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I wasn't around when man landed on the moon in 1969. When I see the moon, I always wonder, were people able to see the rocket?

Yesterday, I looked at the moon in daylight and wondered again.

My question is: how far were people able to see the rocket after it launched?

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No, the orbiting rocket was not visible to the naked eye. Orbiter plus lem were about 65 square meters in size, about 25 X 25 feet. At lunar distance they subtended about 0.000001 square degrees, and be at most 5 to 10 times as bright as the lunar surface; albedo 0.5 to 1 vs 0.1. A speck 1/1000th of a degree on a side, and a little brighter than the moon is not visible in daylight. Likely it's well below the noise level in a daylight adapted eye.

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I think you have an order-of-magnitude error somewhere - I get $\arctan{10m\over 380000km} \approx 10^{-6} \deg$ which is over ten thousand times smaller than the maximum acuity of a human eye with a "perfect" vision. –  JohannesD Aug 3 at 16:46
    
@JohannesD You're right. I converted to ster-degrees which isn't what's wanted here. With regard to visual acuity, stellar discs are a good deal smaller than that, but they're also intrinsically brighter than the tiny amount of sunlight reflected off a small object in lunar orbit. –  Wayfaring Stranger Aug 3 at 17:28

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