How to Calculate Apparent Magnitude/Brightness of Planets from Within the same Solar System

I'd like to be able to determine the appearance of the night sky from an Earth-like planet, in a solar system with multiple other planets, moons, and other bodies. Here on Earth, we can directly measure the apparent magnitude of a body simply through observation, but that's obviously impossible for fictional planets.

I understand that the luminosity of the primary star, the albedo and radius of the object being observed, and the range of distances between the observer and the object (which will vary, because orbits) are the primary factors in determining apparent magnitude -- it's the precise mathematical relationships between these factors which is eluding me.

For illustrative purposes, here is an excerpt from the setup of my solar system, with each planet's semi-major axis in AU, bond albedo, and radius in Earth radii listed. I'm including one planet closer to the star than our observer, one planet further out-system but relatively close, and one rather distant planet.

Sun's Luminosity: 2.248 (relative to Sol's 1)

• Planet B: Semi-Major Axis: 0.47 AU, Bond Albedo: 0.93, Radius 4.29: Earth radii
• Planet E (observer's location): SMA: 2.178
• Planet F: SMA: 3.87, BA: 0.21, R: 0.89

If it helps/matters: Planet B is an in-system ice giant, a.k.a. "Hot Neptune," Planet E is a slightly larger Earthlike planet with a comparable atmosphere, and Planet F is a magnesium-silicate terrestrial.

I'd like to be able to figure out what the apparent magnitude of Planets B and F when observed from Planet E, and how that result was reached so that I can replicate the process for the other planets and bodies within the system. I will also happily absorb any and all tangents on planetary apparent magnitude in general. Thank you in advance!

posted over 4 years ago

A.E. Stephenson‭

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