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A XX century researcher time traveled back into the prehistory. He is not in danger of death or anything, but he has only energy to attempt one jump.

He must jump back during the sunrise either in a solstice or an equinox.

How can he determine when it will be? He only brought handheld analog tools.

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    $\begingroup$ How did humanity determine the equinoxes? We did it long before the invention of computers. What research have you performed prior to asking this question? Why did the methods used historically by humanity not work for you? $\endgroup$ – JBH Aug 5 '18 at 16:54
  • $\begingroup$ How far back did he go? $\endgroup$ – Ash Aug 5 '18 at 17:07
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The dates of the solstices and equinoxes can be determined by observing the apparent north-south position of sunrise from a fixed observation point over the course of a year.

The easiest way to do this, if you are left in peace to make your observations, is to erect a vertical pole where it casts a shadow at sunrise onto an east-facing wall. Mark the position of the shadow at each sunrise, and carefully count the days.

Over the course of several months, you will observe the apparent position of sunrise to march north (or south) day by day. This march will slow and eventually reverse; the day of reversal is the day of summer (or winter) solstice.

Actual solstice is almost impossible to observe directly and in real time, because so many consecutive sunrises seem to occur in the same place. However, after the solstice, the position of sunrise will migrate back over your earlier observations. Choose some earlier sunrise position and note the number of days that elapse before the sunrise returns to it. The solstice was exactly halfway through that period.

The equinox will be 91 days after the solstice.

For complete accuracy, you must repeat these observations over the course of many years. If you are in contact with settled or semi-nomadic locals, they may have already made these observations and are maintaining a calendar, so they can tell you the date of the next solstice or equinox.

Look for a society who have erected a vertical pole in an open space east of a north-south wall.

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Maybe, if he is in the neolithic, he can ask a native medicine man or shaman how when the next solstice or equinox will be. I believe that many primitive societies started keeping track of such matters tens of thousands of years ago.

If there are nearby people who do keep track of astronomical event, if he can learn their language, and if they don't eat him or something, of course.

It seems a little foolish to go back in time without taking something to let him know when the next solstice or equinox will be. If he has any problem finding out it will seem like he leaped before he looked.

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If he knows what part of the world he's in, and has some precision timekeeping instruments, he could measure the length of the days from sunrise to sunset. If he knows exactly how long it takes to go from sunrise to sunset on the day before solstice or equinox, he's all set.

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