Luminosity of Neowise So, I have been trying to figure out the bolometric luminosity of the comet C/2020 F3 (Neowise) on the 22nd of June, 2020. At that time, Neowise was $1.4$ AU away from Earth and had an apparent magnitude of $m=3$. By using the formula $$m=-2.5log\Bigl(\frac{F}{F_O}\Bigl)$$ and $$F=\frac{L}{4\pi D^2}$$ where $F_0$ is the flux of Vega, $F$ is the flux of the comet, $D$ is the distance from Earth to the comet. I found that the bolometric luminosity, $L$ ,of the comet Neowise was around $7.45\cdot10^{14}$ watts when it was $1.4$ AU away from Earth. However, on the 22nd of June, Neowise was also $0.4$ AU away from the Sun. I have tried to use the flux from the Sun at this distance to determine the luminosity of Neowise again. I have found the flux from the Sun at that distance to be $8488.26$ $Wm^{-2}$ using the above formula for flux, but now using $D=0.4 AU$. After that I thought of calculating the luminosity by using flux from the sun times the area of Neowise. Assuming the nucleus of Neowise has a diameter of $5 km$, and assuming that the comet is fully illuminated,
should I assume that the nucleus of Neowise is spherical or circular? And why should the 2 luminosities be different?
I think I get it - you are trying to calculate a luminosity based on some assumption about how much light is reflected/scattered from the Sun towards the Earth - hence the relevance of the flux from the Sun at the comet.
I think it's very hard to adopt this approach. There is uncertainty about what is the appropriate geometry to use for the comet and how the reflection/scattering should be treated. It is doubtful that assuming a comet diameter of 5 km will be appropriate because I would have thought most of the light we see is scattered from a coma around the comet, not from the surface of the comet itself.