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

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

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Answer 1 · 2016-04-26T04:39:07

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

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 $10^{s}$ $10^s$ parsec, where s is given by

s = 1 + 0.2 (m - M).

This could be modified as

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

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

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

$M_{1} - M_{2} = 100^{\frac{1}{5}} (\frac{L_{1}}{L_{2}})$ $M_1-M_2=100^(1/5)(L_1/L_2)$ , L being luminosity, with L = 1 for Sun.

For comparison with Sun, $M_{1} = 4.83, m_{1} = - 26.74 and L_{1} = 1$ $M_1=4.83, m_1=-26.74 and L_1=1$ .

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

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

Reference: http://window2universe.org/kids_space_stars_dist.html.

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

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

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