Bit of Maths by Lesa Moore

• Intensity ratio and magnitude difference
• Distance modulus and distance

Intensity ratio and magnitude difference

• The intensity ratio, I_A/I_B, is equal to 2.512 raised to the power of the magnitude difference, m_B - m_A:

I_A/I_B = 2.512^{(m_B - m_A)}

• By taking base 10 logs of both sides and rearranging, the formula may be solved for the magnitude difference:

m_A - m_B = 2.5 log (I_B/I_A)

• Sample results from this relationship are given in the following table.

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Distance modulus and distance

• The distance modulus relates the distance (d) to a star to the difference between its apparent magnitude (m) and its absolute magnitude (M_V). 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-M_V is called the distance modulus.
• The distance to a star (in parsecs) may be derived from the following equation.

d = 10 ^{(m - M_V + 5)/5}

• Some sample distances derived from distance moduli are shown in the following table.

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Author: Lesa Moore, 26th July 2017