1. Gyroscope

2. What causes the seasons?
Seasons are NOT caused by varying distances from the Earth to the Sun
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.
23.5o tilt
The Seasons in the Northern Hemisphere
Note: the Earth is actually closest to the Sun in January 4!
Perihelion: × 106 km; Aphelion: × 106 km

3. 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:
the Sun rises higher in the sky and is above the horizon longer,
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.

4. Puzzle: Ice Ages! Myr ago 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!

5. Last Glacial Maximum: 18,000 yr ago
32% of land covered with ice
Sea level 120 m lower than now

6. 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

7. Figure 2.7: Precession. (a) A spinning top precesses in a conical motion around the perpendicular to the floor because its weight tends to make it fall over. (b) Earth precesses around the perpendicular to its orbit because the gravity of the sun and moon tend to twist it upright.

8. 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

9. Precession cycle
26,000 yr cycle

10. 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

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

13. f1 = sin[2 t + 1]
f2 = 0.7 sin[3.1 t + 2.4]
f3 = 1.3 sin[4.5 t + 0.3]
Adding oscillations with different phases and incommensurate frequencies
f1+f2 f1 f2
f1+f2+f3 f3

15. Very good agreement! Thousand years
Figure 3.17: The Milankovitch theory predicts periodic changes in solar heating (shown here as the equivalent summer latitude of the sun). Over the last 400,000 years, these changes seem to have varied in step with ocean temperatures measured from fossils in sediment layers from the seabed. (Adapted from Cesare Emiliani)
Thousand years

16. Adding Milankovitch cycles of solar irradiation for 65 degree North latitude
Note the last peak 9,000 years ago when the last large ice sheet melted
(Berger 1991)

17. Future?
Anhtropogenic effects???

18. 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

19. 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.