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short answer if things went a little different on the cosmic scale it could have harboured life.

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The Earth receives approximately $6.8\text{mW/m}^2$ of reflected sunlight from the moon (see below for details of how I calculated that). However, the sunlight is also absorbed by the moon and this raise the surface temperature. So the moon also emits thermal radiation towards the Earth (assuming the highest day time temperature of 400K, see comments below ...

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Assume the moon is at roughly the same distance from the Sun as the Earth and so receives the same amount of solar energy / area. Find the area of the moon facing the Earth (hint, it's roughly the area of the moon's disk). Multiply by the reflectivity of the moon (about 12%). But that power is reflected from the moon in all directions, so you need to ...

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To a first approximation distance covered by the Moon is the same as the Earth's, but you can also estimate the correction to first order. Assume both orbits are circular and in the same plane since any deviations will affect only smaller order corrections. Represent the position in the orbital plane as a complex number \$Z = R e^{2\pi i (t/Y)} + r ...

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