Understanding Our UniverseFIRST EDITIONPalen | Kay | Smith | Blumenthal

© 2012 by W. W. Norton & Company

CHAPTER 2

Patterns in the Sky—Motions of Earth

Our focus:• Daily rotation of Earth• Annual orbit of Earth• Monthly orbit of the Moon• Consequences of the above• Behavior of all Solar System planetary orbits

As viewed from above the North Pole, Earth rotates counterclockwise on its axis.

One rotation takes 24 hours.

The celestial sphere is a projection of Earth’s axes and equator into space.

A useful fiction. Points on the sphere do

not correspond to actual distances.

It rotates around the north and south celestial poles each day.

Celestial equator: midway between.

Ecliptic: path of the Sun, inclined 23.5 degrees to equator.

At Earth’s North Pole, we would see half the celestial sphere.

The north celestial pole is directly overhead.

Stars rotate counterclockwise in 24 hours. No star rises or sets: all are circumpolar. Observers can never see the south celestial

pole.

At Earth’s equator, all stars rise and set. The celestial poles are on the northern

and southern horizons. Observers can see the whole celestial sphere

as it rotates.

At an intermediate latitude on Earth, one pole is above the horizon.

The angle to the horizon equals the latitude.

Some stars are circumpolar. Some stars rise and set. Some stars are never visible.

Earth’s orbit is nearly circular. The average distance to the Sun is called

the astronomical unit, or AU. 1 AU = 150 million km.

The Sun’s motion on the ecliptic reflects Earth’s orbit around the Sun.

As Earth moves, the Sun is seen against different constellations—the zodiac.

Earth’s axis is not perpendicular to the ecliptic plane.

Instead, it is at an angle of 23.5 degrees. This is why there are seasons.

Two reasons for the seasons, due to this 23.5-degree tilt:• The angle of sunlight is more direct in summer.

» Energy is more concentrated.

• The sun is in the sky longer in the summer.

Southern Hemisphere experiences the opposite situation of the Northern Hemisphere.

Summer solstice: • Sun most directly in

direction of North Pole (June 21).

• Longest day.

Autumnal equinox: • Sun on the celestial

equator (Sept. 23).• Equal hours of day

and night.

Winter solstice: • Sun most directly opposite

the direction of North Pole (December 22).

• Shortest day.

Vernal equinox: • Sun on the celestial

equator (March 21).• Equal hours of day

and night.

Currently the north celestial pole is near the bright star Polaris.

Earth’s axis orientation changes over a period of 26,000 years.

Location of the poles slowly shifts.

We only see one face of the Moon.

Synchronous rotation.

Completes one full rotation in one full orbit around Earth.• “Near side” and “far

side,” NOT “light side” and “dark side.”

The Moon shines because of reflected sunlight.

Half of the Moon is always bright.

The phase is determined by how much of the bright side we see.

New Moon: Moon between Earth and the Sun.

Waxing crescent Quarter: Moon at

right angles with Earth and the Sun.

Waxing gibbous Full Moon: Moon

on opposite side of Earth from the Sun.

Solar eclipses happen at new Moon. Moon passes between Earth and the Sun. Only a small portion of Earth can witness

each one.

Three types:• Total: the Moon

completely blocks the Sun’s light.

• Partial: only part is blocked.

• Annular: the Sun appears as a bright ring surrounding the Moon.

Lunar eclipses happen at full Moon. Earth is between the Sun and the

Moon. Visible over a wider area of Earth. Last a lot longer than solar eclipses.

Eclipses do not occur every month because the Moon’s orbit is tilted about 5 degrees with respect to Earth’s orbit around the Sun.• If not, there would be a solar eclipse every new

Moon and a lunar eclipse every full Moon.

Copernicus realized the Solar System was heliocentric—centered on the Sun.

Planets exhibit apparent retrograde motion due to their distances from Earth.• Appear to turn

around.

Kepler’s 1st Law: Planet orbits are ellipses. Each ellipse has two foci. The Sun is at one focus of a planet’s elliptical

orbit.

An ellipse has a size, described by the semimajor axis.

The longest length is twice the length of the semimajor axis.

Each orbit has a shape and a size.

The eccentricity describes how elongated the ellipse is and how far the foci are separated.

Kepler’s 2nd Law: the Law of Equal Areas. The line between the Sun and the planet

“sweeps” out equal areas in equal times.

Consequences:• A planet will go fastest when closest to the Sun.• It will go slowest when farthest from the Sun.

Applies to only one planet at a time.

Kepler’s 3rd Law Consequences:

• Distant planets take longer to orbit the Sun.

• Distant planets travel

at slower speeds.

The Sun rises in the east and sets in the west. Which way is Earth rotating?

A. Toward the westB. Toward the northC. Toward the eastD. Toward the south

If Earth rotated in 12 hours but its orbit were the same, which of the following would NOT be true?

A. Each season would happen twice per year.B. We would still see only one hemisphere of the Moon.C. The cycle of lunar phases would last as long

as it does now.D. Observers at the North Pole would only see one half

of the celestial sphere.

If the ecliptic were aligned with the celestial equator, whatwould happen to the seasons?

A. Nothing. They would be the same as now.B. Each season would last longer.C. We would not have seasons at all.D. Can’t tell from the information given.

AstroTour The Celestial Sphere and the Ecliptic

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AstroTour View from the Poles

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AstroTour The Earth spins and revolves

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AstroTour The Moon’s Orbit, Eclipses, Phases

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AstroTour Kepler’s laws

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