So, the final formula is:

  Power = (p ^ m) * F * (c / λ) * π * r²

where:

p - Pogson's ratio [] (dimensionless)

m - magnitude [] (dimensionless)

F - flux [J / (s * cm² * Hz)]

c - speed of light [cm / s]

λ - wavelength [cm]

r - Earth's radius [cm]

π - pi [] (dimensionless)

Checking units:

  Power = ([] ^ []) * [J / (s * cm² * Hz)] * [cm / s] * [1 / cm] * [] * [cm²]
  Power = [J / (s * cm² * Hz)] * [1 / s] * [cm²]
  Power = [J / (s * cm² * Hz)] * [Hz] * [cm²]
  Power = [J / s] * [(Hz * cm²) / (Hz * cm²)]
  Power = [J / s] = [W]

No problems here.

Using our values:

p = 2.512

m = 4

F = 3.64E-27 [J / (cm² * Hz * s)]

c = 3E10 [cm / s]

λ = 5.5E-5 [cm]

r = 6E8 [cm]

pi = 3.14

we obtain:

  Power = (2.512 ^ 4) * 3.64E-27 * (3E10 / 5.5E-5) * 3.14 * (6E8)²
  Power = 8.94E7 [W]

So… pretty close and the difference comes down mainly to rounding. Other than that, under your assumptions, I see no problems with reasoning or method. Sorry for taking so long to respond, though.

Hey, what're you up to just after January 28th of 2024? Asking for a friend.

You need to double it, that's when Centaurs would get your message.