Can we put mirrors on the moon to reduce the need for street lighting at night?

Answer

I don’t think such a thing is feasible.
You should almost completely fill the moon, given that the lunar disk in our terrestrial sky is the same size as the solar disk.

First, those mirrors would have to change direction permanently so that they would always be pointed toward Earth. After all, the moon also revolves around its axis. So you would have to fill the entire moon. Where are you going to get the energy for the motors that keep the mirrors pointed at Earth? From solar energy of course, but then you have to install the necessary solar panels (best also adjustable, so computer-controlled) and you lose a lot of usable surface again.

Second, if it were to succeed, it would only be effective for a small portion of the time, due to the phases of the moon. At the new moon, the moon is between the sun and the earth. The illuminated side of the moon, where the mirrors that are illuminated are then located, are then not visible from Earth. Even at the first quarter of an hour, only half of the lunar surface visible from Earth is illuminated, and the moon also sets around midnight. So what do you do in the second part of the night?
By the way, during the day you should consciously point the mirrors away from the earth, because if you assume that it is an effective system to effectively illuminate/heat the earth at night, you have to make the same assumption during the day. You would then shine too much on the earth : sun + moon.

Third: Who should place them? Astronauts, but then you also have to ensure that they can survive there, so also build a large number of moon bases, provide transport on the moon itself, construction sites… In the 1970s we just managed to get two to get people on the moon for three days. That required an organization (NASA) with several tens of thousands of scientists and engineers, plus many more in hundreds of American companies that worked for NASA. A moon rocket had a weight of 3000 tons, in order to eventually put a lunar lander of (I thought) about 15 tons on the moon. That is less than one percent payload. The lander was also only usable once. Of those 3000 tons, 5 tons eventually landed back on Earth… How many thousands of men would you need to fill the entire moon.
And how many mirrors do you actually need? The moon has an area of ​​38 million square kilometers. That’s 38,000 billion square meters. How many mirrors is that?
If you see that it costs more than 100 000 euros to bring a single kilo to the ISS, what would all those mirrors + solar panels + … bring to the moon.

Further… Maintenance? Safety ? Reliability ? Efficiency?
And wouldn’t the mirrors erode slowly through micrometeorites, through UV light? Ditto for those solar panels… and those electronics that have to keep working in an environment where the temperature changes extremely during the course of a Monday.

You can see that I have some reservations, and most likely there are still a few things that I don’t think of right away. But I admit it, it’s a fun thought exercise, perhaps to give to a group of students in high school during a science lesson. Just an open question to see what they’re thinking.