I recently saw a great photo [1] by Ben Cooper of a Falcon 9 on ascent crossing the Moon from the photographer’s perspective. I wonder how much math went into finding that vantage point.
It's not really that hard. I set up several systems to do this for the previous total solar eclipse. The ephemerides for the moon are easy to download and calculate the position in the sky (IE, altitude and azimuth at time t) with a python script.
I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time.
A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).
I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time.
A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).