I've read that length contraction occurs only in the direction of motion, but I'm confused on how to interpret this question. If I travel toward the moon at a significant fraction of $c$ then distance between the moon and I should contract, and I should see the moon as a larger circular cross section, but If I do a similar experiment in MIT game lab's simulator I see that the mushrooms which I approach at a significant fraction of the speed of light appear to get smaller, not larger which makes no sense to me. My professor suggested ignoring the simulation's results which may be largely a related to a resulted to a result in GR and to just focus on understanding this one situation.

What will happen to the size of the circular cross section of the moon I see as I move towards it at a significant fraction of the speed of light and why?

  • $\begingroup$ Not much, because you'll smash into the Moon in a couple of seconds traveling at that speed. :) Can we have a slightly more distant target? But anyway, you need to distinguish between effects due to Fitzgerald contraction and those merely due to the finite time of flight of light. In the mean time, see en.wikipedia.org/wiki/Terrell_rotation $\endgroup$ – PM 2Ring Oct 8 '18 at 6:37
  • $\begingroup$ i'll eagerly await your answer. Take your time, but sometime before noon EDT today would be awesome. I have an exam at 2 on this $\endgroup$ – rjm27trekkie Oct 8 '18 at 8:10
  • $\begingroup$ Is your exam question is closely related to the visual appearance of the "approaching" moon (something else)? What is your idea, what causes the moon to be further away as considered in the frame of the moon (the camera moves) or in the frame of the camera (the moon moves)? $\endgroup$ – Albert Oct 8 '18 at 8:23
  • $\begingroup$ No idea. My best guess is that a good multiple guess question would be this question with 3 answers: the same size, smaller, or larger. I don't know how to justify any of them. I would think it should be larger since I got closer by length contraction in the direction of my motion, but the experimental (simulated) data shows such a circumstance where it gets smaller. So I'm not sure what I'll be guessing if it shows up. $\endgroup$ – rjm27trekkie Oct 8 '18 at 8:25
  • $\begingroup$ Think about: in camera's frame: speed of light is finite, the Moon catches up its own light. So when the Moon is at some distance from you, do you see it "as it is right now" or how it looked some time before? In the frame of the Moon first imagine picture by "stationary camera". Then imagine picture by "moving" camera which approaches the Moon. When pinholes of these "stationary" and 'moving" cameras coincide, the same information goes through the pinhole, but in the moving camera distance between its pinhole and the film Lorentz contracts. $\endgroup$ – Albert Oct 8 '18 at 8:57