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

1 Answer
A. S. Adikesavan
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 (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# parsec, where s is given by

s = 1 + 0.2 (m - M).

This could be modified as

#M = m - 5 log (d/10)#,

using #d = 10^s, and so, s = log d.#.

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

#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#.

Pogson's ratio #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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