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Kleppner and Kolenkow, An introduction to mechanics

The period of the precession is 26000 years. 13000 years from now, the polar axis will not point toward Polaris, the current north star; it will point 2 × 231 2 ◦ = 47◦ away. Orion and Sirius, those familiar winter guides, will then shine in the midsummer sky, and the winter solstice will occur in June.

Elsewhere on the internet I found that the summer will always come in June and such as this picture showsenter image description here

Is the book incorrect?

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The book is incorrect. The calendar is designed to keep track of the seasons. What will happen in 13000 years is that the Northern Hemisphere summer solstice will still occur near the end of June, but it will occur near perihelion rather than near aphelion. In 13000 years, summers in the Northern Hemisphere will be short but intense, and winters will be both long and intense.

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  • $\begingroup$ The winter solstice already occurs in June in the southern hemisphere. Do your climate predictions match what currently happens in the southern hemisphere? (I already know the distribution of land and ocean is somewhat different north and south of the equator which might have some effect on the answer...) $\endgroup$
    – alephzero
    Jul 3 at 1:36
  • $\begingroup$ @alephzero The seasons are opposite in the northern and southern hemispheres. Northern Hemisphere winter occurs during Southern Hemisphere summer, and vice versa. That's why I was very careful to write "Northern Hemisphere summer solstice" and "[i]n 13000 years, summers in the Northern Hemisphere will be short but intense, and winters will be both long and intense." $\endgroup$ Jul 3 at 3:08
  • $\begingroup$ So in 13000 years, summers in the Southern Hemisphere will be slightly milder but longer, and Southern Hemisphere winters will be slightly milder but shorter. The reason for my use of 'slightly' is that most of the Southern Hemisphere is a bit of land surrounded by ocean. The one exception might be Antarctica, which is a lot of land completely surrounded by ocean. $\endgroup$ Jul 3 at 3:11
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The diagram from Astronomy magazine is correct; the book excerpt is a little confused. Winter solstice is not when the Sun appears opposite certain stars, but when the Sun appears farthest from the Earth's north pole. The time-dependent difference between these is due to axial precession.

There are several different definitions of a year:

Name Mean Length Significance
Tropical 365.2422 d Based on equinoxes and solstices
Gregorian 365.2425 d Modern calendar; approximates tropical
Julian 365.2500 d Old calendar; used in some astronomical formulas
Sidereal 365.2564 d Based on extragalactic reference frame
Anomalistic 365.2596 d Based on perihelion and aphelion

If we keep using the Gregorian calendar, 10000 years from now:

  • solstices and equinoxes will occur about 3 days earlier
  • any given star or galaxy near the ecliptic will culminate at midnight about 139 days later
  • perihelion and aphelion will occur about 171 days later
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