SUN'S APPARENT MAGNITUDE FROM A PLANETARY STAR
 --------------------------------------------
 John Pazmino
 NYSkies Astronomy Inc
 www.nyskies.org
 nyskies@nyskies.org 
 2012 January 27 initial 
 2020 November 13 current 

Introduction 
 ----------
    In my table of planetary stars in the NYSkies website I give for 
each star the brightness of the Sun as seen from that star's distance. 
This figure brings out the weakness of our whole Sun in the sky of 
extrasolar planets. He is usually among the dimmer stars of bare=eye 
vision. 
    This magnitude, as the text explained, was a matter of 
balancing the apparent and absolute magnitudes of Sun and star. 
    While the arithmetic was simple it did call for a quantity omitted 
from the table, the star's absolute magnitude. This comes from some 
external reference that the reader had to look up. 

From lightyears to parsecs 
 ------------------------
    On 27 January 2012 as part of routine maintenance of the table, I 
switched the star distances from lightyears to parsecs. Parsecs are 
the more common unit of distance, directa mente cited in planetary 
star announcements. As a side benefit they now let me skip the 
nuisance of converting the cited parsec distances into lightyears. 
    This at first seemed to be a trivial change, but one that you must 
carefully mind for manipulating the table's data. Programming code 
that treated the distance as lightyears must be altered to deal with 
parsecs. 
    There was an other boon, one span off from the Seminar of 16 
December 2011 on distance scales in the universe. One takeaway showed 
how the inverse-square rule of radiation turns into the distance 
modulus formula. This was a real treat for the astronomers who thought 
the two formulae were developed independently. 

Distance modulus
 -------------- 
    In the distance modulus equation the distance is in parsecs: 

    (dist mod) = Mapp - Mabs = 5 * log(parsecs) - 5 

    This equation is normally used to find the absolute magnitude from 
the apparent magnitude and distance but in the planetary table I 
realized it can be applied to find the apparent magnitude of the Sun 
at the star's distance. That is: 

    Mapp - Mabs = 5 * log(parsecs) - 5 

    Mapp = 5 * log(parsecs) - 5 + Mabs 

Here Mabs is the absolute magnitude of the Sun, +4.8 nearly enough. 
Plugging this into the gives a fetchingly simple formula: 

        Mapp = 5 * log(parsecs) - 5 + (+4.8) 
             = 5 * log(parsecs) - 0.2 


    +-----------------------------------------+ 
    | SUN'S Mapp AS SEEN FROM A DISTANCE STAR | 
    |                                         | 
    | Mapp = 5 * log(parsecs) - 5 +- 0.2      | 
    +-----------------------------------------+
 
    In addition to being quick and simple, this formula no longer 
needs an external figure, the star's absolute magnitude. The only 
ingredient, the star's distance in parsecs, is in the table.        

Conclusion 
 --------
    I rewrote the explanation to show how this equation works for 51 
Pegasi, the example from previous editions of the table. I then 
recomputed the Sun's magnitude for all of the stars, finding a few 
typos and small adjustments in the values. 
    The new table as at January 27th, 2012,  is mounted in the website at 

    www.nyskies.org/articles/pazmino/planstar.htm

The table is revised irregularly thenafter to update planet 
information and add new planetary stars.