Hi-
I'm a newbie with a new Celestron 8 se. Fascinated with space since I was a kid. Took it out for the first time the other night and was ecstatic I saw M42 and Uranus on my first night. Couldn't see the Crab Nebula, though (Bortle 4)
I'm also an engineer and do a lot of math.
Assuming Betelgeuse and the star that formed the Crab Nebula are the same size:
Area of the surface of a sphere is 4 * pi * r^2.
So if the energy is uniformly radiated to the surface of the sphere, each unit of area will recieve an amount of radiation inversely proportional to (4*pi*d^2) where d is the distance to the star, or 1/(4*pi*d^2)
Doing the math:
Big B = 1 / (4 * pi * 6500 * 6500) = 1.88349045079e-9
Crab Nebula = 1 / (4 * pi * 650 * 650) = 1.88349045079e-7
Therefore, Betelgeuse should give us about 100 times the brightness/energy of the Crab Nebula based on the distance.