Precession of Solstices and Equinoxes

1. Precession of Solstices and Equinoxes The position of the solstices and equinoxes in relation to the eccentric orbit have not always been fixed at the present day locations. They gradually shift position with respect to Earth�s orbit.

2. This is important because the distance from Earth to the Sun has varied over time for each of the seasons. These changes in distance have produced changes in the amount of solar radiation received on Earth.

4. The Earth�s wobbling motion is called the axial precession. This is caused by the gravitational pull of the Sun and the Moon. The slow turning of Earth�s elliptical orbit is it�s precession of the ellipse. The elliptical shape of the Earth�s orbit itself rotates.

5. Both of these motions together are called the precession of the equinoxes. The solstices and the equinoxes move around the Earth�s orbit, completing one full 360 degree orbit around the sun every 23,000 years.

9. This process involves complicated angular motions in 3-D space so we need to reduce these motions to a simple mathematical form. To do this we must make use of the two main geometric characteristics of processional motion

10. Angular Form Omega (w) is the angle formed between two imaginary lines connecting Earth to the Sun. The line linking the Sun and the position of the Earth at perihelon. The line connecting the Sun to the Earth�s position at the March 20 Equinox.

11. The angle w summarizes the combined relative effect of the two motions. (axial and and the ellipse) w is the angle that opens up in the arc between those two moving lines. Changes in this angle gradually sweep out to a 360 degree arc around the sun. Starting at 0 degrees and increasing to 90, 180, 270, and finally to 360.

12. Now we need to further simplify these angular relationships. We can do this by using basic geometry and trigonometry to convert the angular motions to a simpler form of an oscillating wave in a rectangular coordinate system.

14. Earth�s Eccentricity The second aspect of Earth�s motion we need to consider is it�s eccentricity Because of Earth�s non-circular orbit, the movement of the solstices and the equinoxes result in long term changes in the amount of solar radiation received by Earth.

15. In an eccentric orbit gradual movements bring the solstices and the equinoxes to orbital positions at varying distances from the Sun. Thus altering the amount of solar radiation received by Earth.

16. The Effect of changes in Eccentricity Changes in eccentricity will affect the perihelion and aphelion positions. With greater eccentricity the distance between a close pass and an distant pass will be magnified.

17. Precessional Index The complete expression for the effect of precession must also include a term that represents the effect of changing eccentricity. The precessional index is the result. Esinw

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19. Long term variations in the precessional index show two major characteristics. They appear in cycles with periods near 23,000 years. (2)The large variations in amplitude. The cycle swings back and forth between extreme maxima and minima.

20. The source of this modulation is the eccentricity of the Earth�s orbit This modulation is not a real cycle. Why?

21. Eccentricity varies at cycles of 100,000 and 413,000 years. Cycles at this length shape the amplitude of the trend by creating upper and lower envelopes of modulation.

22. The envelopes of moderation are not the same as real cycles. The upper and lower envelopes cancel each other out.

23. The gradual changes in Earth�s orbit around the Sun result in changes in solar radiation received by season and by hemisphere at two cycles. The tilt cycle with a wavelength of 41,000 years. The precession cycle at 23,000 years.

24. Changes in Insolation Received by Earth. Climate scientists refer to the radiation arriving at the top of the Earth�s atmosphere as insolation.

25. Insolation Changes by Month and Season. The long term trends of tilt and of the precessional index contain all the information needed to calculate the amount of insolation arriving on Earth at any latitude or season.

26. Climate scientists usually show the amount of insolation during the solstice months of June and December in W/m2 . June and December insolation values over the last 300,000 years show a strong dominance of the 23,000 year cycle of precession at lower and middle latitudes and even higher at latitudes during the summer season.

28. Just like the precessional index, individual insolation cycles at lower latitudes occur at wavelengths near 23,000 years with modulation at periods of 100,000 and 413,000 years

30. The 41,000 year cycle of tilt is not evident in the low-latitude signals. It shows up in variations of the winter insolation at high latitudes. (January in the northern hemisphere and June in the southern hemisphere.) It�s less obvious in the summer insolation signals at high latitudes.

31. During the summer season the insolation changes at the tilt cycle actually exceed those in the winter cycle. As a result, changes in the annual mean of insolation at high latitudes have the same sign as the summer insolation anomalies.

32. Monthly and seasonal insolation changes are dominated by the precession at low and middle latitudes. The effects of the tilt are more evident at higher mid-latitudes. No cycle of insolation change at 100,000 or 413,000 years is obvious in any of the latitudinal signals. Eccentricity is not as significant as a direct cycle of insolation change.

33. Small variations in received insolation do occur in connection the the Earth�s eccentricity, but they only appear as changes in the total energy received by Earth, not seasonal.

34. Fundamentally the hemispheric and seasonal patterns of insolation changes are different. Insolation values at high latitudes are caused by changes of tilt are in phase between the hemispheres and from a seasonal perspective.

35. In the northern hemisphere, the summer insolation maxima occur at the same time in the 41,000 year tilt cycle as the summer insolation maxima in the southern hemisphere. The higher tilt produces more insolation at both poles during their summers because they are more directly facing the Sun. This is the same reason why there are more insolation minima also occur at both winter poles. They tilted away from the Sun.

36. Earth-Sun distance is the major control on precessional insolation. Earth�s postion close to the sun (at perihelion) produces a higher amount of insolation over all of the surface. Distant positions of the Earth (at aphelion) will diminish the amount of insolation all over the surface.

37. Seasons are reversed across the equator. Because of this, insolation signals considered in terms of the season are out of phase between the hemispheres for precession.

39. We can also look at the relative phasing of precessional insolation by tracking the changes between the season with in a single hemisphere.

40. There is another characteristic found in precessional changes that are not found in tilt changes. An entire group of insolation curves exist for each month and each season. Precessional motion involves the movement of both the solstices and equinoxes in addition to other times of the year.

41. Each of these months and seasons precesses into parts of the eccentric orbit that are farther from the Sun and closer to the Sun at the same 23,000 year cycle. They experience the same cycle of increasing and decreasing insolation values relative to the long term mean. The anomalies are offset slightly in time from the preceding month or season.

42. Example: The June 21 summer solstice will move into perihelion position once every 23,000 years. The same thing will happen for the September 22 equinox at a later time. This means the September equinox will pass through the perihelion about 5750 years after the June position.

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