Re: why hasn't anyone put a satellite around the moon?

There have been recent fly-bys of the Moon. An example is the Clementine spacecraft.

Clementine was a fly-by mission for a number of reasons. One of these is that keeping a satellite in orbit around the Moon is quite difficult. The Moon is littered with mascons or mass concentrations. These result from areas like the maria on the surface, areas where the material density is slightly higher meaning that there is slightly more mass. These mascons change the gravitational force that a satellite experiences, which in turn changes the satellite's orbit. The result is that a satellite around the Moon would find its orbit changed quite quickly and changed so much that it would impact the Moon.

Another difficulty with your idea is that a fairly substantial satellite would be required. Suppose that one wants to be able to see objects about 1 meter across on the Moon's surface from an orbit about 300 km high. Even that fairly coarse resolution requires a mirror about 20 cm in diameter, for a camera working at optical wavelengths. Given how expensive it is to launch material into orbit, this would be a fairly expensive satellite.

Finally, and perhaps most importantly, no such mission would put an end to the "moon hoax" nonsense. People who refuse to acknowledge that NASA did not put men on the Moon are not going to believe pictures from a NASA satellite around the Moon.