1. Seasons Revisited

Why are there seasons?

Earth's rotational axis is tilted by 23.5 degrees from the direction perpendicular to the plane of the ecliptic

Why does the tilt have this effect?

According to the book:

- ``length of day''

- ``height of Sun in sky''

Actually, three effects determined from this ``height:''

- light (energy, heat) per unit area per unit time

- absorption of light by atmosphere depends on height, or airmass

- length of day

NB:

(i) Seasons are a critical aspect of our life cycle. They create weather, and in part determine the movement of water and nutrients.

(ii) Not all planets have the same axial tilt as the Earth. See Table 2B in the Appendix.

2. Retrograde motion: The planets

The apparent change in position of the planets on the celestial sphere -

- ``loops on the sky''

Why does this happen?

- planets orbit the Sun in concentric orbits:

circles within circles (actually ellipses)

- planets rotate at different angular speeds:

a ``year'' on Mars is longer than a ``year'' on Earth

- co-planar orbits -- roughly:

all roughly in the sampe plane, except Pluto

3. Phases: Moon, Earth, and other planets

Why are there phases of the Moon?

Just the Moon?

What about other planets?

Inner planets? Yes!

Outer planets?

No ``New'' phase; the larger the orbit (relative to the Earth) the smaller the range of phases from ``Full''

What about if we were on another planet?

4. Sidereal vs. Synodic Months

Analogy to sidereal vs. solar day

What's the difference in these months?

about 2 days

Why?

Earth moves about 1 degree per day, and it takes about 27 days for the Moon to orbit the Earth.

Earth moves about 27 degrees in its orbit

x 27 days = 2 days

Remember:

Sidereal: with respect to the fixed stars

Solar or Synodic: with respect to the Sun

5. Eclipses

- Solar

- Lunar (``blood red'' - actually copper-brown)

- partial, total, or annular (only solar)

- penumbra, umbra

Cosmic coincidence for solar, but not lunar eclipse:

Sun and Moon have comparable apparent size

31'5'' = 1865 arcseconds -- about 1/2 a degree

The moon always produces either partial, total, or annular eclipses.

However, it is only sometimes when these particular shadows hit the Earth.

Why? Geometry!

Moon's orbit is tilted 5.2 degrees from the plane of the ecliptic

What is necessary for a solar eclipse to occur on Earth?

(i) Line of intersection of Moon's orbital plane and Earth's orbital plane (ecliptic) must lie along Earth-Sun line

(ii) New Moon

ERRATUM:

p.16, col. 1: ``partial solar eclipse''

``partial lunar eclipse''

6. Precession

Why does Earth's axis stay ``pointed'' in the same direction with respect to the celestial sphere?

But actually Earth's axis does change -- it precesses like a top.

Time scale: 26,000 years (2.6 x 10⁴ yr)

Why?

Gravitational forces of Moon and Sun tug on the Earth as it spins, like Earth's gravity tugs on a spinning top here on Earth.

What about seasons?

Not too worry -- tilt with respect to the direction perpendicular to the ecliptic remains 23.5 degrees.

Precession of Earth's axis describes a cone perpendicular to the ecliptic with half-angle 23.5 degrees

7. Parallax

* Primary measurement of distance in astronomy

-- very important!

* First rung on the ``cosmic distance ladder''

Using the Earth's orbit around the sun as baseline for triangulation:

distance (parsecs) = 1 / parallax (arcsecond)

parsec = 3.26 light years

arcsecond = arcminute

arcminute = degree

How can we do better?

Bigger baseline --

- deep-space grid: telescopes in large orbits about the Sun (does not yet exist)

- solar-system's orbit around Milky Way (have to wait 250 million years!)

- Better angular resolution --

Hipparchus satellite (results soon to be known)

(a) decrease orbit of the Earth

(b) increase size of the Moon

(c) decrease size of the Sun

(d) decrease orbit of the Moon

(e) travel towards the Moon

(a) Yes; full moon

(b) Yes; but only during an eclipse

(c) No

(d) Yes; quarter moon

(e) Yes; new moon