Any old time. Powering and maintaining it would be a chore, and since it's on a rotating body it wouldn't always be pointing the direction we wanted it to, but solve those problems and we're great.
Also somewhat fun is the idea of "solar sailing." Both the particulate solar wind and the raw solar radiation have momentum, and by redirecting either one you can get a push. Since increasing / decreasing the "height" of your orbit is actually a function of causing acceleration in the direction of orbit (or opposite that direction), we should be able to change the shape of a vessel's orbit by deflecting outward-streaming sunlight and particles so they're facing along the orbital path (i.e. a 90-degree turn, with a 45-degree-angle mirror). You'd need a lot of surface area for a reasonable amount of delta-V in a human timeframe, but nothing we know of makes this approach impossible. JAXA demonstrated it can work (https://en.wikipedia.org/wiki/IKAROS); the Planetary Society has been looking into it (https://www.planetary.org/sci-tech/lightsail).
On the side facing the earth probably never as it will become trivial to threaten earth with a giant laser on the moon. Same objection with kinetic launchers (aka flinger, mass drivers) on the moon. On the side facing away, maybe but you lose half the utility.
Also somewhat fun is the idea of "solar sailing." Both the particulate solar wind and the raw solar radiation have momentum, and by redirecting either one you can get a push. Since increasing / decreasing the "height" of your orbit is actually a function of causing acceleration in the direction of orbit (or opposite that direction), we should be able to change the shape of a vessel's orbit by deflecting outward-streaming sunlight and particles so they're facing along the orbital path (i.e. a 90-degree turn, with a 45-degree-angle mirror). You'd need a lot of surface area for a reasonable amount of delta-V in a human timeframe, but nothing we know of makes this approach impossible. JAXA demonstrated it can work (https://en.wikipedia.org/wiki/IKAROS); the Planetary Society has been looking into it (https://www.planetary.org/sci-tech/lightsail).