Gyroscope

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

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.

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!

Last Glacial Maximum: 18,000 yr ago 32% of land covered with ice Sea 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

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.

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

Precession cycle 26,000 yr 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

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?

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

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

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)

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.