# Tilting cycle vs orbital cycle of earth

Common sense tells us a year is conveniently divided exactly into four seasons. I'm wondering whether that means the earth's tilting cycle is equal to its orbital cycle. If so, there must be a reason. Do we have a proof?

There is no tilting cycle.

The Earth continues to tilt the same way all year round. The axis points towards the pole star. But as the Earth goes round the sun, in December the northern hemisphere points away from the sun. In June the Northern hemisphere points towards the sun, as the Ascii art below shows (not to scale)

N                    N
\                    \
O         *          O
\                    \
S                    S
Earth                 Earth
in Dec     Sun       in Jun

So no special explanation is required. The Earth points the same way all year, it just moves relative to the sun.

The tilt of the Earth relative to the stars doesn't change. So the tilt of the Earth relative to the sun is entirely due to the Earth's orbit. This proves that the cycle of tilting relative to the sun will take exactly one orbit to complete. It is no coincidence; the cycle of seasons will take exactly one year.

(There is variation in the direction of tilt, called precession, but this is a much slower cycle, lasting 25000 years)

• I understand the basic principle that 4 seasons are result of tilting of the earth forward and backward in relative to the Sun. By cycle, I meant the length of this pattern. – techie11 Aug 3 '19 at 3:05
• Exactly. The earth doesn't change its tilt, so the apparent tilting of the earth forward and backward relative to the sun is due entirely to the orbit of the earth. this proves that the length of the pattern must be exactly the same as the time for one orbit. – James K Aug 3 '19 at 6:19
• Sort of understand Michael & your points now. I thought tilting was a movement independent of orbiting, just like rotation. – techie11 Aug 3 '19 at 12:21

It is no coincidence that the Earth's 4 seasons fit exactly into one orbit of the sun. As everyone knows, the Earth rotates on its axis every 24 hours, and this turns it into a gigantic gyroscope, so despite a very slight wobble, the north pole of its axis always points more or less at the star Polaris. This means that in the summer the northern hemisphere is tilted towards the sun, so the sun is higher in the sky. At the equinox, both northern and southern hemispheres get equal daylength and equal amounts of solar radiation. Then, because the north pole of this gigantic gyroscope is still pointing at Polaris, the southern hemisphere becomes tilted toward the sun and the northern tilted away from the sun, so we have our winter while the southern hemisphere has its summer. You can work this out for yourself by using a table lamp to represent the sun and a tennis ball marked with a north pole and south pole to represent the axis. You will see that as you walk the tennis ball around the lamp, taking care to keep the tilted axis always pointed toward an imaginary Polaris, first one hemisphere and then the other will be tilted toward the lamp. The seasons have no option but to fit precisely into one orbit.

• 4 seasons are formed when the earth tilts forward and backward in relative to the Sun, when orbiting and rotating simultaneously. By cycle, I meant the time length of this tilting pattern which is (exactly?) one year. My question is why the coincidence of this time length with Solaris oribital cycle. Would be great if you could explain why The seasons have no option but to fit precisely into one orbit. – techie11 Aug 3 '19 at 3:15

I'm wondering whether that means the earth's tilting cycle is equal to its orbital cycle.

The Earth's "tilting cycle" is about 26000 times longer than its orbital cycle, which is one year long. This means there is very little change in the seasons from one year to the next, or even one century to the next. Even after 13000 years (half of a cycle), the changes are subtle. January will still be winter in the Northern Hemisphere, summer in the Southern Hemisphere, and July will still be summer in the Northern Hemisphere, winter in the Southern Hemisphere.

What will change in 13000 years are the durations of the seasons. Currently, the Earth is closest to the Sun a couple of weeks after the December solstice and furthest from the Sun a couple of weeks after the June solstice. In 13000 years the situation will be reversed, with Earth aphelion occurring near the December solstice and Earth perihelion occurring near the June solstice. This will make Northern Hemisphere winters longer and colder than they are now, summers shorter and hotter.

This 26000 year cycle is one of the key reasons the Earth currently undergoes long periods of glaciations ("ice ages") interspersed by (typically) short interglacials. (The current interglacial is atypical.) A glaciation starts when snow in high northern latitudes doesn't melt over the course of a long but cool summer and later ends when all of that accumulated snow and ice finally melt more than they do accumulate over the course of a short but hot summer.

• See USNO on "precession of the seasons." Apsidal precession makes that cycle shorter than the axial precession period. – Mike G Aug 4 '19 at 13:37
• @MikeG - Apsidal precession and other effects make the anomalistic year (one perihelion to the next) slightly longer than the sidereal year (the amount of time it takes the Earth to return to the same place with respect to the remote stars), which in turn is slightly longer than is tropical year (the year based on seasons). But the apsidal precession period itself is considerably longer than is any of those concepts of what qualifies as a year. – David Hammen Aug 4 '19 at 18:59
• Thank you for the summary of my own answer. The perihelion date migrates around the calendar in 21000 years, not 26000. – Mike G Aug 4 '19 at 23:41
• @MikeG - Sorry, you are wrong. – David Hammen Aug 5 '19 at 2:01
• Good to know difference b/w sidereal and tropical years. Thanks. – techie11 Aug 5 '19 at 2:32

That depends on the definition of a year. Compared to the annual cycle of the Sun's declination north and south of the equator:

• The tropical year, measured relative to equinoxes and solstices, is the same length (365.2422 days) by definition. The Gregorian calendar is designed to approximate this.

• The sidereal year, measured relative to distant stars, is a few minutes longer (365.2564 days) because axial precession moves the equinoxes 0.014°/year retrograde.

• The anomalistic year, measured relative to perihelion and aphelion, is slightly longer still (365.2596 days) as apsidal precession moves those points 0.0032°/year prograde.

The US Naval Observatory article The Seasons and the Earth's Orbit explains tropical and anomalistic years further. The 21,000 year cycle mentioned there is a combination of axial precession (26,000 year cycle) and apsidal precession (110,000 year cycle).

• I mainly sought to understand the "tilting" which I misunderstood as being a sort of independent oscillating movement :-). The previous two posts did good jobs. But thanks for this additional information. – techie11 Aug 4 '19 at 2:50