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Lets say you have a planet that is like Earth. But it's a moon orbiting around a larger gas or ice giant. How would this affect plant life on the near and far sides, how would they be different from one another?
Or if you have a planet with multiple moons, would that affect plant life? Could plant life get energy from the reflected light if it is bright enough?
In a word: no. Photosynthesis needs a far greater photonic energy density than that reflected from a solid object. In fact, a large host planet or multiple large moons would have more effect on plant life with gravitational effects like tides, rather than offering light. There are certain types of simple photosynthetic life like algeas that use the minute amounts of moonlight they can find to power metabolisms - but this is exceedingly rare. These algeas are aquatic, so moonlight is of limited use. Perhaps a pervasive terrestrial algea could make use of a sufficiently bright source of moonlight on a moon or many-mooned planet - but only if there were no other sources of more available energy. Besides being too weak for anything other than a specialized metabolism, moonlight is actually pretty unreliable as a source of energy because it is so intermittent, with its periods and phases.
To extend on the facts presented above, moonlight can also have an adverse
affect on plants and animals. The different phases of our one moon often screws with the circadian rhythm of many creatures, especially nocturnal ones. Brighter moons or one big moon could make the diurnal/nocturnal cycles of any planets with life nearby very different than what we are used to on Earth. However, I think these would be exceptional in the universe, since even in SE, there are many moon systems that don't seem to differ to much from ours in terms of brightness. There will be some variation - but maybe not as much as our wilder sci-fi spoofs would have us believe.