My source is a paper by Philip Massey et al 2006 ApJ 646 1203-1208, who believe that VY CMa has been overrated in regard to its size and luminosity, and underrated in regard to its effective temperature.
VY Canis Majoris
T = 3650 K
R = 600 solar radii = 4.176e11 meters
Ï = 5.6704e-8 W m⁻² K⁻⁴
L = 4Ï Ï R² T⁴ = 2.206e31 watts
L/Lsun = 57646
м = 4.75 â 2.5 log(L/Lsun) = â7.15
d = 1 light year = 9.4607e15 meters
Apparent angular diameter, D, of VY CMa from a distance of 1 light year.
D = 2 Arctan(R/d) â 18 arc seconds
That's about the same angular size as Mars at a typical opposition.
Apparent magnitude, m, of VY CMa from a distance of 1 light year.
d₀ = 3.0856e17 meters
m = м + 5 log (d/d₀) = â14.7
It would be 7 times brighter than the full moon.