Couldn’t the Federations exploration and astronomical organizations set up telescopes dedicated solely to viewing into the Federation’s past?

For instance: say you wanted to view the moon landings. Assuming you’re in the TNG era, you could theoretically put an extremely powerful telescope just under 300 lightyears away from Earth’s position. If you point it backwards at Earth’s moon in its position in 1960 you’d be able to view Earth in the late 1990s. I think…. And I imagine the logic would apply to other planets and star systems. Obviously there’d be limitations on resolution but there’s more than just the visible spectrum.