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The moon trip was fake but not the earth orbiting bit.
The problem with this is that anybody can just look up at the sky and see satellites passing over. Try it yourself, they look like moving stars. The Apollo command module, service module and lunar module together were a substantial size. It would have been the brightest satellite of the time. You couldn't miss it. I have written an entire book and website on the subject ‘Satellite Spotting & Operations Handbook’ available via www.satellitespotting.com
I have recorded many satellites with an image intensifier. It just demonstrates how easy they are to see. The Apollo-LM configuration would have stood out like a beacon; brighter than any other satellite at the time.