How bright (L in watts)?
Luminosity at the source is determined from apparent brightness and distance (R).
Apparent magnitude (old way). We can see about 1,000 stars in Northern Hemisphere with naked eye. Hipparchus rated them from 1 to 6. A ‘1’ is 2.52 x brighter than a ‘2’, etc. We see things ranging in brightness from the sun at ‘-26′ magnitude to the faintest objects seen at about ’26’ magnitude.
Flux (new ‘apparent brightness’):
f (watts/m2) = L/4R2 = Power/unit area of sphere.
From R, the distance, we get L, the luminosity (watts of source).
How Big (r in meters)?
The Stephan-Boltzman Law gives the surface flux from surface temperature, T.
f(surface) = constant x T4 for a black body.
(Recall the black body spectrum provides T.)
Thus, the radius of a star r comes from,
f(surface) = L/4r2.
Flow of ideas: parallax–>R, R & f –>L, L & T–>r.