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If a sealed elevator were subjected to a massive acceleration in interstellar space and two weights were dropped from ceiling to floor, as far apart as possible on opposite sides of the elevator, their paths from ceiling to floor would be parallel. But supposing this hypothetical, thought experiment lift were resting on the surface of a planet-like body where it is subjected to an identical g force, would the paths of the falling weights still be parallel?

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  • $\begingroup$ In reality no. But assuming the horizontal separation was small relative to the radius of curvature of the earth and that the distance it fell is also small you will not likely measure this drift. You can probably predict the amount using 2 neighboring lines of force and some simple geometry. $\endgroup$ – ggcg May 14 '19 at 19:21
  • $\begingroup$ If the planet-like body were small enough the deviation from parallel would be detectable,so the two accelerations would not be the same for an occupant of the elevator. However,you might object that to be detectable,the acceleration would have to be so great that any occupant of the lift would be killed,& unable to carry out the necessary measurement. But this is a thought experiment in which principles still apply even though the experiment cant be carried out in real life. Therefore it IS possible to tell whether your elevator is in a gravitational field or being accelerated in outer space. $\endgroup$ – Michael Walsby May 14 '19 at 19:44
  • $\begingroup$ I am not disagreeing with you. My statements are pragmatic. Measurements govern science. Here is another thought experiment. We can take the limit a the text particle and chamber become arbitrarily small and are in the far field limit of the planet. In this limiting case the lines of force will become parallel. I have seen these discussions before. $\endgroup$ – ggcg May 14 '19 at 19:55
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No, they would not still be parallel.

This is because a planet-like body has a curved surface, and the acceleration due to gravity will point towards the centre of the (approximate) sphere. This means that at each different point on the surface of the sphere, the acceleration is pointing in different directions, and cannot be parallel.

For a planet the size of Earth, the diameter is very large, so the direction of gravity between two close points is approximately parallel, and it may not be possible to measure the angular difference between the two paths unless they are spaced significantly far away. This would obviously depend on how you are measuring the paths.

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