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Imagine someone is standing on the surface of the Earth (let's assume it is completely flat) and they start going exactly in the direction their shadow is cast (that is, exactly opposite of where the Sun is in the sky). What kind of path that would produce after a certain time, say a few days? I assume they stop when the Sun sets and wait for the sunrise to continue with their journey. I also assume they just embark a boat should they encounter water.

I realize this question is a bit under-defined as the precise answer depends at least on 3 parameters (the exact time and location they start the journey from, and their speed) but I'm interested in an answer that takes these into account as parameters.

How to approach this problem? In particular, what kind of formula would give the position of the Sun in the sky as seen from the Earth at any given moment?

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    $\begingroup$ It is rather complicated, so you may find people reluctant to answer until you show a bit more progress. $\endgroup$ – Andrew Steane Mar 18 at 15:41
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    $\begingroup$ Interestingly the opposite question, what kind of path will be formed by going towards the sun, seems to be easier to think about, because it ends up going back and forth on the equator, rather than with confusing situations at the poles. Maybe try that one first. $\endgroup$ – coldwave Mar 18 at 16:19
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    $\begingroup$ either start on a spherical globe in a circular orbit with no atmosphere and zero obliquity, or try: en.wikipedia.org/wiki/Equation_of_time $\endgroup$ – JEB Mar 18 at 16:20

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