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I’m not a physicist but I want to test my understanding of Galileo’s ship thought experiment.

Out space with some light, but no light sources nor features to give away the actual motion(s) there is an astronaut and a small moon separated.

The astronaut gets a brief window, too short for conducting any real experiments, not that they have any equipment to do so.

Can she discern which option(s) of the moon coming directly her, the moon simply growing/expanding regardless of their two motions, or her going directly toward the moon is actually happening? There’s no acceleration. She simply observes the moon taking up more of her field of view.

I think they’d all appear the same to her. Only one could be happening, or any combination of all three, and she couldn’t tell.

Let’s say there is a distant body we are making these motions relative too, too far for her to see though. So that there is a difference between her moving vs the moon moving. (I think I need this last paragraph or else there is no answer between those two)

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    $\begingroup$ Galileo's ship is not about looking out the window. It's about performing experiments inside the cabin, which turn out to be completely independent of the constant motion of the ship relative to some other rest systems. $\endgroup$
    – FlatterMann
    Commented Jul 27 at 21:49
  • $\begingroup$ @FlatterMann Okay but isn’t the astronaut opening her eyes to see the moon taking up more of her FOV an “experiment” independent of the relative motions, and space is playing a similar role to the inside of a cabin (can’t look at external cues)? I guess it’s not perfect but it’s where my mind went after reading the thought experiment $\endgroup$
    – J Kusin
    Commented Jul 27 at 21:57
  • $\begingroup$ Not in Galileo's ship. What you are talking about is optical navigation in the solar system, which can, of course, be done. The astronauts on the Apollo mission had it (and even had to use it at least once during the Apollo 13 mission) as a backup if their gyroscopes and radio based navigation systems would have failed. But the problem there was not about the motion of a book inside the spacecraft but about the motion of the spacecraft relative to Earth and Moon. $\endgroup$
    – FlatterMann
    Commented Jul 27 at 22:07
  • $\begingroup$ Hmm maybe I messed up tying to too close to Galileo's actual experiment. I was trying to reason through this thought experiment via implications of Galileo's conclusions on his, not make something exactly similar. $\endgroup$
    – J Kusin
    Commented Jul 28 at 0:45

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Get a great big cabin, large enough to hold the astronaut and the moon. Allow her any length of time she wants to measure the velocity of the moon and any tools she wants to do the measurement.

Galileo's point is that she will not be able to tell how the world outside the cabin is moving.

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