# How can we find the distance to a star that is too distant to have a measurable parallax?

##### 1 Answer
Apr 26, 2016

If m is visual magnitude of a star, M is the absolute magnitude and d its distance from us, $M = m - 5 \log \left(\frac{d}{10}\right)$.

#### Explanation:

Brightness faints in proportion to square of the distance.

Brightness is measured from light from the star.

With the notations m for visual magnitude, M for absolute magnitude and d for the distance of the star from the observer,
the distance is ${10}^{s}$ parsec, where s is given by

s = 1 + 0.2 (m - M).

This could be modified as

$M = m - 5 \log \left(\frac{d}{10}\right)$,

using $d = {10}^{s} , \mathmr{and} s o , s = \log d .$.

Comparison with other stars is also useful. The formula used is

${M}_{1} - {M}_{2} = {100}^{\frac{1}{5}} \left({L}_{1} / {L}_{2}\right)$, L being luminosity, with L = 1 for Sun.

For comparison with Sun, ${M}_{1} = 4.83 , {m}_{1} = - 26.74 \mathmr{and} {L}_{1} = 1$.

Pogson's ratio ${100}^{\frac{1}{5}} = 2.51193$, nearly.

Madras ( now Chennai) based Pogson/s research in 19th century is quite relevant..

I think that I have paved the way for further studies, by the interested readers. .

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