Quintuple Star System

[radtech497]

A method I have used is to first find the minimum distance separating the star from the planet, by taking the separation distance between the stars and subtracting the planet's apoastron distance (remembering to keep the distance in Astronomical Units). Then square that distance, take the inverse of that squared number, and multiply the inverse together with the luminosity of the star in question and the value of the Solar Constant (1361 or 1366 Watts per square meter, depending on which source you prefer). Then, divide that number (in W/m^2) by four, and multiply that by (1 - planetary albedo). Divide that number by 5.670373e-8, and finally, take the fourth root to find the equilibrium temperature in Kelvin.

If you, like me, want to also find a minimum contribution from that star, simply add the planet's apoastron distance to the distance separating the two stars, and repeat the above.

Hope this helps,

Radtech497