, the inverse square law for electromagnetic energy.
No, radio telescopes receive, though one COULD potentially make a radar, the beam width and frequency won't resolve at that level, even to large boulders. I should know radar well enough after having an over 27 year military career! The optical telescope again, lacks the capability to see even large boulders or even small hills. Look up the formulae for optics, you'd need a kilometer sized telescope to accomplish what you suggest! And when I was in junior high school, we had an observatory that was donated to the school that we used, seeing anything that small just is physically impossible at even THAT size (16 inch unit is what we had).
The space race wasn't part of any arms race, but part of the cold war, which had multiple series of arms races of varying classes of weapons. SDI was part of a strategy to destroy the Soviet economy, as they tended to match whatever we spent, hence, with our much higher amount of funding available, they'd have to match an impossible amount, which they DID attempt to do. Hence, the collapse of the Soviet Union and George Bush Sr announced that we had won the cold war. However, the expenses HAD to be made, as the Soviets did and the Russians still do have a highly capable espionage network, with quite a few assets inside of the US. Indeed, their spy network was so extensive and successful that during WWII, detailed reports, to include copies of diagrams and plans were on Stalin's desk before Washington got the reports. That was verified when the KGB files were opened for outside scrutiny. Even the anti-war movement during the Vietnam war had Soviet assistance and "guidance", not agents doing the protesting, only "egging on" the protesters leaders and suggestions given, a few bucks here and there to help with transport, etc (though the Soviets were notoriously low paying, even for the "big time" spies that they payed for information from).
So, what was Apollo 1? A stage accident?