If The blue giant and the red dwarf have the same apparent diameter from the planet, the blue giant will provide essentially all of the warmth and the light for the planet.

This is simple to prove as the spherical angle of the 2 suns in the same, the difference in perceived luminosity will be proportional the 4th power of the surface temperature. The blue giant will most likely be 12-40 thousand Kelvin, and the red dwarf will be around 4000 K. The blue giant will be most likely be about 80-1000 times as bright (and hot) as the red dwarf.

The planet is correctly speaking a planet, not a moon.

To make the brightness and warmth contribution identical, the dwarf would have to have an apparent area 80-1000 times that of the blue giant, or square root of 80 to square root of 1000 times that of the blue giant.

If The blue giant and the red dwarf have the same apparent diameter from the planet, the blue giant will provide essentially all of the warmth and the light for the planet.

This is simple to prove as the spherical angle of the 2 suns in the same, the difference in perceived luminosity will be proportional the 4th power of the surface temperature. The blue giant will most likely be 12-40 thousand Kelvin, and the red dwarf will be around 4000 K. The blue giant will be most likely be about 80-1000 times as bright (and hot) as the red dwarf.

The planet is correctly speaking a planet, not a moon.

To make the brightness and warmth contribution identical, the dwarf would have to have an apparent area 80-1000 times that of the blue giant, having a diameter of square root of 80 to square root of 1000 times that of the blue giant.

If The blue giant and the red dwarf have the same apparent diameter from the planet, the blue giant will provide essentially all of the warmth and the light for the planet.

This is simple to prove as the spherical angle of the 2 suns in the same, the difference in perceived luminosity will be proportional the 4th power of the surface temperature. The blue giant will most likely be 12-40 thousand Kelvin, and the red dwarf will be around 4000 K. The blue giant will be most likely be about 80-1000 times as bright (and hot) as the red dwarf.

The planet is correctly speaking a planet, not a moon.

If The blue giant and the red dwarf have the same apparent diameter from the planet, the blue giant will provide essentially all of the warmth and the light for the planet.

This is simple to prove as the spherical angle of the 2 suns in the same, the difference in perceived luminosity will be proportional the 4th power of the surface temperature. The blue giant will most likely be 12-40 thousand Kelvin, and the red dwarf will be around 4000 K. The blue giant will be most likely be about 80-1000 times as bright (and hot) as the red dwarf.

The planet is correctly speaking a planet, not a moon.

To make the brightness and warmth contribution identical, the dwarf would have to have an apparent area 80-1000 times that of the blue giant, or square root of 80 to square root of 1000 times that of the blue giant.