Gyroscope. What causes the seasons? 1.Seasons are NOT caused by varying distances from the Earth to the Sun 2.The primary cause of seasons is the 23.5.

Gyroscope

What causes the seasons?1. Seasons are NOT caused by varying distances from the Earth to the Sun

2. The primary cause of seasons is the 23.5 degree tilt of the Earth's rotation axis with respect to the plane of the ecliptic.

Note: the Earth is actually closest to the Sun in January 4!

The Seasons in the Northern Hemisphere

Perihelion: 147.09 × 106 km; Aphelion: 152.10 × 106 km

23.5o tilt

We experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N. Hemisphere is oriented more toward the Sun and therefore:

1. the Sun rises higher in the sky and is above the horizon longer, 2. The rays of the Sun strike the ground more directly.

Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely.

Myr ago

Puzzle: Ice Ages!

• Occur with a period of ~ 250 million yr• Cycles of glaciation within the ice age occur with a period of 40,000 yr• Most recent ice age began ~ 3 million yr ago and is still going on!

Last Glacial Maximum: 18,000 yr ago32% of land covered with iceSea level 120 m lower than now

Ice Age: Cause

• Theory: climate changes due to tiny variations in the Earth’s orbital parameters– Precession of the rotation axis

(26,000 yr cycle)– Eccentricity (varies from 0.00 to

0.06 with 100,000 and 400,000 yr cycles)

– Axis tilt (varies from 24.5o to 21.5o with 41,000 yr cycle

Milutin Milankovitch 1920

Due to precession, Earth’s rotation axis points to different directions with respect to stars (the position of North celestial pole makes a circle on the sky)

This has been known to Greeks, and possibly much earlier

26,000 yr cycle

Precession cycle

• Varies from 0.00 to 0.06 (currently 0.017)• Periodicity 100,000 and 400,000 yr• Eccentricity cycle modulates the amplitude of the precession cycle

As a result, the flux of solar radiation received by the Earth oscillates with different periodicities and amplitudes

This triggers changes in climate

Why are these changes so irregular?

Our Earth makes a complicated motion through space , like a crazy spaceship

2 4 6 8 10

-1

-0.5

0.5

1

2 4 6 8 10

-1

-0.5

0.5

1

2 4 6 8 10

-1

-0.5

0.5

1

f1

f2

f3

2 4 6 8 10

-2

-1

1

2

f1+f2

2 4 6 8 10

-2

-1

1

2

f1+f2+f3

Adding oscillations with different phases and incommensurate frequencies

f1 = sin[2 t + 1]f2 = 0.7 sin[3.1 t + 2.4] f3 = 1.3 sin[4.5 t + 0.3]

Very good agreement!

Thousand years

Adding Milankovitch cycles of solar irradiation for 65 degree North latitude

(Berger 1991)

Note the last peak 9,000 years ago when the last large ice sheet melted

Future?

Anhtropogenic effects???

Combination of center of mass motion and rotation

• Kinetic energy of the combined motion

• Yo-yo

• Rolling without slipping

Often beneficial to split the motion into the motion of the center of mass and rotation around center of mass

Yo yo

First evidence of the yo-yo is dated back to 500BC.  The evidence is a picture painted on an ancient Greek vase painting.  It is also suspected that the Chinese had yo-yo’s before then.