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The difference of apparent (m) and absolute (M) magnitudes of an object is called "distance modulus", which is related to the distance $d$ to the object in parsecs with equation

$$m - M = 5 \log \Big(\frac{d}{10 \ \textrm{pc}}\Big) \tag{1}.$$

I'm trying to understand why $m - M$ is called "distance modulus". The word "distance" makes sense, because there is a distance d term in Eq. (1). But what is "modulus" word doing there? In math, modulus means the remainder after division of two numbers. For example, modulus of 5 and 3 is 2.

Another meaning of "modulus" is length of a vector. I don't see how either of these two meanings can be relevant to Eq. 1.

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According to Oxford Dictionary of English, the word "modulus" is the diminutive of the Latin modus, meaning measure (modus, in turn, comes from Proto-Indo-European mod-os, Nocentini & Parenti 2010.

Hence, the distance modulus is a "measure of distance", just like the modulus of a vector is a way of measuring its size, and Young's modulus is a way of measuring the stiffness of a material.

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